Lotka-Volterra
Benchmarks
| Task Name | Dataset Name | SOTA Result | Trend | |
|---|---|---|---|---|
| Long-term Time-Series Forecasting | Lotka-Volterra (L.-V.) synthetic (test) | MSE0.63 | 27 | |
| Interpolation | Lotka-Volterra Simulated | Normalized Log-Likelihood-3.46 | 12 | |
| Equation Discovery | Lotka-Volterra (LV) | F1 (u)80 | 9 | |
| Trajectory Inference | Lotka–Volterra Path Measure | KL Divergence (nu^A || nu^B)0.271 | 7 | |
| Trajectory Inference | Lotka–Volterra tau=0.875 | EMD0.061 | 7 | |
| Trajectory Inference | Lotka–Volterra tau=0.625 | EMD0.036 | 7 | |
| Trajectory Inference | Lotka–Volterra (tau=0.375) | EMD2.6 | 7 | |
| Trajectory Inference | Lotka–Volterra tau=0.125 | EMD0.018 | 7 | |
| Model Reconstruction | Lotka Volterra | Reconstruction MSE0.03 | 6 | |
| Reconstruction | Lotka-Volterra Real | Normalized Log-Likelihood-4.29 | 6 | |
| Forecasting | Lotka-Volterra Real | Normalized Log-Likelihood-5.01 | 6 | |
| Interpolation | Lotka-Volterra Real | Normalized Log-Likelihood-4.18 | 6 | |
| Forecasting | Lotka-Volterra Simulated | NLL-4.87 | 6 | |
| Trajectory Prediction | Lotka-Volterra 5x Extrapolation | Trajectory MSE0.022 | 5 | |
| Trajectory Prediction | Lotka-Volterra 2x Extrapolation | Trajectory MSE0.0049 | 5 | |
| Parameter Recovery and Trajectory Prediction | Lotka-Volterra In-distribution | Trajectory MSE0.0008 | 5 | |
| Estimating source distributions | Lotka-Volterra (LV) high-dimensional (test) | C2ST Accuracy62 | 5 | |
| Hamiltonian approximation | Lotka-Volterra eq. B.7 Domain [0, 8] × [0, 8] | Relative L2 Error0 | 4 | |
| Hamiltonian approximation | Lotka-Volterra eq. B.6, Domain [-5, 5] × [-5, 5] | Relative L2 Error0 | 4 | |
| Hamiltonian approximation | Lotka-Volterra eq. B.6 Domain [-2, 2] × [-2, 2] | Relative L2 Error0 | 4 | |
| State Prediction | Lotka-Volterra simulations (test) | RMSE0.048 | 4 | |
| Black-box optimization | Lotka Volterra | Fraction Successful Runs98 | 3 | |
| Time to Threshold Optimization | Lotka Volterra epsilon=0.05 | Success Rate98 | 3 | |
| Regression | Lotka Volterra predator-prey system (val) | MSE (Data)0.0092 | 3 | |
| Dynamics Modeling | Lotka Volterra LV 1 (single densely observed trajectory) | Log Likelihood1.96 | 3 |
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