H^{-1} norm equivalence to expected squared evaluations on domain-dependent random test functions enables SV-PINNs that recover accurate solutions to challenging second-order elliptic PDEs faster than standard PINNs.
Self-adaptive physics-informed neural networks.Journal of Computational Physics, 474:111722, 2023
4 Pith papers cite this work. Polarity classification is still indexing.
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AD-RaNN learns an effective low-dimensional sampling distribution for hidden parameters in randomized neural networks by optimizing a vector p via PDE-driven or data-driven adaptation and a two-stage least-squares procedure, improving accuracy on benchmark PDE problems.
PINNs fail on spurious solutions admitted by the residual loss; adaptive pseudo-time stepping with Jacobian-based step selection improves accuracy and robustness on PDE benchmarks.
PINNACLE is an open-source framework for classical and quantum PINNs that supplies modular training methods and benchmarks showing high sensitivity to architecture choices plus parameter-efficiency gains in some hybrid quantum regimes.
citing papers explorer
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Random test functions, $H^{-1}$ norm equivalence, and stochastic variational physics-informed neural networks
H^{-1} norm equivalence to expected squared evaluations on domain-dependent random test functions enables SV-PINNs that recover accurate solutions to challenging second-order elliptic PDEs faster than standard PINNs.
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Adaptive-Distribution Randomized Neural Networks for PDEs: A Low-Dimensional Distribution-Learning Framework
AD-RaNN learns an effective low-dimensional sampling distribution for hidden parameters in randomized neural networks by optimizing a vector p via PDE-driven or data-driven adaptation and a two-stage least-squares procedure, improving accuracy on benchmark PDE problems.
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When PINNs Go Wrong: Pseudo-Time Stepping Against Spurious Solutions
PINNs fail on spurious solutions admitted by the residual loss; adaptive pseudo-time stepping with Jacobian-based step selection improves accuracy and robustness on PDE benchmarks.
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PINNACLE: An Open-Source Computational Framework for Classical and Quantum PINNs
PINNACLE is an open-source framework for classical and quantum PINNs that supplies modular training methods and benchmarks showing high sensitivity to architecture choices plus parameter-efficiency gains in some hybrid quantum regimes.