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Boundary neuron method for solving partial differential equations

https://doi.org/10.2139/ssrn.6482329
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Outgoing claims: the papers this work cites, builds on, or argues with.

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Potential Theory
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The Boundary Element Method
inferredcites →https://doi.org/10.1007/s42967-024-00389-8openalex-snapshot
Optimization of Random Feature Method in the High-Precision Regime
inferredcites →https://doi.org/10.1016/0307-904x(83)90119-1openalex-snapshot
Boundary element method in elastostatics: theory and applications
inferredcites →https://doi.org/10.1016/j.cnsns.2025.109343openalex-snapshot
Solving partial differential equations with random feature models
inferredcites →https://doi.org/10.1016/j.ijmecsci.2024.109525openalex-snapshot
Boundary integrated neural networks for 2D elastostatic and piezoelectric problems
inferredcites →https://doi.org/10.1016/j.jcp.2018.10.045openalex-snapshot
Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
inferredcites →https://doi.org/10.1016/j.jcp.2021.110668openalex-snapshot
Solving and learning nonlinear PDEs with Gaussian processes
inferredcites →https://doi.org/10.1016/j.jcp.2024.113488openalex-snapshot
Error analysis of kernel/GP methods for nonlinear and parametric PDEs
inferredcites →https://doi.org/10.1109/allerton.2008.4797607openalex-snapshot
Uniform approximation of functions with random bases
inferredcites →https://doi.org/10.1109/tpami.2021.3097011openalex-snapshot
Random Features for Kernel Approximation: A Survey on Algorithms, Theory, and Beyond
inferredcites →https://doi.org/10.1137/0519043openalex-snapshot
Boundary Integral Operators on Lipschitz Domains: Elementary Results
inferredcites →https://doi.org/10.1137/110821846openalex-snapshot
Scattered Data Interpolation on Embedded Submanifolds with Restricted Positive Definite Kernels: Sobolev Error Estimates
inferredcites →https://doi.org/10.3390/app9081642openalex-snapshot
The Boundary Element Method in Acoustics: A Survey
inferredcites →https://doi.org/10.4208/cicp.oa-2020-0191openalex-snapshot
Finite Neuron Method and Convergence Analysis
inferredcites →https://doi.org/10.4208/csiam-am.so-2022-0014openalex-snapshot
BINet: Learn to Solve Partial Differential Equations with Boundary Integral Networks
inferredcites →https://doi.org/10.4208/eajam.2023-065.050423openalex-snapshot
The Random Feature Method for Time-Dependent Problems
inferredcites →https://doi.org/10.4208/eajam.2024-070.150524openalex-snapshot
Solving Diffusion Problems by a Random Feature Method
inferredcites →https://doi.org/10.4208/jcm.2406-m2023-0143openalex-snapshot
A Neuron-Wise Subspace Correction Method for the Finite Neuron Method
inferredcites →https://doi.org/10.4208/jml.220726openalex-snapshot
Bridging Traditional and Machine Learning-Based Algorithms for Solving PDEs: The Random Feature Method
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