Adaptive Local Domain Decomposition for Learning Large-Scale Multi-physics Numerical Simulations

Applying physics-informed neural networks (PINNs) in engineering scenarios involving millions of elements presents a significant computational challenge, as the complexity and diversity of the physics can exceed the capacities of machine learning (ML) models and available GPU memory. Recently, methods have been developed for PINNs to segment the input domain and perform concurrent inference on smaller subdomains, improving computational efficiency. Building on this concept, we introduce the Adaptive Local Domain Decomposition (ALDD) method, which enhances performance in two primary ways: (1) It employs domain decomposition to boost the efficiency of training and inference, achieving near-linear reductions in computation time with the addition of parallel GPUs. (2) It uses adaptive domain scheduling to divide the physics domain into subdomains according to the physical features, applying specialized sub-ML models to each subdomain. We utilize the energy spectrum of each subdomain, combined with k-means clustering of the spectrum's Wasserstein distance, to determine the most effective distribution of submodels across the subdomains according to the local physical features. This approach shows superior performance compared to other partitioning methods. With ALDD, we can extend the prediction capabilities of modern ML methods for forward problems on discretized domains with over 6 million elements and achieve over 99.6% accuracy in complex physical issues such as turbulent boundary layer flow.