Physics-based Deep Learning

Thuerey, N., Holzschuh, B., Holl, P., Kohl, G., Lino, M., Liu, Q., Schnell, P., Trost, F.

arXiv.org Artificial Intelligence 

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. Note What's new in v0.3? This latest edition takes things even further with a major new chapter on generative modeling, covering cutting-edge techniques like denoising, flow-matching, autoregressive learning, physics-integrated constraints, and diffusion-based graph networks. We've also introduced a dedicated section on neural architectures specifically designed for physics simulations. All code examples have been updated to leverage the latest frameworks.