Invited Sessions

This Invited Session (IS) aims at providing an overview and outlook on the use of numerical modelling to address current industrial challenges at the intersection of applied analysis, scientific computing and artificial intelligence (AI). High-fidelity numerical simulations (finite elements, finite differences) remain the gold standard for accurately representing complex physical systems such as mechanical structures, fluid flows, and wave propagation. However, their computational cost limits their use in industrial contexts requiring repeated evaluations. Typical examples are shape optimization, non-destructive testing, exploration, uncertainty quantification, or real-time decision support. We will build this IS around contributions focusing on strategies to overcome these barriers, in particular: • the construction of reduced-order models, using linear algebra tools (SVD, eigenvalue decomposition, reduced bases) to project problems onto subspaces of limited dimension, while maintaining satisfactory fidelity to the reference model; • the use of acceleration technologies (GPU computing, massive parallelization, accelerated iterative solvers) to process large-scale systems within time-frames compatible with operational constraints; • the integration of AI into modelling, through surrogate models, physics-informed models (PINN, PINO), or hybrid approaches combining machine learning and physical knowledge of the problem. We invite submissions presenting methodological developments or concrete industrial applications that illustrate the integration of these approaches for the design of digital twins, optimization, or decision support.

Microbial processes underpin applications ranging from food and precision fermentation to biomanufacturing, waste valorization, environmental remediation, and human and animal health. Mathematical and computational models offer powerful tools for understanding these systems and improving their operation, yet their predictive use remains challenging due to nonlinear interactions, partially observed dynamics, biological variability, parameter uncertainty, and limited availability of informative experimental data. This invited session will bring together advances at the interface of applied mathematics, computational science, control, machine learning, and microbial biotechnology. It will address methodological developments for the modeling, simulation, identification, and control of microbial and bioprocess systems, with a focus on how mechanistic and data-driven approaches can be combined to develop predictive and dynamically updated models of microbial processes. Topics will include mechanistic models of microbial populations and metabolic resources; qualitative and stability analysis; parameter identifiability and sensitivity; state and parameter estimation from sparse or heterogeneous observations; experimental design; optimal control; and uncertainty quantification. Particular attention will be given to hybrid approaches combining mechanistic knowledge with data-driven methods, including physics-informed learning, neural ordinary differential equations, hybrid models, and surrogate-based control. Such approaches offer new possibilities for reconstructing latent biological states, learning unresolved dynamics, optimizing operating conditions, and designing feedback strategies. Applications may span food and alcoholic fermentation, microbial production, anaerobic digestion, gut and rumen fermentation, and the management of microbial communities. By connecting fundamental mathematical questions to experimentally grounded, industrially relevant applications, the session aims to identify common methodological challenges and opportunities across microbial systems and operating regimes. Recent work has framed microbial system digital twins as collections of models dynamically connected to their physical counterparts through data and control flows. Building on this perspective, the session will explore how models can evolve from retrospective descriptions to predictive, dynamically updated tools for monitoring, optimization, and control.

This minisymposium aims to bring together researchers working on the numerical analysis and computational treatment of partial differential equations (PDEs) and integral equations, with particular emphasis on the discretization and integration challenges that arise in engineering simulations. The session intends to provide a forum for the discussion of both theoretical advances and computational strategies, fostering exchange between methodological developments and their application to real world problems. Contributions are welcome on a broad spectrum of topics, including but not limited to: novel quadrature schemes, such as adaptive refinement strategies and approaches based on unstructured node distributions inspired by meshless methods; accurate and efficient algorithms for the discretization of integral operators; and discretization techniques including the Boundary Element Method (BEM), the Finite Element Method (FEM), the Virtual Element Method (VEM), and their mutual coupling [1,2]. Particular attention will be devoted to applications spanning wave propagation, fluid dynamics, elastodynamics, imaging, ecology, epidemiology, and inverse problems, as well as to industrial and engineering contexts such as aerospace, naval and offshore engineering, civil and structural engineering, automotive systems, and energy technologies. Consistent with the spirit of the session, proposals demonstrating the interplay between rigorous numerical methodology and practical, industry-relevant challenges are particularly encouraged, in order to strengthen the dialogue between academic research, industrial practice, and public stakeholders. The minisymposium further aims to serve as an inclusive and stimulating venue for PhD students and early-career researchers, offering them the opportunity to present recent results, receive constructive feedback, and establish connections within the broader computational and numerical methods community. REFERENCES [1] Antonietti, P.F., Beirão da Veiga, L., Manzini, G. (Eds.). The Virtual Element Method and its Applications. SEMA SIMAI Springer Series, vol. 31. Springer, Cham, 2022. [2] Steinbach, O. Numerical Approximation Methods for Elliptic Boundary Value Problems: Finite and Boundary Elements. Texts in Applied Mathematics. Springer, New York, 2008.

Building a sustainable society requires a transition away from fossil fuels toward green energy solutions. At the European level, targets for this transition were set out in the EU Green Deal. This includes the generation of energy from renewable sources, while also electrifying technology which is currently powered by fossil fuels. In parallel, reducing the energy consumption of rapidly growing information and computing technologies must also be addressed. Achieving these goals at a necessary scale will require the development of new materials and devices that combine high performance, long operational lifetimes, and an efficient use of resources. A variety of technologies will be needed to reach these objectives, including efficient and stable solar cells, batteries, and advanced electronic components. These are united by common mathematical and numerical challenges. The underlying problems include (1) describing similar physical processes across multiple length and time scales, (2) understanding and predicting degradation, (3) identifying relevant parameters for underlying models, and (4) exploring high-dimensional design spaces under multiple objectives. Addressing these challenges involves a combination of modeling and computational methods at different scales. These include first-principle approaches which are limited to small domain sizes, continuum-based PDE models which can be scaled to larger systems but may neglect physical effects, and data-driven techniques which require a large amount of experimental or accurate simulation data in order to make predictions about new devices. The goal of this invited session is to bring together researchers from different electronic and energy-device communities to discuss shared mathematical and computational challenges. In particular, we will explore how multiscale modeling, degradation modeling and data-driven methods can be combined to guide device design toward high performance, long lifetime, and sustainable use of resources.

