Workshop on industrial applications of numerical analysis and machine learning

Benjamin Peherstorfer is Associate Professor at Courant Institute of Mathematical Sciences. Until 2016, he was a Postdoctoral Associate in the Aerospace Computational Design Laboratory (ACDL) at the Massachusetts Institute of Technology (MIT), working with Professor Karen Willcox. He received B.S., M.S., and Ph.D. degrees from the Technical University of Munich (Germany) in 2008, 2010, and 2013, respectively. His Ph.D. thesis was recognized with the Heinz-Schwaertzel prize, which is jointly awarded by three German universities to an outstanding Ph.D. thesis in computer science. Benjamin was selected for a Department of Energy (DoE) Early Career Award in the Applied Mathematics Program in 2018 and for an Air Force Young Investigator Programme (YIP) award in Computational Mathematics in 2020. In 2021, Benjamin received a National Science Foundation (NSF) CAREER award in Computational Mathematics. His research focuses on computational methods for data- and compute-intensive science and engineering applications, including scientific machine learning, mathematics of data science, model reduction, and computational statistics.

Elena Celledoni is a professor at the Department of Mathematical Sciences at the Norwegian University of Science and Technology, Trondheim, Norway. She has a Ph.D in computational mathematics from the University of Padua, Italy. She held post doc positions at the University of Cambridge, UK, at the Mathematical Sciences Research Institute, Berkeley, CA.

Her research field is numerical analysis structure preserving algorithms for differential equations and geometric numerical integration. More recently she has also been working on structure preservation in neural networks, and geometric methods for shape analysis.

She is the vice President of the European Consortium of Mathematics in Industry and the secretary of the Society of Foundations of Computational Mathematics. She has served as the co-chair for research at the Department of Mathematical Sciences at NTNU.

Jakob Sauer Jørgensen is a Senior Researcher at the Department of Applied Mathematics and Computer Science at the Technical University of Denmark (DTU). His research lies in mathematical methods, algorithms and software for computational imaging, with particular emphasis on image reconstruction and uncertainty quantification for incomplete-data and multi-channel/modality X-ray and neutron computed tomography. He received his PhD in applied mathematics from DTU in 2013. From 2015 to 2018 he was a postdoctoral researcher at The University of Manchester, Departments of Mathematics and Materials and from 2018 a University of Manchester Presidential Fellow (tenure-track assistant professor). In 2020 he moved to DTU as a Senior Researcher (associate professor). Scientific software for computational imaging is a focus area and he is one of the founders behind the Python packages Core Imaging Library (CIL) and CUQIpy - Computational Uncertainty Quantification for Inverse problems in python.

Marcelo Pereyra's research advances the statistical foundations of quantitative and scientific imaging. Over the past 15 years, he has made important contributions to Bayesian imaging sciences and developed significant connections between the statistical, variational and machine learning approaches to imaging. He is particularly interested in robust uncertainty quantification in imaging inverse problems, automatic calibration and verification of statistical image models, scalable Bayesian computation algorithms derived from stochastic diffusion processes, and applications of imaging with high social or environmental value.

Nicolas Boullé is an Assistant Professor in Applied Mathematics at Imperial College London. He obtained a PhD in numerical analysis at the University of Oxford in 2022 and was a postdoc at the University of Cambridge from 2022-2024. His research focuses on the intersection between numerical analysis and deep learning, with a specific emphasis on scientific machine learning and learning physical models from data, particularly in the context of partial differential equations learning. He was awarded a Leslie Fox Prize in 2021 and a SIAM Best Paper Prize in Linear Algebra in 2024 for his work on operator learning .

Andreas Rosskopf studied Applied Mathematics with a focus on Numerical Simulation in Erlangen, Germany. Since 2012 he's with Fraunhofer IISB in Erlangen; in 2018 he founded the working group "AI-augmented Simulation “ combing AI and numerical approaches for the simulation and optimization of power electronic devices and systems. Since 2023 he's head of the "Modeling and Artificial Intelligence" department of the Fraunhofer IISB designing digital solutions in the field of power electronics, Technology Computer-Aided Design and lithography.

