  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.
