General Information
Speaker: Dr. Qian Huang, University of Stuttgart, Institute of Applied Analysis and Numerical Simulation (IANS)
Dates: Find more information below
Location: University of Stuttgart, Pfaffenwaldrig 57, seminar room of the IANS PWR57 room 7.122 and online
Registration: via C@MPUS or if not possible contact us via mail: graduiertenschule@simtech.uni-stuttgart.de
More Information
Lecture 1: 27 Oct, 25 (Monday) 9:45 -- 11:15
Lecture 2: 04 Nov, 25 (Tuesday) 16:00 -- 17:30
Lecture 3: 17 Nov, 25 (Monday) 9:45 -- 11:15
Lecture 4: 25 Nov, 25 (Tuesday) 9:45 -- 11:15 (online)
Lecture 5: 01 Dec, 25 (Monday) 9:45 -- 11:15
Lecture 6: 11 Dec, 25 (Thursday) 16:00 -- 17:30 (online)
Lecture 7: 15 Dec, 25 (Monday) 9:45 -- 11:15
Seminar 1: 12 Jan, 26 (Monday) 9:45 -- 11:15
Seminar 2: 13 Jan, 26 (Tuesday) 16:00 -- 17:30
Seminar 3: 20 Jan, 26 (Tuesday) 16:00 -- 17:30 (optional)
Online meetings will be informed later. Any changes in time or location will be informed by emails and on the ILIAS page.
The lectures (except the 2 online ones) will be held at the seminar room of IANS/University of Stuttgart (Pfaffenwaldring 57, Room: 7.122).
This course is organised by the GS SimTech and SFB 1313
You can find the ILIAS page (https://ilias3.uni-stuttgart.de/go/grp/4233577) under “Natural Sciences and Mathematics / Mathematics / Arbeitsgruppen” and should be able to register directly.
Alternatively, you can send an emails to Dr. Qian Huang: qian.huang@mathematik.uni-stuttgart.de, and he will add you to the ILIAS group.
Will be added soon
Partial differential equations (PDEs) are central to the modeling of natural, engineering and social phenomena. Traditional numerical methods for solving and analyzing PDEs, have been highly successful and remain indispensable in scientific computing. However, recent advances in machine learning and deep learning have created a new paradigm for treating PDEs and opened intriguing possibilities for tackling long-standing challenges like reducing computational cost for high-dimensional PDEs, learning closure models from data, and discovering governing equations from observations. This course explores the emerging interface between numerical mathematics, scientific computing, and modern AI, offering students a unified view of how machine learning tools can be systematically integrated into PDE workflows. While the motivation comes from concrete applications (e.g., turbulence modeling, multiphysics simulations, reactive flows), the focus will be on understanding the underlying ideas and computational strategies.
The course is structured as a mixture of 7 lectures (including 3 guest lectures) and 2-3 seminars, each lasting 90 minutes. The lectures are planned to be held before the Christmas holiday, while the seminars will be started from Jan, 2026.
The lectures will (tentatively) be structured as follows:
- Lecture 1: Course introduction
- Lecture 2: Basics of physics-informed neural networks (PINNs)
- Lecture 3: (by Jens Keim, Stuttgart) Reinforcement learning for fluid-related PDEs
- Lecture 4: (online, by Yuntian Chen Eastern Institute of Technology, Ningbo) PDE knowledge discovery
- Lectures : Basics of neural operators
- Lecture 6: (online, by Lu Lu, Yale) Advanced topics on PINN and neural operators
- Lecture 7: Data-driven PDE modeling
The seminars will be presented by students who read papers on selected topics (which will be revealed on the ILIAS page before the first lecture). Students are also welcome to propose their own topics or selected papers, subject to approval.
One seminar may talk about (potentially-large) neural operators for turbulence modeling. Other potential topics may include: PINNs, neural operators, benchmarks, PDE modeling aspects, AI-related PDE inverse problems, symbolic regression, LLM+PDE, mathematical theories, and real-world applications.
Prerequesites: None.
Language: English
ILIAS page: https://ilias3.uni-stuttgart.de/go/grp/4233577 (still under construction)