GAMM2025

Session

S25: Machine Learning and Data Science in Applied Mathematics and Mechanics

S25

8 Apr 2025, 08:30

Lecture and Conference Centre

Conveners

S25: Machine Learning and Data Science in Applied Mathematics and Mechanics: S25.01

• Maximilian Penka
• Martin Stoll

S25: Machine Learning and Data Science in Applied Mathematics and Mechanics: S25.02

• Marius Harnisch
• Nour Hachem

S25: Machine Learning and Data Science in Applied Mathematics and Mechanics: S25.03

• Karl A. Kalina
• Hagen Holthusen

S25: Machine Learning and Data Science in Applied Mathematics and Mechanics: S25.04

• Thomas Richter
• Dirk Lorenz

S25: Machine Learning and Data Science in Applied Mathematics and Mechanics: S25.05

• Benjamin Klusemann
• Lena Dyckhoff

S25: Machine Learning and Data Science in Applied Mathematics and Mechanics: S25.06

• Valentin Würz
• Orkun Furat

S25: Machine Learning and Data Science in Applied Mathematics and Mechanics: S25.07

• Patrick Kurzeja
• Max Rosenkranz

S25: Machine Learning and Data Science in Applied Mathematics and Mechanics: S25.08

• Agnieszka Ozga
• Qi Wang

395. On uniqueness in structured model learning

Erion Morina

08/04/2025, 08:30

In this talk, we address the problem of uniqueness in learning physical laws for systems of partial differential equations (PDEs) [1]. Contrary to most existing approaches, we consider a framework of structured model learning, where existing, approximately correct physical models are augmented with components that are learned from data. Our main result is a uniqueness result that covers a...

396. Genetic column generation for adversarial multi-class classification

Maximilian Penka

08/04/2025, 08:50

Adversarial training procedures can alleviate the problem of overfitting in multi-class classification. Exploring this approach from a distributional perspective leads to robust optimization using a Wasserstein distance. Recent theoretical results showed a similarity to the multi-marginal formulation of Wasserstein-barycenter in optimal transport. Unfortunately, both problems suffer from the...

398. Kernel-based Greedy Approximation of Parametric Elliptic Boundary Value Problems

Bernard Haasdonk

08/04/2025, 09:10

We consider general linear PDE boundary value problems in the strong form on arbitrary bounded Lipschitz domains. For such problems, we recently presented a scale of meshless greedy kernel-based collocation techniques [1]. The approximation spaces are incrementally constructed by carefully collecting Riesz-representers of (derivative operator) point-evaluation functionals. The approximants are...

399. Data analysis of architected structural geometries with persistent homology

Abel Henri Guillaume Milor

08/04/2025, 09:30

Metamaterials are artificial and architected materials, offering various possible designs for achieving peculiar mechanical properties thanks to their structural arrangement. Although promising, with potentially broad applications in, e.g., medicine [1] or mobility [2], apprehending their geometry is challenging due to their complex and often disordered configuration. In this regard, applied...

400. Centralities in urban multilayer networks

Martin Stoll

08/04/2025, 09:50

In this talk we introduce some urban transport networks that we can analyze using multilayer complex networks. For these we show several multilayer centrality measure and how they can be computed efficiently.

401. Data-Driven Prediction of Dynamic Systems based on Sparse Reconstruction and Neural Networks

Lin Du

08/04/2025, 10:10

The report mainly introduces two types of system identification methods based on sparse identification and neural network frameworks, including the fast SINDy method based on model selection and dictionary learning, and the ODE-RC algorithm by combining Symplectic Integrator and Reservoir Computing. The identification and prediction performance of several types of dynamic systems have verified...

362. A Neural Operator based Microscale Surrogate Model for Multiscale Simulations of Time Dependent Materials

Dhananjeyan Jeyaraj

08/04/2025, 16:30

The behavior of materials is influenced by a variety of phenomena that take place across diverse time and length scales. Multiscale modeling strategies are required to have a better understanding of the effect of the microstructure on the macroscopic response. Numerical approaches, such as the FE2 method, consider the macro-micro interaction to predict a global response in a concurrent manner....