Many challenging problems arising in science and engineering involve the interaction of physical phenomena described by coupled partial differential equations on domains of different dimensions, scales, or geometrical complexity. Examples include fluid-structure interaction, flow and transport in networks and fractured media, solid-fluid interactions, biomedical systems, modeling of new materials, and coupled processes in geophysical applications. The differences in dimensionality and physical nature of the coupled models raise fundamental questions concerning mathematical modeling, coupling conditions, discretization, stability and error control, while also posing significant computational challenges for large-scale simulations. This session aims to bring together recent developments in the mathematical analysis and numerical approximation of multidimensional and multiphysics coupled problems. Particular emphasis will be placed on the interplay among mathematical models, discretization strategies and efficient solvers, with the goal of connecting theoretical advances with challenging applications. Topics of interest include, but are not limited to multiphysics and multiscale systems, non-conforming and immersed discretizations, and interface and contact problems, with the aim of highlighting the challenges, capabilities, and effectiveness of mixed-dimensional models. The session welcomes contributions ranging from mathematical analysis and numerical methods to computational mechanics and application-driven modeling. A particular goal is to foster interaction between different communities and to identify common numerical and analytical structures underlying seemingly different coupled problems, highlighting how advances in theory can translate into robust and efficient computational tools for real-world applications.

Medical and industrial imaging increasingly serve as the foundation for digital twins — virtual, patient- or process-specific replicas that support diagnosis, monitoring, design, and decision-making. This minisymposium brings together mathematicians, computational scientists, and engineers working at the intersection of imaging, mathematical modeling, and scientific machine learning to build imaging-based digital twins with real-world impact, spanning biomedical and industrial applications. We will discuss algorithmic advances for digital twins and for solving the underlying governing equations, covering both classical numerical methods and emerging machine-learning-based techniques. Talks will address model-driven, data-driven, and hybrid strategies that combine physics-based simulation with learned representations, together with methods for uncertainty quantification, model-order reduction, and real-time simulation needed to make digital twins deployable in practice. Particular attention will be devoted to the translation of these methods beyond the laboratory: validation against real data, integration into clinical and industrial workflows, and the challenges of scaling personalized or process-specific models to cohorts or production settings. By connecting biomedical applications (e.g., cardiovascular and organ-level digital twins) with broader industrial and sustainability-oriented use cases, the session aims to foster cross-fertilization between academia, industry, and end users, in line with M2P's mission of turning mathematical and computational advances into deployable, reliable quantitative tools.

Land-use change, intensive agriculture, climate variability, biodiversity loss and increasing pressure on natural resources are strongly interconnected challenges for sustainable development. Addressing them requires the integration of mathematical modelling, computational methods, data analysis and enabling technologies to understand complex systems, exploit heterogeneous data, explore future scenarios and support sustainable decision making. These challenges arise naturally in terrestrial systems, where quantitative tools can support sustainable farming, ecosystem management, environmental monitoring and resource optimisation. They become even more demanding in controlled and space environments, where water, energy, nutrients and human intervention are severely constrained, and where autonomy, robustness and closed-loop operation are essential. The session aims to explore current advances and frontier challenges across terrestrial and space-based green systems, highlighting common needs, complementary approaches and opportunities for cross-disciplinary exchange. Topics of interest include, but are not limited to: • data-driven modelling and dynamical systems; • multiphysics and multiscale methods; • optimisation and optimal control; • uncertainty quantification, stochastic methods, inverse problems and parameter estimation; • remote sensing, data assimilation, sensing and monitoring; • statistical learning and scientific machine learning; • reduced order and surrogate modelling; • digital twins and model-based decision support; • sustainable and precision agriculture; • greenhouse and vertical farming; • ecosystem and land management; • resource-efficient systems; • controlled environments and space farming. In the spirit of M2P, the session is intended to foster interaction among mathematicians, engineers, computational and data scientists, agronomists, environmental scientists, technology developers, industry and other stakeholders, encouraging the transfer of methods and ideas from research to real-world applications.

Numerical methods for differential equations play an important role in the modeling and simulation of complex phenomena in science and engineering. In recent decades, considerable progress has been made in both the mathematical analysis of numerical methods and their application to increasingly challenging problems. However, turning theoretical results into computational methods that are accurate, efficient, and reliable in practice remains a challenging task. This requires a good balance between mathematical rigour, algorithm development, and practical implementation. This minisymposium brings together researchers working on the analysis, development, and application of numerical methods for differential equations. The contributions will focus on numerical methods that combine solid theoretical properties with good computational performance and reliability in practical simulations. Particular emphasis will be given to topics such as stability, convergence, and preservation of important mathematical structures. Topics include, but are not limited to, numerical methods for ordinary and partial differential equations, efficient computational techniques, and numerical experiments for testing and comparing different methods. Applications range from physics, biology, chemistry, and engineering to fluid dynamics, materials science, medicine, and with particular attention to sustainability applications, highlighting the role of numerical methods in connecting mathematical models with practical simulations.

