Randomized neural networks require a sampling domain sized to target smoothness for optimal approximation, and an adaptive PIRaNN method with partition-of-unity refinement solves PDEs with limited local regularity.
Xu , The finite neuron method and convergence analysis , arXiv preprint arXiv:2010.01458, (2020)
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Adaptive Randomized Neural Networks with Locally Activation Function: Theory and Algorithm for Solving PDEs
Randomized neural networks require a sampling domain sized to target smoothness for optimal approximation, and an adaptive PIRaNN method with partition-of-unity refinement solves PDEs with limited local regularity.