Felix Köhler: From numerical simulators of PDEs to neural emulators and back

The potential for computational speedups and tackling unsolved problems has motivated the use of neural networks (NNs) for helping solve PDEs. In particular, image-like models that operate on state-discrete representations that approach time autoregressively gained popularity over the past years.

In this talk, I will present a holistic perspective on learning autoregressive neural emulators from simulated data, starting with the synthetic data generation using classical numerical simulators, covering the training process and ultimately investigating their benchmarking. Using a wide range of experiments with different PDEs and neural architectures, I will highlight the similarities between emulators and simulators. This shows how emulator architectures were inspired by classical schemes for solving the laws of nature and thereby inherit both their merits and limitations. 

Moreover, I will elaborate on the impact of reference data fidelity and discuss a counterintuitive yet interesting finding when emulators can become better than their training data source.

Felix Koehler is a fourth-year PhD student at the Technical University of Munich under the supervision of Prof. Nils Thuerey. His research interests span numerical simulations of PDEs, reduced-order models, neural emulators, optimization theory, automatic differentiation and adjoint methods. 

In particular, he is interested in discovering deep insights on neural networks solving physics problems, e.g., in fluid or structural mechanics. He holds an M.Sc. in Computational Science & Engineering from TUM. Besides research, he works on free educational material covering Machine Learning & Simulation on his YouTube channel.