Space-time finite element methods treat time as an additional dimension of the finite element discretization, rather than marching forward from time step to time step, allowing to solve the full space-time domain at once or in a slab-wise fashion. This perspective offers a natural framework for problems with evolving domains and topologies, adaptive resolution in both space and time, and formulations with attractive stability and conservation properties – while also overcoming the limitation of being inherently sequential in time that classical time-marching schemes face in parallelization, opening the door to scalable space-time solvers on HPC and exascale systems. Realizing this potential in practice, however, depends on a step that is often taken for granted in three spatial dimensions but becomes a genuine research problem in four: mesh generation for the space-time domain. While different mesh types are used throughout the space-time finite element community, unstructured simplex meshes are of particular interest for boundary-fitted geometry representations. Robust, efficient, and parallel algorithms for their generation, together with adaptation, refinement, error estimation, and mesh deformation strategies, remain active areas of development at the interface of computational geometry and numerical analysis. This invited session aims to foster interdisciplinary exchange between researchers working on the mathematical and algorithmic foundations of space-time meshing and those developing and applying space-time finite element formulations to real-world problems in engineering and applied mathematics – moving space-time finite elements from an elegant mathematical framework toward a mature, broadly applicable simulation technology. We invite contributions spanning the full pipeline from mesh to product: - Space-time mesh generation and visualization workflows, in particular unstructured simplex meshing in 4D - Mesh adaptation and a posteriori error estimation - Stabilized space-time finite element formulations - Applications in fluid & solid mechanics, and multiphysics, including fluid-structure interaction, free-surface flows, and other evolving-domain problems - Deployment of space-time methods in HPC and exascale settings, including parallelization and domain decomposition - Case studies motivated by specific problems and application domains

Cancer is one of the leading causes of mortality worldwide. Tumours evolve, adapt, and exploit their environment in ways that experiments alone cannot easily capture. Tumour complexity spans molecular heterogeneity, dynamic tumour–host interactions, treatment resistance, and patient-to-patient variability. Mathematical modelling and computational approaches offer a way to translate multi-scale biological data into predictive frameworks and reveal mechanisms that experiments alone often cannot isolate. Nowadays, models help us understand how tumours grow and invade surrounding tissue, predict how patients will respond to therapy, and design smarter treatment protocols that avoid resistance. This minisymposium brings together researchers at the intersection of mathematical modelling, computational biology, and clinical oncology to present how rigorous modelling is shaping the next generation of cancer research and patient care. Contributions are invited from all areas where researchers working on mathematical and computational tools are advancing our understanding of approaches to tumour biology, treatment response, and improving clinical decision-making, including but not limited to: • Multi-scale models of tumour growth, invasion, and metastasis • Mechanistic and data-driven modelling of treatment response, including chemotherapy, radiotherapy, targeted agents, and immunotherapy • Optimisation and control of treatment schedules, including adaptive therapy and strategies to manage resistance • Patient-specific modelling and digital twins, calibrated from clinical imaging and clinical data • Modelling the tumour microenvironment, including angiogenesis and immune interactions • Pharmacokinetic and pharmacodynamic modelling for drug development, delivery, efficacy, and toxicity • Machine learning and hybrid physics-informed approaches in oncology • Evolutionary and game-theoretic frameworks for tumour heterogeneity • Mathematical frameworks to support clinical trial design and in silico experimentation This session will provide a forum for exchanging ideas across disciplinary boundaries, from applied mathematicians and biomedical engineers to computational scientists. We welcome contributions that bridge rigorous mathematics with clinical relevance and demonstrate translational potential. The event aims to advance the vision of precision oncology, in which mathematical models can support clinicians in providing tailored and effective patient care.

The European Service Network of Mathematics for Industry and Innovation (EU-MATHS-IN) links 17 national networks across Europe (https://eu-maths-in.eu/ ). It fosters high-impact collaborations by facilitating communication and information exchange between researchers and industrial partners. This minisymposium showcases successful technology transfer projects achieved through EU-MATHS-IN. Researchers and industry representatives present real-life examples that demonstrate the power of mathematics to drive innovation. In addition, we present the EU-MATHS-IN OpenDesk (https://opendesk.eu-maths-in.eu/ ), an innovative support platform for European companies, start-ups and public administrations. This service provides valuable resources and guidance on how to use mathematics for problem solving and technological progress.

High-fidelity simulation increasingly supports the design, optimisation and operation of complex systems across engineering, energy, manufacturing, environmental sciences and emerging technologies. Its predictive potential, however, can only deliver real impact if simulations remain reliable, computationally affordable and sufficiently automated. Mesh adaptation is therefore a key enabling technology, allowing computational resolution to follow the physics, geometry and evolving scales of a problem rather than being fixed a priori. Adaptation is particularly important for multiphysics and multiscale phenomena, moving interfaces, evolving geometries, localised structures, strongly directional features and large computational domains, where uniform discretisation rapidly becomes impractical. Growing application complexity is also driving adaptation beyond traditional refinement towards scalable, geometry-aware, data-informed and increasingly autonomous computational pipelines. This session will explore recent advances and emerging directions in adaptive meshing, particularly the challenges of translating methodological developments into large-scale, real-world applications. Established approaches such as error estimation, goal-oriented methods and isotropic or anisotropic adaptation increasingly need to interact with HPC, parallel mesh modification, automated workflows, machine learning and data-driven decision making. Topics of interest include, but are not limited to: • adaptive methods for multiphysics and multiscale problems; • anisotropic and geometry-aware adaptation; • moving meshes and evolving domains; • error estimation and goal-oriented adaptation; • parallel and distributed mesh adaptation; • scalable algorithms and HPC implementations; • adaptive strategies for complex industrial workflows; • machine-learning and data-driven adaptation; • adaptive pipelines for design, optimisation and digital twins; • applications across engineering, energy, manufacturing, environmental sciences and other large-scale computational settings. By bringing together numerical analysts, computational scientists, HPC and data experts, software developers, engineers and industrial practitioners, the session aims to foster cross-fertilisation of ideas and help shape the next generation of adaptive simulation workflows, bridging complex physics, scalable computation and real-world applications.

