Proves H^{-1} norm equivalence to expectation over random test functions and introduces SV-PINNs that outperform standard PINNs on eight elliptic problems.
Learning nonlinear operators via deeponet based on the universal approximation the- orem of operators.Nature machine intelligence, 3(3):218–229
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Random test functions, $H^{-1}$ norm equivalence, and stochastic variational physics-informed neural networks
Proves H^{-1} norm equivalence to expectation over random test functions and introduces SV-PINNs that outperform standard PINNs on eight elliptic problems.