On Autoregressive Neural Emulators for PDEs | Talk @ IRMA Strasbourg

Thank you, IRMA Strasbourg PDE Team (Emmanuel Franck & Victor Michel-Dansac), for inviting me to talk about my research on autoregressive surrogates for partial differential equations. This presentation is based in part on APEBench (https://arxiv.org/abs/2411.00180 ) and extended with some personal thoughts of mine. You can find their talk series here: https://seminaire_edp.pages.math.unistra.fr

Slides are here: https://seminaire_edp.pages.math.unistra.fr/slides/2025-05-13.pdf

I am a PhD student in the group of Prof. Thuerey at TUM. If you like APEBench or this talk, I imagine you also enjoy our toher research you can find here: https://ge.in.tum.de/

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Timestamps:
00:00 Intro
02:03 Classical Approaches to Simulating PDEs
04:20 Accuracy-Speed Trade-Off for Simulation Techniques
06:08 Pushing the Pareto Frontier
07:42 Overview of Neural Approaches
10:13 Why replace the numerical solver?
15:52 Autoregressive Emulators and how to handle time
20:51 One-Step Supervised Training
24:52 Designing a Benchmark Suite for Markovian Emulators
28:41 Fast ETDRK-based JAX solver
30:02 Reparameterized PDE descriptors
33:00 What to Study with APEBench?
35:20 Recap: Feed-Forward Convolutional Neural Networks
37:37 Advection Emulation Study with ConvNets only
43:27 More Emulator Architectures
46:08 Advection Study with more architectures
48:35 Emulators across different PDEs
57:09 Architecture Decision Chart
58:45 APEBench in a nutshell
01:02:06 Outro