Parameterizing the temporal derivative in PINNs and reconstructing via Volterra integral yields 100-200x lower errors on advection, Burgers, and Klein-Gordon equations while proving equivalence to the original PDE.
Ciarlet.The finite element method for elliptic problems
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Learning on the Temporal Tangent Bundle for Physics-Informed Neural Networks
Parameterizing the temporal derivative in PINNs and reconstructing via Volterra integral yields 100-200x lower errors on advection, Burgers, and Klein-Gordon equations while proving equivalence to the original PDE.