Solving partial differential equations

Benchmarks

Dataset Name	SOTA Method	Metric
6D Nonlinear Darcy flow equation	TGPS-TR-NT	Relative L2 Error0.004	27	2mo ago
4D Allen-Cahn equation a=15 d=4	TGPS-TR-NT	Relative L2 Error0	24	2mo ago
Burgers' equation viscosity ν = 0.02	TGPS-NT	Relative L2 Error0.0001	20	2mo ago
Burgers v = 1/100pi	Method [33]	Relative L2 Error1.38	7	21d ago
Two-body Allen-Cahn equation 10KD	SDZE	Memory Usage (MB)723	7	2mo ago
Two-body Allen-Cahn equation 1KD	SDZE	Memory (MB)512	7	2mo ago
Two-body Allen-Cahn equation 100D	SDZE	Memory (MB)485	7	2mo ago
Damped Wave Equation		Wall-clock Time (CPU)3.35	6	12d ago
Burgers Equation		Wall-clock Time (CPU)2.18	6	12d ago
1D Heat Equation alpha1=1.0, alpha2=2.0, s=10.0 35 (test)	CGMPINN	eLoss0	6	14d ago
1D Advection-Diffusion Equation (a=1.0, ν=10⁻²) (test)	CGMPINN	eLoss0	6	14d ago
1D convection-dominated equation epsilon = 10^-6 (test)	AEH-PINN	Relative L2 Error0	6	3mo ago
Poisson-Gauss PG-4		Wall-clock Time (CPU)3.35	5	12d ago
Poisson-Gauss PG-3		Wall-clock Time (CPU)6.91	5	12d ago
Poisson-Gauss PG-2		Wall-clock Time (CPU)19.32	5	12d ago
Helmholtz	Method [31]	Relative L2 Error2	5	21d ago
Two-body Allen-Cahn equation 100KD	SDZE	Memory (MB)982	5	2mo ago
Committor E.2.4	FK-PINNs	L2 Abs Error0.791	4	1d ago
Mean Escape Time E.2.3	FK-PINNs	L2 Absolute Error1.755	4	1d ago
Schrödinger-type 7	FK-PINNs	L2 Absolute Error0.073	4	1d ago
Poisson E.2.2	FK-PINNs	L2 Absolute Error0.761	4	1d ago
Three-dimensional Helmholtz equations (25) (test)	MS-SFNN	L2 Error0	4	2d ago
Wave	double PINN	Loss0	4	2d ago
Reaction	double PINN	Loss0	4	2d ago
Convection	double PINN	Loss0	4	2d ago

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