Scientific Machine Learning and Numerical Methods – Autumn School

Biography:
Andrea Walther studied business mathematics at the Universität Bayreuth and earned her PhD from TU Dresden in 1999, where she also received her habilitation in 2008. In 2009, she became a professor of Mathematics and its Applications at the Universität Paderborn. Since October 2019, Andrea Walther has been a MATH+ Professor of Mathematical Optimization at Humboldt-Universität zu Berlin.

Her research interests lie in the field of nonlinear optimization, with a focus on adjoint-based optimization and non-smooth optimization, as well as algorithmic differentiation.

She is the Chair of the Cluster of Excellence MATH+, Interim Vice President of the Zuse Institute Berlin, and a member of the board of the International Association of Applied Mathematics and Mechanics (GAMM).

Lecture: The theory behind backpropagation
Backpropagation is also known as the reverse mode of algorithmic differentiation. In this lecture, we will discuss the existing complexity results for this approach and highlight its features that can be exploited in a machine learning setting. There will also be some hands-on exercises.

Photo: © Kay Herschelmann / MATH+

Biography:
Andrew Stuart is Bren Professor of Computing and Mathematical Sciences at the California Institute of Technology.

After postdoctoral research in applied mathematics at Oxford and MIT, Stuart held permanent positions at the University of Bath (1989–1992), in mathematics, at Stanford University (1991–1999), in engineering, and at Warwick University (1999–2016), in mathematics. He is currently Bren Professor of Computing and Mathematical Sciences at the California Institute of Technology. In 2009 he was elected an inaugural fellow of SIAM, and in 2020 he was elected a Fellow of the Royal Society. He was named a Vannevar Bush Faculty Fellow, by the Department of Defense, in 2022.

Lectures: Inverse Problems, Data Assimilation and Machine Learning.
These lectures overview the use of machine learning as a tool to find improved inverse problem and data assimilation methods.

1. Machine Learning Tools
2. Learning State Estimators
3. Learning Probabilistic Estimators
4. Practical session

Biography:
Ben Moseley is an expert in scientific machine learning, with a focus on developing scalable algorithms that can solve simulation, inverse, and model discovery problems in Earth Science, space science, and other scientific disciplines. He leads the Scalable Scientific Machine Learning Lab at Imperial, where his research spans hybrid numerical-ML methods, physics-informed neural networks, foundation models for science, and physics-based computer vision methods. He has applied these techniques across seismic simulation, planetary satellite image interpretation, elephant conservation, population balance modelling, multiscale porous fluid flow, and the extension of quantum theories. He holds a Lecturer position at the Department of Earth Science and Engineering at Imperial and an Eric and Wendy Schmidt AI in Science Fellowship at the Imperial I-X Center for AI in Science.

Lecture: Improving the efficiency of physics-informed neural networks with domain decomposition, linear algebra, and JAX
This lecture explores how to design efficient physics-informed neural networks (PINNs). Whilst PINNs are a promising approach for solving problems related to differential equations, they are often hindered by the computational cost of gradient descent and their poor convergence on multi-scale problems. In this lecture, we will discuss how leveraging domain decomposition, linear algebra, and the JAX framework can improve their accuracy and efficiency. First, we will give a foundational overview of scientific machine learning, PINNs, and JAX, followed by a hands-on session focused on training PINNs and improving their efficiency using domain decomposition, NLA, and JAX. The goal of the lecture is to offer a modern perspective on scalable scientific machine learning.

Biography:
Chris Budd OBE, is based at the University of Bath, where he is Professor of Applied Mathematics. He is also Professor of Maths at the Royal Institution and Gresham Professor of Geometry. He has also been the Education Officer of the London Mathematical Society, and Vice-President of the Institute of Mathematics and its Applications.

Chris is the director of a large programme of work between Bath, UCL, and Cambridge working on Scientific Machine Learning. This project is working on the mathematical underpinning of machine learning, aiming to provide rigorous mathematical guarantees of the performance of machine learning algorithms. See. https://maths4dl.ac.uk/

Chris also has strong interests in the practical applications of maths to real world problems, and has worked in many areas, including food distribution and cooking, climate change, weather forecasting, electricity supply, telecommunications, aerospace and saving the whales. His algorithms are now incorporated into the Met Office operational weather forecasting code where they have made a significant difference to their accuracy. He is also interested in the recreational side of maths, including magic, voting, origami, and folk dancing. During the pandemic he worked flat out to apply mathematical modelling methods to help in the fight against COVD-19.

