Duffing Oscillator
Benchmarks
| Task Name | Dataset Name | SOTA Result | Trend | |
|---|---|---|---|---|
| Dynamical system prediction | Duffing Oscillator | MSE0.0113 | 24 | |
| Stochastic Trajectory Modeling | Duffing oscillator | W2 Distance Error0.075 | 7 | |
| Dynamics Prediction | Duffing oscillator noise level σ=0 | MSE (acceleration)1.11 | 7 | |
| Trajectory Prediction | Duffing oscillator noise level 0 | SSIM (acceleration)99.97 | 7 | |
| Learning Nonlinear and Non-Periodic Responses on ODEs/PDEs | Duffing Oscillator c=0.5 (test) | Relative Error0.0725 | 7 | |
| Learning Nonlinear and Non-Periodic Responses on ODEs/PDEs | Duffing Oscillator (c=0) (test) | Relative Error0.4416 | 7 | |
| Dynamics Prediction | Duffing oscillator noise level σ=0.01 | MSE (Acceleration)1.18 | 6 | |
| Dynamics Prediction | Duffing oscillator noise level σ=0.005 | MSE (Acceleration)1.25 | 6 | |
| Dynamics Prediction | Duffing oscillator noise level σ=0.001 | MSE (acceleration)1.41 | 6 | |
| Trajectory Prediction | Duffing oscillator noise level 0.01 | SSIM (acceleration)99.9 | 6 | |
| Trajectory Prediction | Duffing oscillator noise level 0.005 | SSIM (acceleration)0.9995 | 6 | |
| Trajectory Prediction | Duffing oscillator noise level 0.001 | SSIM (acceleration)99.97 | 6 | |
| Hybrid Modeling (Parameter Estimation and Prediction) | DUFFING OSCILLATOR (test) | Theta Error (x10^-2)0.0132 | 6 | |
| State Estimation | Duffing Oscillator noise-free yk (test) | RMSE q (m)0 | 5 | |
| State Estimation | Duffing Oscillator noisy (test) | RMSE q (m)0.02 | 5 | |
| Nonlinear control | Duffing oscillator | Evaluation Cost1.92 | 5 | |
| Symbolic ODE discovery | Duffing oscillator Benchmark 3 | Mean Relative L2 Error ($u_t$)0.109 | 4 | |
| Learning deterministic mean dynamics | Duffing oscillator | True MSE2.6 | 4 | |
| System Identification | Duffing oscillator | F1 Score63 | 3 | |
| Predictive Performance | Duffing oscillator parameter shifts Param-Ext (OOD T3) | MSE3.44 | 3 | |
| Predictive Performance | Duffing oscillator cross-basin Regime-Ext (OOD T2) | MSE (OOD T2)4.93 | 3 | |
| Predictive Performance | Duffing oscillator ID (in-distribution) | MSE4.75 | 3 | |
| Dynamical System Identification | Duffing Oscillator | Derivative R2 Score1 | 3 | |
| Dynamics Reconstruction | Duffing Oscillator (test) | NRMSE0.317 | 3 | |
| Modeling Dynamical Systems | Duffing Oscillator | Metric- | 0 |
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