Marta D'Elia is the Director of AI and ModSim at Atomic Machines and an Adjunct Professor at the Institute for Computational and Mathematical Engineering at Stanford University. She previously worked at Pasteur Labs, Meta, and Sandia National Laboratories as a Principal Scientist and Tech Lead. She holds a PhD in Applied Mathematics and master's and bachelor's degrees in Mathematical Engineering. Her work deals with development and analysis of machine-learning models and optimal design and control for manufacturing applications, especially at the micro scale. She is an expert in multiscale modeling and simulation, optimal control, and scientific machine learning. She is an Associate Editor of SIAM and Nature journals, a member of the SIAM industry committee, and the Vice Chair of the SIAM Northern California section.

Martin Verlaan is senior specialist in Mathematics/Oceanography at Deltares, and a professor in group of Mathematical Physics at the Faculty of Electrical Engineering, Mathematics and Computer Science of the Delft University of Technology (TU Delft). He is also one of the team leaders for the Dutch storm surge warning service (SVSD), which is the responsible authority in The Netherlands for issuing warnings in the event of a severe storm.

For several years he has been responsible for the coordination of research and development in the field of data-assimilation and for the scientific coordination and quality control of projects related to storm surge forecasting, marine operational forecasting, Kalman filtering, automated calibration, design of monitoring networks, operational databases and tidal prediction.

In recent years, he has focused on advancing innovations in scientific machine learning (SciML), initiating and leading multiple research projects as collaboration of Deltares, TU Delft, the Dutch Ministry of Infrastructure and Water Management (Rijkswaterstaat), the Royal Netherlands Meteorological Institute (KNMI), and others. His work spans topics such as surrogate modeling with deep learning methods, hybrid modelling, generative AI, building reanalysis dataset for AI training, etc.

Tiago Botari is a computational physicist working as a Senior Machine Learning Researcher at ASML, developing physics-informed AI for fast image processing in metrology and inspection within the semiconductor industry. He earned his PhD in Physics from the University of Campinas (UNICAMP) and conducted postdoctoral research at UC Berkeley, TU Berlin, and the University of São Paulo. His interdisciplinary work combines physics, computer science, and engineering to tackle complex industrial challenges.

Computer-aided design (CAD) tools are ubiquitous in numerous engineering disciplines, allowing the design of complex, free-form geometries. Neural solvers such as physics-informed neural networks (PINNs) face significant challenges when applied to CAD domains, especially multi-path ones. Common problems include: solution conformity along patch interfaces; correct imposition of boundary conditions; and data sampling and normalization. PINN methods inspired by isogeometric analysis (IGA) have emerged in recent years as possible solutions, however, they are mostly confined to simple, single-patch domains. In this talk, we will present a framework based on variational PINNs and IGA for solving PDEs on complex, multi-patch CAD geometries. Applications include highly non-trivial problem settings, such as electromagnetic and solid mechanics simulations in 2D and 3D.

Covariance information is commonly used in machine learning to reveal data interdependencies such as network topology inference (e.g., graphical lasso) and dimensionality reduction (e.g., Principal Component Analysis (PCA)). However, such information is often only the first step in a machine learning pipeline that is performed separately from the task. Because of finite-data estimation errors, we end up working with a sample covariance matrix that leads to uncertainties in its spectrum. For example, PCA is notoriously unstable to covariance estimation errors, i.e., small data perturbations might lead to large changes in principal directions. To address this, coVariance Neural Networks (VNNs) were introduced. These networks perform graph convolutions on the sample covariance matrix, an operation that, similarly to PCA, modulates the data principal components, but with enhanced representation power and greater stability against covariance estimation errors. However, in sparse, high-dimensional settings with limited data, covariance estimation is particularly difficult, which hinders VNNs’ performance despite their stability. Sparse VNNs overcome this by using theoretically grounded covariance sparsification, which improves stability, reduces the impact of spurious correlations on performance and improves computation and memory efficiency. The success of VNNs motivates their extension to different settings. SpatioTemporal VNNs, for instance, process multivariate time series by applying graph convolutions on the online estimated covariance and temporal convolutions over time, achieving stability to estimation errors in both covariance and model parameters due to streaming data.

Finally, VNNs’ stability promotes fairness in datasets with poorly represented groups. Building on this, Fair VNNs leverage equitable covariance estimates and fairness penalties in the loss function to ensure a more balanced treatment of these groups.

