Physics-based Deep Learning

N. Thuerey, B. Holzschuh, P. Holl, G. Kohl, M. Lino +3 more
9/11/2021
cs.LGphysics.comp-ph

Official code: tum-pbs/PhiFlow (1,950 stars, MIT, last commit 2026-07-16). 5 more implementations below.

Abstract

This document is a hands-on, comprehensive guide to deep learning in the realm of physical simulations. Rather than just theory, we emphasize practical application: every concept is paired with interactive Jupyter notebooks to get you up and running quickly. Beyond traditional supervised learning, we dive into physical loss-constraints, differentiable simulations, diffusion-based approaches for probabilistic generative AI, as well as reinforcement learning and advanced neural network architectures. These foundations are paving the way for the next generation of scientific foundation models. We are living in an era of rapid transformation. These methods have the potential to redefine what's possible in computational science.

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Code Implementations(6)

tum-pbs/PhiFlowOfficial100%
MIT

A differentiable PDE solving framework for machine learning

1,950236PythonDec 4, 20193 months agoMIT
deep-learningdifferentiable-simulationsfluid-simulationsneural-networkspde-solver
thunil/Physics-Based-Deep-LearningOfficial100%

Links to works on deep learning algorithms for physics problems, TUM-I15 and beyond

1,912317Sep 15, 20181 years ago
tum-pbs/pbdl-bookOfficial100%

Welcome to the Physics-based Deep Learning Book v0.3 - the GenAI Edition

1,376221TeX, ShellJan 4, 20211 years ago
artificial-intelligencebayesian-inferencedeep-learningfluidsmachine-learning+4 more
tum-pbs/Diffusion-based-Flow-PredictionOfficial100%
Apache-2.0

Official implementation of the AIAA Journal paper "Uncertainty-aware Surrogate Models for Airfoil Flow Simulations with Denoising Diffusion Probabilistic Models"

908C++, GLSLNov 28, 20231 years agoApache-2.0
baysian-networkdeep-learningdiffusion-modelsflow-matchingfluid-dynamics+4 more
tum-pbs/pbdl-datasetOfficial100%
Apache-2.0

Dataset handling for physics-based deep learning tasks

74PythonSep 12, 20247 months agoApache-2.0
thunil/Deep-Flow-PredictionCommunity100%
Apache-2.0

A framework for fluid flow (Reynolds-averaged Navier Stokes) predictions with deep learning

354120C++, GLSLSep 16, 20183 years agoApache-2.0

Cite this paper

@article{thuerey2021physicsbased,
  title  = {Physics-based Deep Learning},
  author = {N. Thuerey and B. Holzschuh and P. Holl and G. Kohl and M. Lino and Q. Liu and P. Schnell and F. Trost},
  year   = {2021},
  eprint = {2109.05237},
  archivePrefix = {arXiv},
  url    = {https://arxiv.org/abs/2109.05237}
}

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