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

• URL: http://arxiv.org/abs/2210.05837v1
• Date: Tue, 11 Oct 2022 23:50:16 GMT
• Title: A composable machine-learning approach for steady-state simulations on high-resolution grids
• Authors: Rishikesh Ranade, Chris Hill, Lalit Ghule, Jay Pathak
• Abstract summary: CoMLSim (Composable Machine Learning Simulator) can simulate PDEs on highly-resolved grids. Our approach combines key principles of traditional PDE solvers with local-learning and low-dimensional manifold techniques.
• Score: 0.6554326244334866
• License: http://creativecommons.org/licenses/by/4.0/
• 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-of-distribution 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.

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