A composable autoencoder-based iterative algorithm for accelerating numerical simulations

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 (Composable AutoEncoder Machine Learning Simulation), 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).

References in corpus (10)

• Hidden Physics Models: Machine Learning of Nonlinear Partial Differential Equations
• Flow over an espresso cup: Inferring 3D velocity and pressure fields from tomographic background oriented schlieren videos via physics-informed neural networks
• Efficient training of physics-informed neural networks via importance sampling
• Deep Equilibrium Models
• Learning to Control PDEs with Differentiable Physics
• NVIDIA SimNet^{TM}: an AI-accelerated multi-physics simulation framework
• Turbulence forecasting via Neural ODE
• An unsupervised learning approach to solving heat equations on chip based on Auto Encoder and Image Gradient
• Geometry encoding for numerical simulations
• A Latent space solver for PDE generalization