Application of PDE emulators for a multi-material, multi-physics simulation problem

Diane Oyen, Morgan Jones, Adithan Kathirgamaraju, Abu Bucker Siddik, Alexander Most +17

Machine learning (ML) architectures are being developed for fast emulation of numerical simulators to accelerate both scientific discovery and engineering design. While these approaches are well-tested on popular PDE (partial differential equation) benchmarks, it is necessary to evaluate their performance on datasets that more accurately reflect industrial and engineering applications. We evaluate several computer vision-based architectures trained as surrogate models on a challenging computational physics task involving multiple materials, revealing significant implementation challenges for adapting certain pre-trained models, including transformer-based architectures. For such multi-physics multi-material datasets, our results underscore the importance of learning algorithms designed for sparse and imbalanced data, techniques for adapting spatial encodings and physical consistency metrics, in addition to methods for reducing the cost of generating sufficient training data.