364. Towards data-driven inelasticity for spatial problems: A neural network-based propagator approach

Marius Harnisch

08/04/2025, 16:50

Data-driven mechanics, introduced by Kirchdoerfer and Ortiz [1], replaces traditional material models with datasets of discrete stress-strain pairs. The solution to boundary value problems is obtained by minimizing a distance between these pairs, denoted material states, and pairs of stress and strain, which fulfill equilibrium and kinematic compatibility and are termed mechanical...

365. Deep learning for non-iterative generation of optimized finite element meshes

Martin Legeland

08/04/2025, 17:10

The finite element method is a cornerstone of computational science and engineering, providing approximate solutions to boundary value problems. The solution quality is highly dependent on the underlying mesh, traditionally optimized through iterative adaptive refinement. We present a novel deep learning architecture that limits training data requirements by leveraging invariance and...

366. Mathematical and numerical analysis of the robustness of Data-Driven Identification (DDI) method

Nour Hachem

08/04/2025, 17:30

The Data-Driven Identification (DDI) method introduced by Leygue et al. (2018) aims to estimate the mechanical response of materials without relying on a predefined constitutive model. The main output of DDI is the stress field identified from full-field kinematic measurements and load cell measurements, with the intuition that similar strain values should yield similar stress values. It...

367. Coupled CANN-DEM Simulation in Solid Mechanics

Jonathan Georg Friedrich

08/04/2025, 17:50

Machine learning (ML) methods have been successfully applied to a broad variety of problems, such as structural engineering, elastostatics, heat transfer, fluid flow and material modelling [1-3]. A general, unified neural network approach as an ML-based counterpart of the finite element method without the need for analytic expressions for material laws is suggested [4]. The simulation process...

368. Comparison of Generative Learning Methods for Turbulence Modeling

Claudia Drygala

08/04/2025, 18:10

Numerical simulations of turbulent flows represent a significant challenge in fluid dynamics due to their complexity and high computational cost. High-resolution techniques such as Large Eddy Simulation (LES) are able to capture fine details of turbulent structures but are generally not computationally affordable, particularly for technologically relevant problems. Recent advances in machine...

370. On the performance and convergence of PINNs for problems in linear elasticity

Dipraj Kadlag

09/04/2025, 08:30

Artificial Neural Networks (ANNs) are algorithmic structures used in Machine Learning (ML), which is the ability to learn without being explicitly programmed. Recently, ANNs have been used to solve boundary value problems as an alternative to traditional numerical methods in computational mechanics. Physics-informed Neural Networks (PINNs) are the most promising type of ANNs in this context....

371. Model discovery and challenges using inelastic Constitutive Artificial Neural Networks (iCANN s) at finite strains

Hagen Holthusen

09/04/2025, 08:50

Centuries of physics have established thermodynamically sound laws for solids in continuum mechanics, forming the basis for hyperelastic material models. However, these models often struggle with diverse materials, where pre-selecting a model to fit experimental data risks inadequacy. This challenge intensifies when modeling not just the (elastic) stress-strain relationship but also inelastic...

372. Hard-constraining techniques and architectures in physics-informed neural networks for silicidation simulations

Christopher Straub

09/04/2025, 09:10

For the optimization of semiconductor components, a detailed understanding of low-resistance ohmic contacts between metal and semiconductor is essential. This process is known as silicidation. On a macroscopic level, it can be described mathematically by coupled reaction-diffusion equations. A promising approach to solving such systems of non-linear differential equations is the use of...

373. Anisotropic hyperelasticity meets physics-augmented neural networks

Karl A. Kalina

09/04/2025, 09:30

The formulation and calibration of constitutive models is still a challenging task for materials which exhibit complex nonlinear elastic or inelastic behavior. For this reason, data-driven methods and in particular the use of neural networks (NNs) have become increasingly popular in recent years. NN-based approaches that fulfill essential physical conditions a priori, often referred to as...

374. Application of Deep Learning Methods to Simulate the Behaviour of Soft Tissue Materials in Biomechanics

Agon Mustafa

09/04/2025, 09:50

The accurate modeling of soft tissue material behavior remains a challenging task in biomechanics due to its complex, non-linear, and anisotropic characteristics. Traditional methods, such as Finite Element Methods (FEM), while reliable, demand significant computational resources and expert knowledge for implementing physical laws. Machine Learning (ML) techniques, particularly Neural Networks...

