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Learning Efficient and Robust Ordinary Differential Equations via Invertible Neural Networks
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add INN (diffeomorphism) with linear base ODE instead of direct neural network dynamics | 3D Lotka-Volterra · 3D Lotka-Volterra | integration time (ms): 9.3 ms vs 264.7 ms (DOPRI5) | Helped |
| add INN with linear base ODE instead of neural network dynamics in latent ODE | Latent ODE on ECG and other tasks · Periodic, Human Activity, ECG, Image Seq. | integration time: hundreds of times faster | Helped |
| linear base ODE with INN in latent ODE | Human Activity classification · Human Activity | accuracy: 0.864 vs 0.869 (DOPRI5) | Mixed |
| non-linear neural network base ODE with INN instead of direct neural ODE | Lorenz and ROBER systems · Lorenz, ROBER | MAE: Lorenz 0.20 vs 7.55; ROBER 0.01 vs 0.039 | Helped |
| add INN layers (0 to 5) to a small 2256-parameter base ODE (ablation) | Lorenz system · Lorenz | MAE: 10.95 with 0 layers to 0.21 with 5 layers | Helped |
| increase NN dynamics parameters without INN (ablation) | Lorenz system · Lorenz | MAE: 10.95 at 2256 params down to 7.08 at 83006 params | Mixed |
| INN with 6 and 7 layers vs 5 layers (ablation) | Lorenz system base ODE with INN · Lorenz | MAE: 0.21 at 5 layers, 0.38 at 6, 0.29 at 7 | Mixed |
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