A composable autoencoder-based algorithm for accelerating numerical simulations

Rishikesh Ranade, Derek Christopher Hill, Haiyang He, Amir Maleki, Norman Chang, Jay Pathak

Keywords: numerical simulations, machine learning

Abstract: Numerical simulations for engineering applications solve partial differential equations (PDE) to model various physical processes. Traditional PDE solvers are very accurate but computationally costly. On the other hand, Machine Learning (ML) methods offer a significant computational speedup but face challenges with accuracy and generalization to different PDE conditions, such as geometry, boundary conditions, initial conditions and PDE source terms. In this work, we propose a novel ML-based approach, CoAE-MLSim, which is an unsupervised, lower-dimensional, local method, that is motivated from key ideas used in commercial PDE solvers. This allows our approach to learn better with relatively fewer samples of PDE solutions. The proposed ML-approach is compared against commercial solvers for better benchmarks as well as latest ML-approaches for solving PDEs. It is tested for a variety of complex engineering cases to demonstrate its computational speed, accuracy, scalability, and generalization across different PDE conditions. The results show that our approach captures physics accurately across all metrics of comparison (including measures such as results on section cuts and lines).

One-sentence Summary: We present a composable, unsupervised autoencoder-based iterative algorithm for accelerating numerical simulations for a variety of engineering applications.