375. Learning regularizers - bilevel opitimization or unrolling?

Dirk Lorenz

09/04/2025, 16:30

In this talk we will consider the problem of learning a convex regularizer from a theoretical perspective. In general, learning of variational methods can be done by bilevel optimization where the variational problem is the lower level problem and the upper level problem minimizes over some parameter of the lower level problem. However, this is usually too difficult in practice and a popular...

376. Time-adaptive SympNets for separable Hamiltonian systems

Konrad Janik

09/04/2025, 16:50

Measurement data is often sampled irregularly i.e. not on equidistant time grids. This is also true for Hamiltonian systems. However, existing machine learning methods, which learn symplectic integrators, such as SympNets [2] and HénonNets [1] still require training data generated by fixed step sizes. To learn time-adaptive symplectic integrators, an extension to SympNets, which we call...

377. Sparse full-order model inference for incompressible fluid dynamics

Süleyman Yıldız

09/04/2025, 17:10

Data-driven modeling represents a fundamental technique in the analysis and design of complex dynamical systems. However, the direct application of machine learning algorithms is not an appropriate methodology for high-dimensional systems. A common approach to address this challenge is to utilize dimension reduction techniques, which inherently introduce additional errors in surrogate systems....

379. Investigation of hydrogel structure parameters in the Flory-Rehner model with data-driven approaches

Yawen Wang

09/04/2025, 17:30

Hydrogels are highly versatile and environmentally responsive materials, designed through specific chemical composition and synthesis methods. The solvent absorption capability in hydrogels can be either enhanced or inhibited by various environmental stimuli, such as temperature, pH, light, or specific ions and molecules. This responsiveness makes hydrogels ideal materials for developing smart...

380. Optimal data selection for learning differential equations

Medard Govoeyi

09/04/2025, 17:50

Training a neural network to learn differential equations requires a significant amount of data. Collecting the data set is sometimes difficult or expensive. When we have a limited budget, it is important to optimize the process of selecting the data we should use to train the neural network. We present two methods for selecting an optimal data set. First, we present a way to select the...

381. An Adaptive Random Fourier Features approach applied to learning Stochastic Differential Equations

Aku Kammonen

09/04/2025, 18:10

We present a novel training algorithm based on adaptive random Fourier features sampling [1] for the learning of the drift and the diffusion components of stochastic differential equations (SDEs). Specifically, we considerItˆo diffusion processes and a loss function [2] derived from the Euler-Maruyama (EM) integration scheme. Promising results, improving both the loss and the training time...

382. A spatiotemporal deep learning framework for prediction of crack dynamics in heterogeneous solids: efficient mapping of concrete microstructures to its fracture properties

Rasoul Najafi

10/04/2025, 08:30

A spatiotemporal deep learning framework is proposed that is capable of two-dimensional full-field prediction of fracture in concrete mesostructures. This framework not only predicts fractures but also captures the entire history of the fracture process, from the crack initiation in the interfacial transition zone (ITZ) to the subsequent propagation of the cracks in the mortar matrix....

384. A baseline study on the potential of combining Machine Learning and dynamic substructuring

Annika Hayn

10/04/2025, 08:50

The integration of hybrid machine learning (ML) models and substructuring methods holds significant potential for advancing dynamic analysis in complex systems. This approach aims to reduce the reliability on extensive physical testing by leveraging data-driven techniques to enhance model accuracy and efficiency.

This work presents a baseline study on integrating machine learning techniques...

385. Physics-Informed Recurrent Neural Networks for Predicting Elasto-Plastic Behavior in Hierarchical Finite Element Modeling

Lena Dyckhoff

10/04/2025, 09:10

Modeling hierarchical nanoporous metals, characterized by complex ligament networks across multiple length scales, is computationally demanding. Multiaxial stresses occur in higher hierarchy ligaments, adding to the complexity of the problem and requiring an understanding of multiaxial material behavior. For finite element (FE) modeling, we separate the hierarchical nanoporous structure into...

408. Denoising Diffusion Model with Pixel Adaptive Convolutions for Sheet Metal Forming Analysis

Syed Sarim Ali

10/04/2025, 09:30

Traditional tool development processes in mechanical forming, especially for pressing tools, are often limited by time-consuming trial-and-error cycles that rely heavily on expert knowledge. These cycles can create bottlenecks in production and increase costs. Machine learning can be imployed here to greatly speed up these processes by using advanced models. In this regard, a Denoising...