In phase retrieval and similar inverse problems, the stability of a solution under different noise levels is crucial for practical applications. To address instabilities, one often employs regularization techniques. However, Tikhonov and other conventional regularizers tend to smooth out high-frequency components, which can be problematic when trying to capture detailed features of a signal. Recently, generative models have emerged as a powerful alternative, allowing the incorporation of prior information on the signal into the problem and thereby enhancing reconstruction stability. The rationale here is that the conditioning of the composition of the generative model and the measurement map is more favorable than that of the measurement map alone, albeit at the cost of introducing a bias in the reconstruction. It has indeed been observed in numerical experiments that for high signal-to-noise ratio, the conventional reconstruction model performs better, while in the case of low signal-to-noise ratio, the generative reconstruction model outperforms it. In this talk, we will explore and compare the reconstruction properties of classical and generative inverse problem formulations and propose a new unified reconstruction approach that mitigates overfitting to the generative model for varying noise levels.

The talk is based on the joint work with Selin Aslan, Tristan van Leeuwen, and Allard Mosk.

In collaboration with Nazanin Abedini (VU Amsterdam) and Jana de Wiljes (U. Of Ilmenau).

Ensemble Kalman filtering is widely used in many applications, and it can be analyzed via the continuous ensemble Kalman-Bucy framework. The corresponding ensemble Kalman-Bucy filter exhibits long-time stability and accuracy with fully observed state, as has been shown in Wiljes and Tong (2020). In this work, under some condition we show similar results but with partially observed state. Furthermore, we claim that this condition needs to be satisfied with high probability in order to provide filter stability, consequently leading to randomized observations.

Abstract: Machine learning offers a powerful alternative to traditional simulation methods, particularly for complex systems where symbolic models are lacking or computationally prohibitive. This talk explores how incorporating geometric symmetries—such as E(n) equivariance, permutation, and scale invariance—into deep learning models enables building efficient simulators for graph dynamical systems. By leveraging the inherent geometric structure of data, these models can achieve more efficient learning from high-dimensional data with significantly lower computational complexity than traditional methods.

We will discuss the successful application of such geometric deep learning approaches for simulating dynamic trajectories in diverse domains, including pedestrian dynamics, meta-material homogenization, and bubbly flows.

09:30 - 10:00 Welcome and registration

10:00 - 11:00 Plenary (N. Boullé)

11:00 - 11:30 Break

11:30 - 12:00 Vlado Menkovski - Deep generative models for simulation of geometric trajectories

12:00 - 12:30 Svetlana Dubinkina - Data assimilation with randomized observations

12:30 - 14:00 Lunch

14:00 - 15:00 TBA

15:00 - 15:30 Break

15:30 - 16:30 Plenary (B. Peherstorfer)

17:00 - 19:00 Poster session with drinks

09:30 -10:30 Plenary (J. Jørgensen)

10:30 - 11:00 Break

11:00 - 12:30 Problem pitches

12:30 - 14:00 Lunch

14:00 - 15:00 Plenary (M. d’Elia)

15:00 - 17:00 Break out sessions

17:00 - 18:00 Panel session

18:00 Dinner at CWI

09:30 - 10:30 Plenary (M. Pereyra)

10:30 - 11:00 Break

11:00 -11:30 Palina Salanevich - PtyGenography: generative priors as regularizers for the phase retrieval problem

11:30 - 12:00 Dimitris Loukrezis - Neural solvers for PDEs on CAD geometries

12:00 - 13:00 Plenary (E. Celledoni)

13:00 Closure / take away lunch

The conference will be held at the Congress Centre of Amsterdam Science Park, next to Centrum Wiskunde & Informatica (CWI).

Address: Science Park 125, 1098 XG Amsterdam.

Google Maps Congress Centre, Science Park 125

Please be aware that hotel prices in Amsterdam can be quite steep. We strongly recommend all participants to secure their hotel reservations as early as possible!

Hotel Recommendations:

• Generator Hostel
• MEININGER Hotel (Amsterdam Amstel)
• Hotel Casa
• The Manor Amsterdam
• The Lancaster Hotel Amsterdam

From these hotels, the venue can be reached in 15-30 minutes with public transport. In all public transportation, you can check in and out with a Mastercard or Visa contactless credit card and also with Apple Pay and Google Wallet.