The advancement of the public understanding of and engagement in science and mathematics has been a central element of his career. He has been involved in developing successful programmes with young people through his positions at the Royal Institution and the Institute of Mathematics and its Applications. One of the most significant of these projects is the Bath Taps into Science Festival, a major hands-on science festival which has won many national prizes since its establishment in 2001. He was awarded an OBE in 2015 for services to science and mathematics education. When not working he likes walking in the mountains with his wife and dog Monty.

Lectures:

1. Approximation using neural nets
2. PINNs. Applications and convergence
3. Deep Ritz methods applications and convergence
4. Neural operators
5. Open challenges

The course will be a mixture of theory, algorithm development, and applications to problems such as weather forecasting and imaging.

Biography:
Gabriele Steidl received her PhD and Habilitation in Mathematics from the University of Rostock (Germany) and held positions as assistant and full professor at the TU Darmstadt, the University of Mannheim and the TU Kaiserslautern. Since 2020, she is Professor at the Department of Mathematics at the TU Berlin.
She worked as consultant of the Fraunhofer Institute for Industrial Mathematics and is in the Scientific Advisory Board of the Helmholtz Imaging Platform of the Helmholtz Association. She is a SIAM fellow (2022) and Editor-in-Chief of the SIAM Journal on Imaging Sciences. She has broad interests in applied mathematics including computational harmonic analysis, continuous optimization and machine learning.

Lecture: Markov Kernels, Stochastic Processes and Transport Plans
Among generative neural models, flow matching techniques stand out for their simple applicability and good scaling properties. Here, velocity fields of curves connecting a simple latent and a target distribution are learned. Then the corresponding ordinary differential equation can be used to sample from a target distribution, starting in samples from the latent one.
We review different techniques to learn the velocity fields of absolutely continuous curves in the Wasserstein geometry and show how flow matching can be used for solving Bayesian inverse problems.

Biography:
Ricardo Baptista is an incoming Assistant Professor at the University of Toronto in the Department of Statistical Sciences. The core focus of his work is on developing the methodological foundations of probabilistic modeling and inference. He is broadly interested in using machine learning to better understand and improve the accuracy of generative models for applications in science and engineering. Before Toronto, Ricardo held positions as a Postdoctoral Scientist at Amazon and as a von Karman Instructor at Caltech. He received his PhD from MIT, where he was a member of the Uncertainty Quantification group.

09:00 - 09:30 Registration / Welcome

09:00 - 11:00 Andrew Stuart Lecture 1

11:00 - 11:30 Coffee/tea break

11:30 - 13:00 Andrew Stuart Lecture 2

13:00 - 14:00 Vegetarian Lunch

14:00 - 15:30 Andrew Stuart Lecture 3

15:30 - 16:00 Coffee/tea break

16:00 - 17:30 Andrew Stuart Practical session

17:30 Reception & Networking

09:00 - 10:30 Chris Budd Lecture 1

10:30 - 11:00 Coffee/tea break

11:00 - 12:30 Chris Budd Lecture 2

12:30 - 14:00 Vegetarian Lunch

14:00 - 15:30 Chris Budd Lecture 3

15:30 - 16:00 Coffee/tea break

16:00 - 17:30 Chris Budd Practical session

18:00 Social Dinner at CWI

09:00 - 10:30 Ben Moseley Lecture 1

10:30 - 11:00 Coffee/tea break

11:00 - 12:30 Ben Moseley Lecture 2

12:30 - 14:00 Vegetarian Lunch

14:00 - 15:30 Ben Moseley Lecture 3

15:30 - 16:00 Coffee/tea break

16:00 - 17:30 Ben Moseley Practical session

09:00 - 10:30 Gabriele Steidl Lecture 1

10:30 - 11:00 Coffee/tea break

11:00 - 12:30 Gabriele Steidl Lecture 2

12:30 - 14:00 Vegetarian Lunch

14:00 - 15:30 Gabriele Steidl Lecture 3

15:30 - 16:00 Coffee/tea break

16:00 - 17:30 Gabriele Steidl Practical session

09:00 - 10:30 Andrea Walther Lecture 1

10:30 - 11:00 Coffee/tea break

11:00 - 12:30 Andrea Walther Lecture 2

12:30 - 14:00 Vegetarian Lunch

14:00 - 15:30 Andrea Walther Lecture 3

15:30 - 16:00 Closing session

The conference will be held in the Turing hall 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.