409. Hybrid modeling via machine learning corrections of friction surfacing process simulations towards experimental measurements

Benjamin Klusemann

10/04/2025, 09:50

For machine learning regression tasks, the combination of physics-based models with data-driven models can enhance prediction performance, data efficiency and physical consistency due to the specific use of prior knowledge in the form of validated physical laws. Because a data-driven correction is assumed to be less complex when fundamental relationships are already represented in the...

410. Hybrid finite element/neural network solver

Uladzislau Kapustsin

10/04/2025, 10:10

In this talk, we present a hybrid finite element/neural network method for correcting coarse finite element solutions of partial differential equations. The method works by computing fine-scale corrections for the coarse solutions using a neural network trained offline. A neural network takes as input the local values of the coarse solution, as well as other local information such as values of...

411. Machine Learning and Stochastic 3D Modeling for Reconstructing 3D Grain Maps from 2D EBSD Data

Orkun Furat

10/04/2025, 14:00

Understanding the microstructures of materials has become increasingly crucial for studying their structure-property relationships, i.e., the influence of structural descriptors on macroscopic material properties. In materials with polycrystalline microstructures, the 3D grain architecture significantly influences mechanical properties. Imaging techniques like diffraction contrast tomography...

413. Comparison of classical ANN architecture and neural operator approach to approximate 2-point probability functions

Luzie Schmollack

10/04/2025, 14:20

To approximate n-point probability functions, different techniques are feasible. Machine learning has proven to be very effective in a wide variety of appplications, such as statistical homogenization, where n-point probability functions play a significant role.
To specifically extract 2-point probability functions from isotropic two-phase microstructures, we achieved good results by...

414. Data-efficient inverse design of elastic spinodoid metamaterials

Max Rosenkranz

10/04/2025, 14:40

Mechanical metamaterials or architected materials are becoming increasingly popular due to rapid developments in additive manufacturing. These architected materials exhibit mechanical properties that significantly differ from those of their base material and offer a high degree of customizability. This is enabled by a rationally designed spatial structure of the base material on the mesoscale,...

415. A Variational Autoencoder Approach to Structure-Property Mapping in Porous Metamaterials

Yousef Heider

10/04/2025, 15:00

This study presents a deep learning framework for the inverse reconstruction of open-cell porous metamaterials, targeting specific hydraulic properties such as porosity and intrinsic permeability. Utilizing a combination of synthetic 3D porous microstructures and CT-scan-based representative volume elements (RVEs) of porous open-foam specimens, the framework leverages a property-variational...

416. A holistic AI approach from model creation to model evaluation in engineering applications

Martin Drieschner

10/04/2025, 15:20

Numerical investigations of real engineering problems have become indispensable due to the continuously increasing complexity of the issues at hand. Especially when analytical solution methods reach their limits and experimental investigations are associated with high effort and costs, simulation offers a pragmatic and promising approach. The development of the finite element method, which was...

418. Inverse Material Design using Deep Reinforcement Learning and Homogenization

Valentin Würz

10/04/2025, 15:40

This study presents an approach to solving an inverse problem through the application of Deep Reinforcement Learning (DRL) coupled with homogenization. The underlying objective is to determine the micro-structural parameters of a composite material, including particle radius, Young’s moduli and Poisson’s ratios in order to achieve a specific target bulk modulus at the macro-scale using DRL....

419. Neural networks for isotropic polyconvex hyperelastic energies, Part 1: Analysis of existing approaches and improved networks

Patrick Kurzeja

10/04/2025, 16:30

Hyperelastic material models are frequently used in the engineering sciences. Application examples include biomechanics and the modeling of the finite elastoplasticity of metallic alloys. Given the rising importance of machine learning approaches, hyperelastic models have also been approximated successfully by neural networks, see [1]. In the present work, the focus is on such approximations...

