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Partial Differential Equation Solving

Benchmarks

Dataset Name	SOTA Method	Metric
(2+1)D Heat Equation on 51x51x51 grid collocation points (train test)	TP-MLP	L-inf Error0	40	5d ago
Burgers Case E8 Mixed BC	SINO	Relative L2 Error0.0376	12	9d ago
Burgers Case E6 2D	SINO	Relative L2 Error0.011	12	9d ago
NSE Case E5 10^-5, f2	SINO	Relative L2 Error0.0132	12	9d ago
KSE 1D (Case E1)	SINO	Relative L2 Error0.004	12	9d ago
2-D Darcy Flow	FNO	MSE0.0002	12	3mo ago
1-D Diffusion	FNO	MSE0	12	3mo ago
1-D Advection	FNO	MSE0.0001	12	3mo ago
NSE 10^-4, f2 (E4)	SINO	Relative L2 Error0.0049	11	9d ago
NSE Case E3 10^-5, f1	SINO	Relative L2 Error0.0199	11	9d ago
NSE Case E2 10^-4, f1	SINO	Relative L2 Error0.0171	11	9d ago
Linear Elasticity PDE Family 10 unseen tasks	LAM-PINN	Average MSE (10 Tasks)0.0011	9	1mo ago
Burgers' PDE Family 10 unseen tasks	LAM-PINN	Average MSE (10 Tasks)0.0588	9	1mo ago
Helmholtz PDE Family 10 unseen tasks	LAM-PINN	Average MSE (10 Tasks)0.145	9	1mo ago
Convection equation	PILIR	Relative L2 Error0.0028	7	1mo ago
Navier-Stokes equation Large regime, Re=2000	PhyTF-GAN	Relative MSE0.183	6	2mo ago
Navier-Stokes equation Medium regime, Re=1000	PhyTF-GAN	Relative MSE0.0007	6	2mo ago
Navier-Stokes equation Small regime, Re=500	PhyTF-GAN	Relative MSE0.0336	6	2mo ago
Klein-Gordon equation Large regime, m=5	PINNs-RAR	Relative MSE0.0016	6	2mo ago
Klein-Gordon equation Medium regime, m=3	PhyTF-GAN	Relative MSE0.0008	6	2mo ago
Klein-Gordon equation Small regime, m=1	PhyTF-GAN	Relative MSE0.0388	6	2mo ago
Allen-Cahn equation Large regime, phi=2	PhyTF-GAN	Relative MSE0.0001	6	2mo ago
Allen-Cahn equation Medium regime, phi=1	PhyTF-GAN	Relative MSE0.0001	6	2mo ago
Allen-Cahn equation Small regime, phi=0.5	PhyTF-GAN	Relative MSE0.0002	6	2mo ago
4D multiscale equation	AEH-PINN	Relative L2 Error0.0001	6	3mo ago

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