Adaptive Mesh Refinement (AMR) has proven its ability to significantly reduce simulation runtime and memory requirements while keeping numerical errors low. Various approaches exist, with unstructured, block-structured and tree-based AMR being the most common. More recently, specialized algorithms tailored to modern hybrid computing architectures have emerged. Despite these advantages, industrial adoption of AMR remains limited. However, NASA’s CFD Vision Report [1] underscores the critical role of AMR in future computational fluid dynamics, highlighting automated in-situ meshes with adaptive control as a primary target. Beyond CFD, AMR offers broader industry benefits such as adaptive resolution and efficient data compression. This should motivate us to bring innovative AMR approaches into industrial practice. In this session, we showcase practical implementations within simulation frameworks and explore novel domains where AMR improves computational efficiency and reduces memory footprints. Additionally, we examine newly emerging AMR algorithms specifically designed to tackle the scaling challenges of modern GPU-focused supercomputers and high-performance research clusters. By exploring these techniques, this session aims to foster dynamic discussion and collaborative exchange between developers, researchers, and end-users to advance the broader industrial adoption of AMR.

Computational electrophysiology enables the investigation of electrical activity in excitable tissues, from single-cell ion dynamics to organ-scale propagation, with applications spanning cardiac, neural, and other bioelectrical systems. Recent advances in mathematical modeling, high-performance computing and data-driven methods are enabling increasingly detailed and predictive simulations across spatial and temporal scales, from ion channels to single cells, tissues and whole organs. The underlying models are demanding: stiff systems of ordinary differential equations describing ionic dynamics are coupled with partial differential equations governing propagation at the tissue level, while their numerical solution must resolve steep, highly localized fronts over long time intervals. This session brings together researchers working on the development, analysis, and application of computational methods for electrophysiology, with particular emphasis on methodological advances that bridge biophysical modeling, numerical simulation, and experimental data. The session focuses on the design and analysis of numerical solvers, their efficient implementation on large-scale computing architectures, and the integration of computational models with real data, where uncertainty quantification and machine learning are playing an increasingly central role. Recent developments in these directions are opening new possibilities for a range of applications, including digital twins, in silico trials, and model-based therapy planning. A further aim is to foster exchange between researchers developing new mathematical and computational methods and those working closely with experimental and clinical data. It is often from this interaction that the most relevant and challenging methodological questions emerge, leading to new computational approaches.

As increasingly challenging problems are addressed using high-fidelity numerical models, new methodologies are required to handle severe nonlinearity, singular coefficients, evolving interfaces, multiscale and multiphysics couplings, while preserving essential properties such as accuracy, stability and robustness. In parallel, the rapid development of data science and machine learning is creating new ways to enhance traditional numerical simulation. Topics of interest include adaptive strategies, error estimation and mesh adaptation, reduced-order modelling, operator learning, physics-informed machine learning, data assimilation, uncertainty quantification, etc. This session will cover recent advances in finite element methods and emerging technologies for the simulation of complex engineering systems. Attention will be given to methods that combine high-fidelity finite element simulations with data-driven techniques to accelerate computations, improve predictive capabilities. Trying to bring together a balanced mix of academic and industrial perspectives, the session aims to promote exchanges on emerging improvement of the finite element technology. Contributions ranging from methodological developments to industrial and societal applications are welcome, with particular emphasis on maintaining the reliability and interpretability required for scientific and engineering decision-making.

The increasing availability of experimental, imaging, clinical, and population-level data, together with rapid advances in computational science, is creating new opportunities for quantitative modeling of complex biological systems. However, biological problems are inherently multiscale, nonlinear, heterogeneous, and data-limited, making it difficult for any single experimental or computational method to fully describe system behavior. Integrative approaches that combine experiments, mechanistic models, data-driven methods, and advanced computational techniques offer a promising path toward more predictive and interpretable models. This invited session will bring together researchers developing and applying integrative methodologies for modeling biological systems. Particular emphasis will be placed on approaches that connect experimental measurements, mathematical and computational models, and heterogeneous sources of biological and biomedical data. Topics will include computational mechanics; experimental-computational integration; physics-based and data-driven modeling; scientific machine learning; reduced-order and surrogate modeling; multiscale and multiphysics methods; parameter estimation and inverse problems; uncertainty quantification; image-based modeling; model calibration and validation; and strategies for integrating sparse or heterogeneous datasets. Applications may span tissues, organs, physiological systems, medical technologies, and other complex biological systems. A central objective of the session is to foster interactions among researchers who traditionally approach biological problems from different perspectives, including applied mathematics, computational science, biomechanics, engineering, data science, and experimental research. The session will highlight how complementary methodologies can be integrated to overcome limitations in individual approaches and enable models that are computationally efficient, experimentally informed, and capable of addressing complex biological questions. Particular attention will be given to emerging methodologies that facilitate translation from fundamental mathematical and computational developments to biomedical and technological applications. IS Topics: Computational modeling; experimental-computational integration; scientific machine learning; physics-informed modeling; reduced-order modeling; surrogate modeling; multiscale and multiphysics methods; inverse problems.

