SOTA Partial Differential Equation Solving benchmarks and papers with code

Benchmarks

Dataset Name	SOTA Method	Metric
(2+1)D Heat Equation on 51x51x51 grid collocation points (train test)	TP-MLP	L-inf Error0	40	1mo ago
Burgers Case E8 Mixed BC	SINO	Relative L2 Error0.0376	12	2mo ago
Burgers Case E6 2D	SINO	Relative L2 Error0.011	12	2mo ago
NSE Case E5 10^-5, f2	SINO	Relative L2 Error0.0132	12	2mo ago
KSE 1D (Case E1)	SINO	Relative L2 Error0.004	12	2mo ago
2-D Darcy Flow	FNO	MSE0.0002	12	4mo ago
1-D Diffusion	FNO	MSE0	12	4mo ago
1-D Advection	FNO	MSE0.0001	12	1mo ago
NSE 10^-4, f2 (E4)	SINO	Relative L2 Error0.0049	11	2mo ago
NSE Case E3 10^-5, f1	SINO	Relative L2 Error0.0199	11	2mo ago
NSE Case E2 10^-4, f1	SINO	Relative L2 Error0.0171	11	2mo ago
Linear Elasticity PDE Family 10 unseen tasks	LAM-PINN	Average MSE (10 Tasks)0.0011	9	2mo ago
Burgers' PDE Family 10 unseen tasks	LAM-PINN	Average MSE (10 Tasks)0.0588	9	2mo ago
Helmholtz PDE Family 10 unseen tasks	LAM-PINN	Average MSE (10 Tasks)0.145	9	2mo ago
Helmholtz-2D	PILIR	Error0.0088	8	22d ago
Convection equation	PILIR	Relative L2 Error0.0028	7	2mo ago
Poisson equation	FNO	Total Training Time (min)11.88	6	18d ago
Allen–Cahn	FNO	Total Training Time (min)20.05	6	18d ago
2D Kuramoto-Sivashinsky (val)		Improvement Ratio (mean)1	6	1mo ago
Navier-Stokes equation Large regime, Re=2000	PhyTF-GAN	Relative MSE0.183	6	3mo ago
Navier-Stokes equation Medium regime, Re=1000	PhyTF-GAN	Relative MSE0.0007	6	3mo ago
Navier-Stokes equation Small regime, Re=500	PhyTF-GAN	Relative MSE0.0336	6	3mo ago
Klein-Gordon equation Large regime, m=5	PINNs-RAR	Relative MSE0.0016	6	3mo ago
Klein-Gordon equation Medium regime, m=3	PhyTF-GAN	Relative MSE0.0008	6	3mo ago
Klein-Gordon equation Small regime, m=1	PhyTF-GAN	Relative MSE0.0388	6	3mo ago

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