Nonlinear Model Reduction: Using ML to Enable Rapid Simulation of Extreme-Scale Physics Models
summary
Uses convolutional autoencoders and LSTM error models to learn a low‑dimensional nonlinear manifold (decoder = parameterization) and solves reduced dynamics via a new manifold LSPG projection that enforces conservation and tangent‑space kinematics. Demonstrated on cavity and reacting‑flow examples: a 1M‑cell, 10k‑step case runs ~30 minutes on 2 cores vs 5 hours on 48 with <1% drag error; claims 1–3 orders of magnitude speedups relative to full models and LSTM error regressors achieve FVU ≲10⁻².
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chapters (10)
- 0:00Introduction to nonlinear model reduction
- 5:19Mathematical formulation of model reduction
- 15:12Challenges in traditional model reduction
- 17:40Kamol width and linear subspaces
- 21:10Nonlinear manifolds with deep learning
- 28:32Manifold Galerkin and LSPG methods
- 37:16Autoencoder-based manifold construction
- 45:18Enforcing physical properties in ROMs
- 51:22Deep learning for error analysis
- 1:01:00Q&A and summary
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