Personalised medicine increasingly relies on computational modelling, yet industrial applications and clinical translation demand tools efficient and affordable enough for routine use. In particular, forward models capturing multiscale, multiphysics processes are often too costly to support parameter estimation or real-time prediction, and standard data assimilation methods for model personalisation quickly become intractable at the scale required for patient-specific digital twins. Scientific Machine Learning offers a route around this bottleneck. Surrogate modelling now generalises across varying inputs and geometries, while physics-informed approaches embed governing equations into the learning process to improve data efficiency. More recently, generative and probabilistic methods such as Bayesian neural networks and diffusion models are being explored for uncertainty quantification, while agentic AI systems capable of orchestrating full calibration pipelines mark a further step towards automated personalisation. These developments are reshaping forward and inverse modelling across biomedicine, though their robustness and reliability in clinical settings still require systematic investigation. This mini-symposium aims to bring together applied mathematicians, biomedical engineers and clinicians working on mathematical modelling and numerical and data-driven methods for personalised computational medicine. We welcome contributions on reduced-order modelling, machine learning for patient-specific parameterisation, data-driven calibration and real-time simulation, integration of multiscale models with clinical data, and industrial applications of digital twins in device design. The session aims to connect academia and industry, encouraging discussion of open challenges and new collaborations within the growing international community working on digital twins in biomedicine.

Charge-transfer and redox reactions, and the solid-state processes they drive, shape the behaviour of materials throughout the life cycle of engineered components. They govern the performance and ageing of batteries, electrolysers and fuel cells; contribute to corrosion, hydrogen uptake and embrittlement; and enable end-of-life material recovery, including the hydrogen decrepitation of rare-earth magnets. By linking longer service life with more effective material recovery, the two principal levers of a circular economy, this session highlights the shared physical principles underlying durability, degradation and recycling. These processes share a common mathematical and computational structure: transport of charged species, nonlinear interface kinetics, and coupling to mechanics through swelling, stress-assisted diffusion and fracture. Their modelling spans the molecular, microstructural and component scales. The resulting systems are multiscale, stiff, often posed on evolving domains such as dissolution fronts and cracks, and depend on parameters that must be inferred from sparse and noisy data. The session brings together communities that meet these challenges separately, so that methods developed in one field reach the others. It addresses the conference themes of energy systems, clean mobility, and waste and resource management. Topics include: (i) models of corrosion and corrosion inhibition, from the molecular design of inhibitors to passive films and protective coatings; (ii) hydrogen uptake, transport, trapping and embrittlement; (iii) electro-chemo-mechanical degradation of batteries, electrolysers and fuel cells; (iv) phase-field, cohesive-zone and unfitted methods for fracture and moving interfaces; (v) electrochemical and solid-state processes for recycling and material recovery; (vi) scale bridging, surrogate modelling, Bayesian calibration and uncertainty quantification; and (vii) digital twins for lifetime prediction. Contributions that confront models with experiments, and contributions from industry and public stakeholders, are particularly welcome.

Fibre-reinforced plastic (FRP) composites - ranging from continuously fibre-reinforced structures to components reinforced with short or long fibres - have become indispensable in a wide array of industries, including automotive, aerospace, energy, and construction. Their increasing adoption stems not only from their outstanding specific mechanical properties but also from the high design freedom they offer in tailoring both geometry and material composition. A particularly promising frontier lies in the simulation-driven optimization of FRP components with graded fibre distributions. These allow local adaptation of stiffness, strength, and failure behaviour to the specific performance requirements of complex load cases. Advances in computational methods now make it possible to design and virtually validate such graded structures, where fibre orientation, volume content, and reinforcement architecture vary continuously across the part. This enables truly functionally optimized, lightweight designs with unprecedented material efficiency and mechanical performance. This invited session will provide a platform for researchers and practitioners to exchange insights on the latest developments in simulation, modelling, and optimization of fibre-reinforced plastic components, with a focus on: • Multi-scale and multi-physics simulation of FRP materials and processes • Optimization of fibre architecture for load-adaptive structures • Computational design and validation of functionally graded composites • Process-structure-property relationships in FRP manufacturing • Integration of simulation and experimental validation • Application case studies involving structurally and materially optimized components

Computational fluid dynamics (CFD) has become an essential tool throughout the industrial product lifecycle, from preliminary design and optimization to performance assessment and post-production analysis. Across these stages, computational efficiency is crucial, particularly for unsteady problems, whose experimental investigation may be costly or difficult. Many industrial applications involve moving bodies and large boundary deformations, posing additional challenges in terms of numerical accuracy, robustness, and computational cost. For body-fitted unstructured discretizations, moving boundaries require the computational mesh to evolve while preserving adequate mesh quality, even under large deformations. At the same time, unsteady flows often feature localized structures that evolve throughout the computational domain, making mesh adaptation an effective strategy to concentrate computational resources where they are most needed. Efficient mesh deformation and adaptation techniques are therefore key ingredients for reliable and affordable unsteady CFD simulations. This invited session will discuss recent advances in mesh deformation and adaptation for complex unsteady CFD applications, with particular emphasis on unstructured grids and moving geometries. Topics include robust mesh-motion algorithms, local and global adaptation, error- and feature-based criteria, predictive and data-driven strategies, conservative solution transfer, and their integration into CFD solvers. Particular attention will be devoted to approaches that improve computational efficiency while retaining the accuracy and robustness required by industrial applications involving moving and deforming geometries and strongly evolving flow features.

