A composable machine-learning approach for steady-state simulations on high-resolution grids

Abstract

In this paper we show that our Machine Learning (ML) approach, CoMLSim (Composable Machine Learning Simulator), can simulate PDEs on highly-resolved grids with higher accuracy and generalization to out-of-distribution source terms and geometries than traditional ML baselines. Our unique approach combines key principles of traditional PDE solvers with local-learning and low-dimensional manifold techniques to iteratively simulate PDEs on large computational domains. The proposed approach is validated on more than 5 steady-state PDEs across different PDE conditions on highly-resolved grids and comparisons are made with the commercial solver, Ansys Fluent as well as 4 other state-of-the-art ML methods. The numerical experiments show that our approach outperforms ML baselines in terms of 1) accuracy across quantitative metrics and 2) generalization to out-ofdistribution conditions as well as domain sizes. Additionally, we provide results for a large number of ablations experiments conducted to highlight components of our approach that strongly influence the results. We conclude that our local-learning and iterative-inferencing approach reduces the challenge of generalization that most ML models face.

NLP Inspired Training Mechanics For Modeling Transient Dynamics

“…These methods provide accurate predictions, but they are computationally very expensive. As a result, researchers in the deep learning community have devised many different models to learn physics behind these engineering problems using supervised learning methods, that determine the input to output mapping [1,2,3,4,5] or unsupervised learning methods, that embed physical laws into loss functions to compute PDE solutions [6,7,8,9]. These physics-informed methods provide a unique benefit over most approaches by imposing initial and boundary conditions in the optimization process.…”