Pflichtseminar Scientific Machine Learning winter term 2023/2024
- Mondays 14:00 - 16:00
- SR 10 5th floor Mathematikon
Computational scientific discovery is at an interesting juncture. While we have mechanistic models of lots of different scientific phenomena, such as the famous Maxwell and Navier-Stokes equations, and abundant data being generated from experiments - our computational capabilities appear unable to keep up. Often, we deal with problems that are too large or too complex for realistic simulations. Besides that, modern scientific problems are often hierarchical, multi-scale, involve mutli-physics approaches and are very stiff. These challenges require thorough work on suitable algorithms, numerically calculating gradients as well as getting code to run on GPUs and supercomputers. A promising way for progress in this field is offered by a combination of scientific computing and machine learning, by combining mathematical models with data based reasoning often referred to as scientific machine learning (SciML).While traditional deep learning methodologies have had difficulties with scientific issues like stiffness, interpretability, and enforcing physical constraints, SciML presents new algorithms which overcome these problems by combining classic machine learning techniques, differential equations, innovative architectures and algorithms while still preserving the data-driven automatic learning features of modern deep learning. All these new methods draw on tools from both machine learning and scientific computing to develop new methods for scalable, domain-aware, robust, reliable, and interpretable learning and data analysis, and will be critical in driving the next wave of data-driven scientific discovery in the physical and engineering sciences.
In this seminar we will deal with these new approaches and discuss tools such as physics-informed neural networks, universal differential equations, neural surrogate models or symbolic regression. Of particular interest for SciML are topics such as uncertainty quantification, interpretability/explainability, model discovery, model fitting or inverse modeling. This seminar addresses interested master students with a background in or basic knowledge of the principles of machine learning and computational physics.
- Universal differential equation (foundation ResNets)
- Physics Informed NNs
- Invertible NNs, bayesian NNs
- Graph NNs and equivariant NNs
- normalizing flows
- diffusion models
Literature and topics will be discussed during the first session.
The grades are determined by the quality of the 45 minutes long scientifc talk, the written report (4 pages) and the cooperation during the entire seminar.