Biomedical devices and organ-on-chip systems are evolving rapidly, thanks in large part to computational models that integrate aspects such as geometry, materials, fluid dynamics, and biological functions. However, translating these complex models into practical tools for design and decision-making is still a challenging endeavor. This is largely due to the need to tackle multiple spatial and temporal scales, to limited experimental data, uncertainties in parameters and boundary conditions, and the high computational costs of running detailed simulations. This Invited Session aims to gather researchers in applied mathematics, computational science, and engineering who are developing models for biomedical devices and organ-on-chip technologies. In this regard, challenging application scenarios include, but are not limited to, the development of reliable digital twins for cardiac and brain function, the design of vascular stents, orthopedic implants, microfluidic devices, and organ-on-chip systems. Topics of interest span the entire modelling pipeline, from initial formulation and discretization to calibration, validation, and predictive analysis. We welcome contributions on partial differential equation-based modelling, e.g., for fluid dynamics and continuum solid mechanics, and design optimization approaches. From the computational viewpoint, particular interest is devoted to adaptive discretization techniques, reduced-order modelling, uncertainty quantification, as well as hybrid approaches that merge physics-based and data-driven strategies. In addition, throughout the session, we will address common challenges, such as integrating patient-specific data and improving prediction reliability, while aiming to strengthen cross-disciplinary collaboration. By connecting device mechanics with engineered biological systems, the session aims to stimulate valuable exchange among academics, clinical researchers, and industry professionals, with the goal of enhancing reproducibility, validation, and the translation of research outcomes into real-world applications.

The study of ecological and technological systems, and the effective management of natural resources, require reliable mathematical and computational tools to understand their dynamics and predict their evolution. The underlying physical and biological processes are often characterized by strong nonlinearities and multiple interacting mechanisms operating across different spatial and temporal scales. These features pose significant challenges in both formulating appropriate mathematical models and obtaining accurate solutions at a reasonable computational cost. Physical and biological insight should therefore guide model formulation, while the analysis of the resulting mathematical structures can inform the design of robust numerical methods. The aim of this session is to bring together researchers working on mathematical modeling and numerical methods for ecological and technological systems. Contributions addressing both methodological developments and specific applications are welcome, with particular emphasis on the interplay between model formulation, theoretical analysis, and numerical simulation. Topics of interest include, but are not limited to: - mathematical modelling of physical and biological processes using deterministic and stochastic differential equations; - stability and bifurcation analysis of nonlinear systems, with particular attention to the emergence of Turing patterns; - accurate and efficient numerical methods for stiff and multiscale problems; - structure-preserving numerical methods that reproduce qualitative properties known a priori for the continuous model; - parameter estimation and uncertainty quantification; - integration of mechanistic models with data-driven approaches, including machine learning and artificial intelligence techniques. Applications of interest include vegetation dynamics, sustainable agriculture, water resource management, pollutant transport, battery performance, material deterioration, and the modelling and optimization of energy systems and industrial processes.

Simulation and optimization are at the core of modern product design, from structural and fluid analysis to materials modelling and logistics planning. As problem sizes and accuracy requirements grow, classical solvers face mounting computational costs. Quantum computing offers new computational paradigms, but turning algorithmic advances into industrial practice remains an open challenge. This session brings together mathematicians, computational scientists and industry practitioners to explore how quantum and hybrid quantum-classical algorithms can address scientific computing problems of industrial relevance. Contributions will cover recent mathematical developments in quantum algorithms for linear systems, partial differential equations, optimization and sampling, as well as realistic use cases in aerospace, energy, automotive and manufacturing. The session will also look critically at resource requirements, error mitigation and the outlook for near-term (NISQ) versus fault-tolerant devices, with emphasis on rigorous benchmarking against state-of-the-art classical methods, data encoding and readout costs, and integration into existing simulation and HPC workflows. Topics: quantum algorithms for linear systems and PDEs; variational and hybrid quantum-classical methods; quantum optimization for industrial problems; quantum machine learning for simulation and surrogate modelling; error mitigation and resource estimation; benchmarking and quantum-HPC integration; industrial case studies.

Optimal control problems (OCP) and sensitivity analysis (SA) are ubiquitous in engineering applications: trajectory control in aeronautics and robotics, path planning in locomotion of vehicles, deformation analysis in elastodynamics and biomechanics, or control of industrial processes, to name a few. The solution of OCPs has also mathematical interest due to the underlying symmetries of the problem statement and the optimal solutions. This MS focuses on the formulation and numerical solution of optimal control problems and the analysis of sensitivity, and intends to gather engineers, scientists and researchers in applied sciences that investigate the development of numerical strategies for OCP and SA, and that can contribute with novel formulations, applications or numerical algorithms for solving efficiently the optimality conditions.

Addressing the challenges of environmental sustainability requires accurate mathematical models and efficient numerical methods capable of simulating complex, multiscale, multiphysics, and stochastic phenomena. This Session focuses on recent advances in numerical analysis, scientific computing, and High-Performance Computing (HPC) for the simulation, optimization, and control of systems relevant to environmental sustainability and sustainable technological innovation. It aims to bring together researchers working on advanced numerical methods for differential and integral equations, including stiff, nonlocal, and stochastic problems, alongside experts in parallel computing, scalable numerical linear algebra and numerical optimization. Particular attention will be devoted to efficient time integration techniques, adaptive discretizations, structure-preserving methods, matrix-oriented approaches, High-Performance numerical solvers, model order reduction, data-driven methods, scientific machine learning, and digital twins, as well as energy-aware computing, resource-efficient algorithms, and sustainable HPC infrastructures will also be addressed. Application areas include renewable energy and energy-efficient technologies, electrochemical processes and energy storage systems, sustainable industrial processes, climate and atmospheric modelling, air quality assessment, precision agriculture and irrigation, soil resource management, ecosystem dynamics and biodiversity, environmental monitoring, and the simulation and mitigation of natural and climate-related hazards, including wildfires and seismic risks. By bridging methodological advances and real-world challenges, the minisymposium seeks to foster interdisciplinary collaboration and highlight the role of accurate, scalable, and computationally sustainable numerical methods in strengthening environmental resilience, promoting efficient resource management, and supporting the transition towards a more sustainable society.

