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Lotka-Volterra

Benchmarks

Task Name	Dataset Name	SOTA Result
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
State Reconstruction	Lotka-Volterra	MAE0.036	6
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
Dynamical system prediction	Lotka Volterra	MSE0.0031	4
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
Parameter Estimation	Lotka–Volterra 20 datasets	Alpha (α) Mean Relative Bias0.02	3
System Identification Quality	Lotka-Volterra modified (combined)	F1 Score24	3

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