Research map / Probabilistic and scientific modeling / Differential equations and PDEs
AutoIP: A United Framework to Integrate Physics into Gaussian Processes
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add physics through an incomplete equation with a latent source | AutoIP versus GPR · Nonlinear pendulum, no damping, exact training data | RMSE: 1.354±0.005 -> 0.585±0.017 | Helped |
| Use the complete equation instead of an incomplete equation (ablation) | AutoIP · Nonlinear pendulum, no damping, exact training data | RMSE: 0.585±0.017 -> 0.416±0.050 | Helped |
| Use the complete equation instead of an incomplete equation (ablation) | AutoIP · Nonlinear pendulum, damping, noisy training data | RMSE: 0.268 ± 0.013 -> 0.133 ± 0.010 | Helped |
| Integrate physics through an incomplete equation with latent source | AutoIP versus GPR · Nonlinear pendulum, no damping, noisy training data | RMSE: 1.44±0.017 -> 0.691 ±0.030 | Helped |
| Place collocation points across the whole trajectory rather than only the training region (ablation) | AutoIP motion capture · CMU motion capture, Joint 1 | RMSE: 1.511 ± 0.007 -> 1.103 ± 0.027 | Helped |
| Use random collocation points within the training region instead of training inputs (ablation) | AutoIP motion capture · CMU motion capture, Joint 1 | RMSE: 1.511 ± 0.007 -> 1.489 ± 0.03 | No clear effect |
| Integrate the diffusion equation with a latent source | AutoIP versus GPR · Swiss Jura, Task 1 | RMSE: 0.299 ± 0.009 -> 0.284 ± 0.011 | Helped |
| Use the complete equation instead of an incomplete equation (ablation) | AutoIP · Diffusion-reaction system | RMSE: 0.1869 -> 0.1865 | Helped |
| Increase PINN collocation points from 100 to 10K (ablation) | PINN · Diffusion-reaction system | RMSE: 0.4388 -> 0.0169 | Helped |
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