Numerical simulations are the backbone of many scientific and industrial applications, and reliability is an essential feature to be fulfilled. The last decades witnessed an increased accuracy in simulation science even for very complex systems, thanks to the access to a larger computational capability. However, it is clear that a balanced trade-off between the required computational cost and the achieved accuracy needs to be pursued, most of all in many-query settings such as optimization and analysis in industrial or manufacturing processes. For this reason, recent techniques to accelerate the computing time for numerical simulations, such as Reduced order models (ROMs) and scientific machine learning (ML) surrogate models have gained a lot of popularity thanks to their capability to reduce the computing time for numerical simulations while still maintaining a successful level of accuracy. In this session, we aim to collect several applications where the usage of such techniques enables new industrial workflows, to accelerate and/or to improve the existing ones. We encourage contributions on applications of recent methods, including but not limited to ROMs and ML-based surrogates, that address computational bottlenecks in industrial simulations. Contributions from industry, spin-offs, and startups are particularly welcome. We also encourage applied-oriented academic contributions to foster dialogue between scientific advances and real-world applications.

Mathematical optimization provides a common framework for developing models, learning from data, and addressing complex problems across scientific disciplines. Computational linguistics and the life sciences offer challenging settings in which theoretical advances and application needs can inform each other, with implications for human health, communication, and society. This invited session brings together researchers in optimization, numerical analysis, machine learning, computational and theoretical linguistics, and the life sciences. Its aim is to connect mathematical foundations and algorithmic developments with applications, encouraging contributions ranging from theoretical investigations to interdisciplinary case studies. Methodological topics include stochastic and nonconvex optimization, regularization, constrained and multiobjective formulations, inverse problems, parameter estimation, and structured representation learning. Theoretical contributions may address convergence, stability, identifiability, computational complexity, and robustness, as well as the development and analysis of efficient numerical algorithms. In linguistics, computational applications include natural language processing, semantic representations, multilingual language technologies, and the analysis of textual data and public discourse; theoretically and methodologically oriented work develops tools to explore the universal structure of language diversity and change. In the life sciences, the scope includes mathematical modelling and data analysis for neurodegenerative diseases, including Alzheimer’s disease, cancer research, and pharmacology. These applications motivate questions about heterogeneous data, limited observations, uncertainty, and the interpretation of computational results. Particular attention will be given to how application-specific knowledge can inform mathematical formulations, and how theoretical properties translate into reliable computational behaviour. Contributions examining predictive performance, computational efficiency, interpretability, and the effects of data quality are welcome. By bringing these perspectives together, the session aims to identify shared mathematical challenges and promote exchanges between methodological research and applications with scientific and societal relevance.

Addressing climate change and the transition towards sustainability requires both anticipating the evolution of environmental systems (e.g., desertification, wildfires, water resources, …) and designing engineering systems that minimise environmental impact while remaining efficient and resilient throughout their lifetime (e.g., electric mobility, renewable energy, …). Despite their different nature and objectives, these two challenges share a fundamental need: predicting the behaviour of complex systems to support reliable decisions on design, operation, mitigation, and adaptation. The behaviour of these systems often depends on many parameters, interacting processes, potentially involving multiple physics and scales, and uncertain conditions that may evolve over time, posing significant scientific challenges. Available knowledge is typically distributed across heterogeneous sources, including high-fidelity simulations, simplified physical and data-driven models, and experimental observations, each with their own accuracy, credibility, and cost. This calls for innovative methods to explore high-dimensional parameter spaces, propagate uncertainties, and enable many-query applications while making parsimonious use of available resources. This invited session focuses on computational methodologies for predictive modelling, with particular attention to scalability and the environmental footprint of the modelling process itself. Parametric surrogates, reduced-order methods, physics-informed and data-driven approaches, and multi-fidelity strategies provide complementary means of integrating models and observations to construct predictive representations. Beyond accuracy, ensuring reliability requires both quantitative assessments, such as error estimates and model calibration, and the ability to capture qualitative changes in system behaviour, including bifurcations and transitions between solution branches. These capabilities support robust optimisation and control, as well as adaptive modelling and monitoring, helping decisions remain reliable in different scenarios, under uncertainty, and as new information becomes available. The session aims to connect methodological advances with environmental and engineering applications, translating predictive modelling into informed decisions, with the goal of reducing the environmental impact of the systems under analysis, while also limiting the computational footprint of the modelling methods themselves.

Space science and space technology present complex challenges that demand robust mathematical models, advanced numerical simulations, and highly efficient predictive tools. As observational datasets from space missions continue to grow exponentially in size and heterogeneity, there is a critical need to translate theoretical advances in applied mathematics into reliable, real-world solutions. This directly aligns with the core mission of the Math to Product congress, which seeks to bridge the gap between academic research and industrial workflows through quantitative predictive science. This Invited Session explores the dynamic intersection of computational engineering, scientific machine learning, and space applications. We focus on innovative methodologies integrating deep physical modeling with data-driven techniques to analyze, reconstruct, and predict complex phenomena. Key topics include inverse problems and regularization methods for space-based imaging and remote sensing; numerical optimization and variational approaches for precise parameter estimation and data assimilation; and statistical learning frameworks designed for high-dimensional, multimodal observational data. Special emphasis is placed on physics-informed learning, hybrid approaches combining numerical solvers with machine learning, uncertainty quantification, and interpretable, trustworthy artificial intelligence. These mathematical tools are vital for extracting actionable information across applications such as solar physics, space weather forecasting, and spacecraft dynamics. Furthermore, by addressing Earth observation and satellite data analysis, this session supports the broader goals of computational sustainability, environmental monitoring, and climate modeling. We encourage contributions that go beyond the standard application of existing algorithms to highlight methodological advances, computational efficiency, and the strict integration of physical constraints into optimization frameworks. By fostering cross-fertilization among mathematicians, computational scientists, domain experts, and industrial stakeholders, this session aims to deliver robust, physically consistent computational tools that address emerging challenges in space engineering, thereby driving new paradigms in science, industrial innovation, and policy making.