420. Neural networks for isotropic polyconvex hyperelastic energies, Part 2: A convex neural network framework with universal approximation capability

Gian-Luca Geuken

10/04/2025, 16:50

Recent developments have shown that machine learning methods, such as neural networks, can significantly benefit from incorporating physical knowledge [2]. However, a correct and non-restrictive implementation remains a major challenge [1,3,4]. Classic invariants of the right Cauchy-Green tensor, for instance, are a sufficient, yet overly restrictive choice for the combination of objectivity,...

421. Multiscale Modelling through Physics-constrained Voigt-Reuss networks

Sanath Keshav

10/04/2025, 17:10

The development of new materials and the optimization of their properties are critical challenges in the field of materials science, particularly within the framework of multiscale modeling and homogenization. Traditional data-driven methods, while effective, often fall short in accurately predicting the complex behavior of microstructures under diverse loading conditions, especially when...

424. VENI, VINDy, VICI: A Generative Approach to Reduced-Order Modeling with Embedded Uncertainty Quantification

Jonas Kneifl

10/04/2025, 17:30

A wide variety of complex phenomena in engineering and science require the solution of expensive, high-dimensional systems of partial differential equations (PDEs). In order to overcome the computational burden and accelerate the calculations, reduced order models (ROMs) have been developed. Non-intrusive methods have been shown to be effective in scenarios involving experimental measurements...

425. Certification of physics-informed neural networks for the solution of partial differential equations

Lewin Ernst

10/04/2025, 17:50

Partial differential equations (PDEs) arise to describe linear and nonlinear physical phenomena. In mechanical engineering, there is a particular need for new black box solvers of PDEs due to ever shorter product development times. The recent success in solving various PDEs with neural networks, particularly with physics-informed NNs (PINNs) suggests that they are a natural candidate for those...

426. Convergence and Implicit Bias: Analyzing Diagonal Linear Networks with Gradient Descent

Wiebke Bartolomaeus

11/04/2025, 08:30

In deep learning, one often operates in a (highly) over parametrized regime. Meaning we have significantly more trainable parameters than available training data. Nevertheless, experiments show that the generalization error after training with (stochastic) gradient descent is still small, while one would expect over fitting, i.e. small training error and relatively large test error.

This...

427. A multilevel proximal trust-region method for nonsmooth optimization with applications to scientific machine learning

Qi Wang

11/04/2025, 08:50

Many applications in PDE-constrained optimization and data science require minimizing the sum of smooth and nonsmooth functions. For example, training neural networks may require minimizing a mean squared error plus an l₁ regularization to induce sparsity in the weights. In this talk, we introduce a multilevel proximal trust-region methods to minimize the sum of a nonconvex, smooth and convex,...

428. Challenges and opportunities of the German Transplant Register using computer models and artificial intelligence

Anton Schnurpel

11/04/2025, 09:10

Transplant registries are of paramount importance to the advancement of transplantation medicine, as they facilitate the centralised and standardised collection of medically relevant data on organ donors, recipients, and living donors. By systematically consolidating this information, registries provide a robust data foundation that enhances quality and transparency throughout the...

429. Convergence of gradient based training for linear Graph Neural Networks

Dhiraj Patel

11/04/2025, 09:30

Graph Neural Networks (GNNs) are powerful tools for addressing learning problems on graph structures, with a wide range of applications in molecular biology and social networks. Nonetheless, the theoretical principles underlying their empirical performance are not well understood. This work provides a convergence analysis of gradient dynamics in linear GNN training. We show that the gradient...

431. Autoregressive and Generative Learning of Time Dynamics in Ergodic Systems

Edmund Ross

11/04/2025, 09:50

This paper presents theoretical and empirical results demonstrating the effectiveness of "Tokenization" in capturing the physical operator of an ergodic flow, a technique used in multiple long video machine learning architectures, in particular in NVIDIA's LongVideoGAN. Complementing the theory, we present novel experimental results on canonical problems, ranging from the wave and heat...

432. Application range of a mathematical model computing distributions of random impulse excitations

Natalia Frankowska, Marek Sulewski

11/04/2025, 10:10

The presentation we will describe the mathematical model of an oscillator with damping, whose vibrations were forced by a random series of impulses. Under appropriate assumptions regarding random variables, in the model, the vibrations of the system become a process which, in the limit as time tends to infinity, is stationary and ergodic. For value of the impulses, which are independent...

422. Data-efficient inverse design of elastic spinodoid metamaterials

Max Rosenkranz