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Equation Discovery

Benchmarks

Dataset Name	SOTA Method	Metric
Gravitational potential	GPLearn (Real+PhysLDM)	MSE12.0125	36	1d ago
Navier–Stokes	PySR (Real only)	MSE0.0799	36	1d ago
Heat conduction	DEAP (Real+PhysLDM)	MSE0.0001	36	1d ago
Boussinesq	SI	Prediction Error0.098	12	2mo ago
Lotka-Volterra (LV)	EqOD	F1 (u)80	9	21d ago
FitzHugh-Nagumo (FHN)		F1 (u)85.7	9	21d ago
Burgers' Equation PDE (Noise Levels: 0%, 1%, 10% (large))		RMSE (0% Noise)0.754	8	3mo ago
Advection Equation Noise Levels: 0%, 1%, 20% (large) PDE	BSL	RMSE (0% Noise)0.26	8	3mo ago
Lorenz 96 Noise Levels: 0%, 1%, 10% (large) ODE	BSL	Mp1	8	3mo ago
Van der Pol Oscillator Noise Levels: 0%, 1%, 5% (large) ODE	PINN-SR	Mp Error Metric0.214	8	3mo ago
Convection-Diffusion Equation 0.1% noise	BLADE	MSE (True Data)0	7	1mo ago
Reaction-diffusion	SI	Complexity (C)16	6	2mo ago
Darcy flow	SI	Complexity7	4	2mo ago
Poisson Equation Noise Levels: 0%, 0.1%, 5% (large) PDE	BSL	Mp1	4	3mo ago
Heat Equation PDE Noise Levels: 0%, 0.1%, 15% (large)	BSL	Mp1	4	3mo ago
Burgers' with Source Noise Levels: 0%, 0.1%, 20% (large) PDE	PINN-SR	RMSE (0% Noise)10.5	4	3mo ago
Johns Hopkins Turbulence Database channel flow (Appendix A Table 5)	SPIDER	Equation Discovery Score1	3	2mo ago
Reaction-diffusion 8	SI	Prediction Error0.008	3	2mo ago
DiffEq Noisy (test)	KeplerAgent	Symbolic Accuracy45	3	3mo ago
DiffEq Clean (test)	KeplerAgent	SA (%)75	3	3mo ago
Convection-Diffusion Equation 1.0% noise	SGN	MSE (on True)3.06	2	2mo ago
Convection-Diffusion Equation 0.5% noise	SGN	MSE (on True)1.43	2	2mo ago
Convection-Diffusion Equation 0.0% noise	PDE-Net 2.0	MSE (True)5.38	2	2mo ago
Darcy flow 7	SI	Prediction Error (%)5.1	2	2mo ago
Convection-Diffusion Equation 10.0% noise	SGN	MSE (on True Values)0.0142	1	2mo ago

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