Proves an n^{-1/(d+2)}-type convergence rate for weak PINNs approximating entropy solutions of geometry-compatible conservation laws on d-dimensional manifolds, with network complexity independent of the ambient dimension.
Neural operator: Graph kernel network for partial differential equations
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Weak Physics Informed Neural Networks for Geometry Compatible Hyperbolic Conservation Laws on Manifolds
Proves an n^{-1/(d+2)}-type convergence rate for weak PINNs approximating entropy solutions of geometry-compatible conservation laws on d-dimensional manifolds, with network complexity independent of the ambient dimension.