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Scale-invariant Learning by Physics Inversion
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace the physical-process gradient with analytic inverse-physics updates | Neural network training on Poisson's equation · Poisson's equation | relative performance vs Adam: a factor of 3 at iteration 60; a full order of magnitude after 5k iterations | Helped |
| Replace the physical-process gradient with damped scale-invariant inverse-physics updates | Neural network training on the heat equation · Heat equation | accuracy vs Adam: 34% more accurate; 130% | Helped |
| Use reverse-simulation inverse-physics updates instead of ordinary backpropagated gradients | Neural network training on Navier-Stokes equations · Navier-Stokes equations | solution accuracy vs Adam: a factor of 2.3; 5x | Helped |
| Use reverse-simulation inverse-physics updates instead of ordinary backpropagated gradients | Neural network training on Navier-Stokes equations · Navier-Stokes equations | iterations to match Adam at 20k iterations: 55 iterations | Helped |
| Use full-rank Hessian-based SIP updates rather than first-order or diagonal-curvature updates | Neural network inversion of coupled, ill-conditioned synthetic physics · Synthetic two-dimensional inverse process | relative accuracy | Helped |
| Use a diagonal Hessian approximation rather than full-rank curvature information | Adam on coupled, ill-conditioned synthetic physics · Synthetic two-dimensional inverse process | relative accuracy | Hurt |
| Use SIP updates instead of SGD, Adam, or AdaHessian | Neural network inversion of Poisson's equation · Poisson's equation | convergence speed: a factor of 3 at iteration 60; a full order of magnitude after 5k iterations | Helped |
| Use SIP updates instead of SGD or Adam | Neural network inversion of the heat equation · Heat equation | convergence speed: 34% more accurate; 130% | Helped |
| Use SIP updates instead of Adam | Neural network inversion of Navier-Stokes equations · Navier-Stokes equations | solution accuracy: a factor of 2.3; 5x | Helped |
| Run a numerical inverse solver per example instead of using a trained neural network | Navier-Stokes inverse problem · Navier-Stokes equations | inference time: 0.11 ms; 2.2 s (7) | Hurt |
| Use GD for direct optimization instead of a neural-network prediction | Navier-Stokes inverse problem · Navier-Stokes equations | time to reach network solution quality: > 4h (20k) | Hurt |
Closest papers by meaning
- Physics-Informed Deep Inverse Operator Networks for Solving PDE Inverse Problems (ICLR 2025 · similarity 0.88)
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- Improving Energy Natural Gradient Descent through Woodbury, Momentum, and Randomization (NeurIPS 2025 · similarity 0.86)
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