Energy-based feature extraction with adaptive local domain decomposition for prediction of transient and turbulence flow with operator regression models

Machine learning (ML) based surrogate models offer the potential to accelerate real-world engineering simulations involving millions of elements by bypassing the need for full-scale numerical simulations. However, current model capacities and available GPU memory often impose severe constraints, limiting our ability to accurately represent the highly variant physical dynamics encountered in complex systems. In traditional numerical methods, these computational limitations are mitigated using domain decomposition. The computational domain is split up to enable parallelization of the computation and reduce memory load. Similarly, ML models can benefit from decomposing the domain into subdomains. However, domain decomposition alone is insufficient to guarantee model performance and accuracy when physical dynamics vary spatially. We introduce the Adaptive Local Domain Decomposition (ALDD) method, which features two key innovations. First, it utilizes domain decomposition to improve the training efficiency of the ML model, with time reduction scaling almost linearly with the number of parallel GPUs. Second, ALDD adaptively partitions the domain and schedules appropriate models by segmenting the physics domain into subdomains based on physical dynamics features. Different ML models explicitly trained to solve different physical dynamics are then strategically assigned to these subdomains, encoding boundary information to ensure a smooth transition at the subdomain interface. This is accomplished by analyzing the energy spectrum of each subdomain and applying k-means clustering on the Wasserstein distances to identify physically coherent regions. We demonstrate superior performance and accuracy compared to baseline ML surrogate models for transitional boundary layer flow and recurrent temporal predictions with over 6 million elements.