Research map / Probabilistic and scientific modeling / Differential equations and PDEs
Gaussian Process Priors for Systems of Linear Partial Differential Equations with Constant Coefficients
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Increase number of Dirac delta measures in S-EPGP from 24 to 384 (ablation) | S-EPGP on Maxwell's equations · Maxwell's equations, RMSE across 5 to 1000 datapoints | RMSE | Helped |
| S-EPGP instead of PINN | Maxwell's equations · Maxwell's equations, 1000 datapoints | RMSE: about two orders of magnitude lower RMSE at best setting | Helped |
| Heat equation: EPGP exact-kernel approach versus PINN | 1D heat equation · Heat equation, initial data and scattered data setups | computation time | Helped |
| Scale parameter sigma^2 in the Gaussian measure (2D heat equation) (ablation) | EPGP for 2D heat equation · 2D heat equation qualitative | fit to initial data | Mixed |
| Sparse Dirac delta approximation (S-EPGP) instead of full Gaussian-measure EPGP | Maxwell's equations · runtime | seconds per 10000 epochs | Helped |
| Increase number of Dirac delta measures from 192 to 384 at 50 datapoints (ablation) | S-EPGP on Maxwell's equations · Maxwell's equations, 50 datapoints | RMSE | Mixed |
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