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Augmenting Physical Models with Deep Networks for Complex Dynamics Forecasting
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| augment incomplete physical dynamics with a learned residual constrained to have minimal norm | APHYNITY · Reaction-diffusion | log MSE: -1.26±0.02 -> -5.10±0.21 | Helped |
| augment incomplete physical dynamics with a learned residual constrained to have minimal norm | APHYNITY · Wave equation | log MSE: 0.51±0.07 -> -4.64±0.25 | Helped |
| augment incomplete physical dynamics with a learned residual constrained to have minimal norm | APHYNITY · Damped pendulum | log MSE: -0.14±0.10 -> -7.86±0.60 | Helped |
| replace APHYNITY decomposition with vanilla augmentation (ablation) | Param PDE (a,b) on reaction-diffusion · Reaction-diffusion | log MSE: -5.10±0.21 -> -4.56±0.52 | Hurt |
| replace APHYNITY decomposition with vanilla augmentation (ablation) | Param PDE (a,b,k) on reaction-diffusion · Reaction-diffusion | log MSE: -9.35±0.02 -> -8.04±0.03 | Hurt |
| replace APHYNITY decomposition with vanilla augmentation (ablation) | Param PDE (c) on wave equation · Wave equation | log MSE: -4.64±0.25 -> -3.90 ± 0.27 | Hurt |
| replace APHYNITY decomposition with vanilla augmentation (ablation) | Param PDE (c,k) on wave equation · Wave equation | log MSE: -6.09±0.28 -> -5.96 ± 0.10 | Hurt |
| replace APHYNITY decomposition with vanilla augmentation (ablation) | Hamiltonian pendulum model · Damped pendulum | log MSE: -3.97±1.2 -> -0.35±0.1 | Hurt |
| replace APHYNITY decomposition with vanilla augmentation (ablation) | Param ODE (ω0,α) on damped pendulum · Damped pendulum | log MSE: -8.31±0.3 -> -7.60±0.6 | Hurt |
| use trajectory-based supervision instead of finite-difference derivative supervision (ablation) | APHYNITY · Reaction-diffusion, wave equation, and damped pendulum | forecasting accuracy | Helped |
| use adaptive optimization of the trajectory-loss weight instead of fixing λ=1 and τ2=0 (ablation) | APHYNITY · Reaction-diffusion, wave equation, and damped pendulum | forecasting accuracy | Helped |
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