Advanced engineering and industrial applications often involve complex computational models, whose high computational costs may limit their use in real-time and many-query scenarios. Reduced Order Methods (ROMs) address these challenges by constructing efficient surrogate models that approximate complex parametric systems at a significantly reduced computational effort. In particular, intrusive approaches, such as Galerkin methods, rely on the explicit knowledge of the governing equations to derive reduced models. While they typically ensure high accuracy and strong physical consistency, their efficiency may deteriorate when dealing with nonlinear dynamics or strongly coupled systems. On the other hand, non-intrusive approaches, often based on data-driven and machine learning techniques, exploit data from experiments or high-fidelity simulations to extract underlying patterns. These methods are flexible and broadly applicable, but they may require large datasets, extensive training, and often lack rigorous error estimation, physical interpretability, and structure preservation. To overcome these limitations, hybrid strategies that combine physics-based and data-driven methodologies offer a promising pathway. Such approaches can enhance both predictive accuracy and computational efficiency, while improving model interpretability and robustness for complex systems. This mini-symposium aims to stimulate discussion on intrusive and non-intrusive ROMs, providing a comparative perspective on their strengths, limitations, and applicability across academic, industrial, and engineering contexts. Topics of interest include both advances in reduced-order modeling and emerging methods integrating ROMs with machine learning and data-driven approaches. Contributions on practical applications in industry are also welcome, emphasizing the role of these strategies in addressing real-world challenges and fostering technological innovation.

The rapid transformation of electric power systems is creating urgent needs for advanced computational methods that can support reliable and affordable energy infrastructure. Increasing proportion of distributed energy resources, electrification of end uses, extreme weather events, and evolving market and regulatory structures are placing new demands on planning and operational decision-making. These challenges require mathematical and computational approaches that can integrate large-scale optimization, uncertainty quantification, data-driven modeling, and high-performance computing into decision-support tools for real-world energy systems. This Invited Session will highlight emerging research at the interface of applied mathematics, computational science, and power systems engineering applications. Topics may include generation and transmission expansion planning, integrated resource planning, grid reliability assessment, stochastic and robust optimization, decomposition and alternate acceleration methods, and evaluation methods for infrastructure investment strategies. Emphasis will be placed on methods that bridge mathematical innovation and practical deployment including approaches that support representation of extreme events; integration of distributed generation and storage resources; coordination across transmission, distribution, and end-use sectors; and decision-making under deep uncertainty.

Mathematical models and computational methods play a fundamental role in the analysis, simulation, and optimization of complex engineering and industrial problems. This invited session aims to bring together early-career researchers working in numerical analysis, scientific computing, and computational engineering to present recent advances, discuss emerging challenges, and promote scientific exchange and interdisciplinary collaborations. Particular emphasis will be placed on the development of innovative numerical methodologies and their application to real-world problems, promoting connections between academia and industry. Topics include, but are not limited to: - advanced numerical methods for partial differential equations (PDEs); - computational mechanics and fluid dynamics; - multiscale and multiphysics problems; - numerical optimization and optimal design; - reduced-order modeling and scientific machine learning; - numerical simulations of industrial processes and advanced materials.

As the leading cause of death worldwide, cardiovascular diseases drive demand for better devices and diagnostics. Computational modeling supports their development, from stents, heart valves, and blood pumps to patient-specific tools such as CT-derived fractional flow reserve Regulatory acceptance of in-silico evidence is also growing. Translating such models into industrial and clinical R&D requires methods that are accurate yet efficient enough for iterative design, validation, and clinical workflows. Computational fluid dynamics (CFD) and fluid–structure interaction (FSI) can capture blood flow in vessels and devices, while biomechanical models describe the mechanics of vessel walls, pumps, and valves. Further models address blood damage and biological responses, including hemolysis, thrombosis, and in-stent restenosis. To make these approaches practical, high-fidelity simulations can be complemented by reduced-order, surrogate, and data-driven models, and supported by high performance computing. The session invites contributions from academia and industry on computational models developed or tailored for R&D of cardiovascular devices and clinical tools, including: • CFD, FSI and biomechanical models of devices and patient-specific anatomies; • models of hemolysis, thrombosis, restenosis and device–tissue interaction; • reduced-order, surrogate and efficient models for many-query simulations; • validation and uncertainty quantification against bench and clinical data; • in-silico trials and computational design testing of devices at R&D level; • software tools supporting clinical decision-making, planning and guidance.

Recent advances in computational intelligence (CI) are transforming computational science through foundation models (FMs) that learn transferable representations across scientific datasets and physical systems. In parallel, agentic CI is enabling new approaches to orchestrating scientific investigations through adaptive decision-making, coordinated use of computational tools, and iterative interactions with simulations and experimental evidence. Together, these developments offer opportunities to move beyond isolated predictive models toward integrated, more reliable, and increasingly autonomous workflows for scientific discovery and engineering. This invited session will examine the mathematical, algorithmic, and computational foundations of scientific FMs and agentic CI, along with their integration into practical research workflows. Topics include: (i) multi-task and transfer learning across heterogeneous data and physical systems; (ii) physics-informed modeling, (iii) CI agents that coordinate predictive models, (iv) autonomous hypothesis evaluation, and (v) adaptive experiment design. Particular attention will be devoted to connecting learned representations with established computational methods, including numerical simulation, optimization, and uncertainty-aware decision-making. Contributions addressing robustness, interpretability, physical consistency, computational efficiency, and verification of data-driven scientific conclusions are especially encouraged. Relevant applications include materials science, computational mechanics, climate modeling, and energy systems.