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Learning Deep Input-Output Stable Dynamics
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the Hamilton-Jacobi projection to enforce input-output stability | Neural dynamics on the glucose-insulin benchmark · Glucose-insulin benchmark test | RMSE: 0.0103 -> 0.0050 | Helped |
| Use the Hamilton-Jacobi projection to enforce input-output stability | Neural dynamics on the glucose-insulin benchmark · Unexpected step inputs, magnitudes 2 to 10 | bounded output behavior | Helped |
| Add the Hamilton-Jacobi loss term to DIOS-fgh (ablation) | Bistable benchmark, DIOS-fgh · Bistable model | robust estimation of stable points | Helped |
| Use vanilla neural networks instead of the stability-constrained method | Neural dynamics on the bistable benchmark · Bistable model | identification of two stable points | Hurt |
| Increase the bistable training dataset size | Compared methods · Bistable model, 100, 1000, and 3000 signals | RMSE | Helped |
| Use vanilla neural networks rather than input-output stability-aware training | Neural dynamics on the bistable benchmark · Bistable model | GainIO error | Hurt |
| Use a piece-wise ARX model instead of the proposed method | Bistable benchmark · Bistable model | GainIO error | Hurt |
| Use DIOS-fgh, which modifies f, G, and h | Bistable benchmark · Bistable model | GainIO error | Helped |
| Use DIOS-f, which modifies only f | Bistable benchmark · Bistable model | GainIO error | Helped |
| Use DIOS-fg, which modifies f and G | Bistable benchmark · Bistable model | GainIO error | Helped |
| Disable stop-gradient for the projection (ablation) | Proposed method · Bistable and glucose-insulin benchmarks | performance | Hurt |
| Add the Hamilton-Jacobi loss term (ablation) | Nominal dynamics in the proposed method · Training | parameter learning | Helped |
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