Research map / Probabilistic and scientific modeling / Differential equations and PDEs
Low-Rank Registration Based Manifolds for Convection-Dominated PDEs
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Register snapshots onto a learned low-rank, time-varying grid instead of reconstructing them on a fixed POD subspace | Low-rank registration manifold · Rotated character A | reconstruction error | Helped |
| Register snapshots onto a learned low-rank, time-varying grid instead of using POD | Euler Riemann problem · Configurations 3 and 12 | density reconstruction error | Helped |
| Wrap the LSTM in the proposed registration-based auto-encoder instead of a neural network auto-encoder | LSTM · Burgers' and wave equations | reconstruction error: up to 3 orders of magnitude | Helped |
| Extend the learned grid by linear extrapolation of its grid coefficients | Low-rank registration manifold · Euler Riemann problem, configuration 12, extrapolation | prediction error | Helped |
| Use the proposed registration-based auto-encoder rather than a neural network auto-encoder | LSTM · Burgers' equation, extrapolation | prediction error | Helped |
| Increase the registration-grid rank from 1 to 2 (ablation) | Low-rank registration manifold · Rotated character A | reconstruction error | Helped |
| Use a time-varying registered grid instead of the fixed grid (ablation) | Low-rank registration manifold · Euler Riemann problem | density reconstruction error | Helped |
| Use the proposed auto-encoder in place of the neural network auto-encoder (ablation) | LSTM · Burgers' equation, extrapolation | prediction error | Helped |
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