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GPINN with Neural Tangent Kernel Technique for Nonlinear Two Point Boundary Value Problems

https://doi.org/10.1007/s11063-024-11644-7

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What this work says

Outgoing claims: the papers this work cites, builds on, or argues with.

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500 Examples and Problems of Applied Differential Equations

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Biologically inspired computing framework for solving two-point boundary value problems using differential evolution

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Training Neural Networks with Krill Herd Algorithm

inferredcites →https://doi.org/10.1007/s11063-016-9551-9openalex-snapshot

Single Layer Chebyshev Neural Network Model for Solving Elliptic Partial Differential Equations

inferredcites →https://doi.org/10.1016/0045-7825(95)00830-topenalex-snapshot

Comput. Methods Appl. Mech. Engrg. 109 (1993) 351–357

inferredcites →https://doi.org/10.1016/j.camwa.2007.10.002openalex-snapshot

A numerical approach to nonlinear two-point boundary value problems for ODEs

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Conservative physics-informed neural networks on discrete domains for conservation laws: Applications to forward and inverse problems

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Exact imposition of boundary conditions with distance functions in physics-informed deep neural networks

inferredcites →https://doi.org/10.1016/j.engappai.2023.107183openalex-snapshot

Augmented Physics-Informed Neural Networks (APINNs): A gating network-based soft domain decomposition methodology

inferredcites →https://doi.org/10.1016/j.jcp.2017.01.060openalex-snapshot

Inferring solutions of differential equations using noisy multi-fidelity data

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

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Adaptive activation functions accelerate convergence in deep and physics-informed neural networks

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Parallel physics-informed neural networks via domain decomposition

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Physics-Informed Neural Networks for Inverse Problems in Supersonic Flows

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A Unified Scalable Framework for Causal Sweeping Strategies for Physics-Informed Neural Networks (Pinns) and Their Temporal Decompositions

inferredcites →https://doi.org/10.1016/j.neucom.2021.10.036openalex-snapshot

Deep Kronecker neural networks: A general framework for neural networks with adaptive activation functions

inferredcites →https://doi.org/10.1016/j.neucom.2022.05.015openalex-snapshot

Self-adaptive loss balanced Physics-informed neural networks

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Deep learning of inverse water waves problems using multi-fidelity data: Application to Serre–Green–Naghdi equations

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Spectral bias and task-model alignment explain generalization in kernel regression and infinitely wide neural networks

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Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators

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Theoretical issues in deep networks

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Pricing and hedging derivative securities with neural networks: Bayesian regularization, early stopping, and bagging

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A Physics-Informed Neural Network for Quantifying the Microstructural Properties of Polycrystalline Nickel Using Ultrasound Data: A promising approach for solving inverse problems

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Numerical Gaussian Processes for Time-Dependent and Nonlinear Partial Differential Equations

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fPINNs: Fractional Physics-Informed Neural Networks

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DeepXDE: A Deep Learning Library for Solving Differential Equations

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When Do Extended Physics-Informed Neural Networks (XPINNs) Improve Generalization?

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Self-Adaptive Physics-Informed Neural Networks

inferredcites →https://doi.org/10.4208/cicp.oa-2020-0164openalex-snapshot

Extended Physics-Informed Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition Based Deep Learning Framework for Nonlinear Partial Differential Equations

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

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Optimizing the optimizer for physics-informed neural networks and Kolmogorov-Arnold networks

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A physics-informed neural network-based method for dispersion calculations

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Unveiling the optimization process of physics informed neural networks: How accurate and competitive can PINNs be?

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A semi-analytical physics-informed neural network framework with hessian analysis for singularly perturbed fractal convection-dominated anomalous diffusion problems

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Fisher’s information matrix approach for Fourier features physics-informed neural networks for two-dimensional local time-fractional anomalous diffusion equations with nonlinear thermal diffusivity

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Neural networks optimized by data-driven gradient physics for soliton pulse equation solutions

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Physics-Informed Neural Networks without Loss Balancing: A Direct Term Scaling Approach for Nonlinear 1D Problems

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Physics-Informed Neural Networks without Loss Balancing: A Direct Term Scaling Approach for Nonlinear 1D Problems

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Physics-Informed Neural Network for the Calculation of Complex Dispersion Relations of Periodic Structures

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Physics-Informed Neural Networks in Polymers: A Review

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