DeepFDM, a differentiable finite-difference solver that learns PDE coefficients, achieves 10 to 40 times lower error than FNO, U-Net and ResNet on five scalar time-dependent PDEs in one to three dimensions.
Pdebench: An extensive benchmark for scientific machine learning
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Numerical PDE solvers outperform neural PDE solvers
DeepFDM, a differentiable finite-difference solver that learns PDE coefficients, achieves 10 to 40 times lower error than FNO, U-Net and ResNet on five scalar time-dependent PDEs in one to three dimensions.