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Solving partial differential equations

Benchmarks

Dataset Name	SOTA Method	Metric
6D Nonlinear Darcy flow equation	TGPS-TR-NT	Relative L2 Error0.004	27	4mo ago
4D Allen-Cahn equation a=15 d=4	TGPS-TR-NT	Relative L2 Error0	24	4mo ago
Burgers' equation viscosity ν = 0.02	TGPS-NT	Relative L2 Error0.0001	20	4mo ago
Parametrized Poisson continuous parameter space (test)	PRISM-STDE	Relative L2 Error0.0005	13	1mo ago
Sine-Gordon continuous parameter space (test)		Memory Usage (MB)1,328	10	1mo ago
Allen-Cahn continuous parameter space (test)		Memory (MB)1,328	10	1mo ago
Burgers (test)	DCGD + ModSync	Absolute Error0.0321	10	1mo ago
Klein-Gordon 3D (test)	NTK	Absolute Error3.177	10	1mo ago
Klein-Gordon 2D (test)	ConFIG + ModSync	Absolute Error0.07	10	1mo ago
Helmholtz 3D (test)	ConFIG + ModSync	Absolute Error19.86	10	1mo ago
Helmholtz 2D (test)	ConFIG + ModSync	Absolute Error0.0384	10	1mo ago
Wave	OSSM-PINN-IMEX	rMAE0	10	1mo ago
Reaction	double PINN	rMAE0.0011	10	1mo ago
Burgers v = 1/100pi	Method [33]	Relative L2 Error1.38	7	2mo ago
Two-body Allen-Cahn equation 10KD	SDZE	Memory Usage (MB)723	7	4mo ago
Two-body Allen-Cahn equation 1KD	SDZE	Memory (MB)512	7	4mo ago
Two-body Allen-Cahn equation 100D	SDZE	Memory (MB)485	7	4mo ago
Poisson equation	LNO	Total Parameters0.0279	6	18d ago
Darcy Flow	LNO	Total Parameters27,937	6	18d ago
Allen-Cahn	LNO	Total Parameters27,937	6	18d ago
Damped Wave Equation		Wall-clock Time (CPU)3.35	6	2mo ago
Burgers Equation		Wall-clock Time (CPU)2.18	6	2mo ago
1D Heat Equation alpha1=1.0, alpha2=2.0, s=10.0 35 (test)	CGMPINN	eLoss0	6	2mo ago
1D Advection-Diffusion Equation (a=1.0, ν=10⁻²) (test)	CGMPINN	eLoss0	6	2mo ago
1D convection-dominated equation epsilon = 10^-6 (test)	AEH-PINN	Relative L2 Error0	6	4mo ago

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