mlsanityData to 7 Oct 2026

Is the neural tangent kernel of PINNs deep learning general partial differential equations always convergent ?

arXiv 2412.06158 ↗First posted 9 Dec 2024stat.ML cs.LG math-phcited by 5

Not on the map. Why?

Abstract (arXiv)

In this paper, we study the neural tangent kernel (NTK) for general partial differential equations (PDEs) based on physics-informed neural networks (PINNs). As we all know, the training of an artificial neural network can be converted to the evolution of NTK. We analyze the initialization of NTK and the convergence conditions of NTK during training for general PDEs. The theoretical results show that the homogeneity of differential operators plays a crucial role for the convergence of NTK. Moreover, based on the PINNs, we validate the convergence conditions of NTK using the initial value problems of the sine-Gordon equation and the initial-boundary value problem of the KdV equation.

Key facts. Cited by 5 papers in the map (data through 7 Oct 2026). Builds on 14 of its 29 references that are in the map. First posted on arXiv 9 Dec 2024.

Builds on

14 of 29 references.

References · 14

  1. 2018Neural Tangent Kernel: Convergence and Generalization in Neural Networkscited by 2,597
  2. 2017DGM: A deep learning algorithm for solving partial differential equationscited by 674
  3. 2020When and why PINNs fail to train: A neural tangent kernel perspectivecited by 629
  4. 2017The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problemscited by 581
  5. 2019On Exact Computation with an Infinitely Wide Neural Netcited by 572
  6. 2017PDE-Net: Learning PDEs from Datacited by 304
  7. 2020On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networkscited by 279
  8. 2018PDE-Net 2.0: Learning PDEs from Data with A Numeric-Symbolic Hybrid Deep Networkcited by 208
  9. 2019Ab-Initio Solution of the Many-Electron Schr"odinger Equation with Deep Neural Networkscited by 195
  10. 2019Data-Driven Deep Learning of Partial Differential Equations in Modal Spacecited by 46
  11. 2021Data-driven peakon and periodic peakon travelling wave solutions of some nonlinear dispersive equations via deep learningcited by 6
  12. 2020Active Importance Sampling for Variational Objectives Dominated by Rare Events: Consequences for Optimization and Generalizationcited by 5
2 more
  1. 2021Deep learning neural networks for the third-order nonlinear Schrodinger equation: Solitons, breathers, and rogue wavescited by 4
  2. 2023Deep learning soliton dynamics and complex potentials recognition for 1D and 2D PT-symmetric saturable nonlinear Schr"odinger equationscited by 3

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 2; 2026: 3.

5 papers.

  1. 2025Convergence and Sketching-Based Efficient Computation of Neural Tangent Kernel Weights in Physics-Based Losscited by 2
  2. 2026Unveiling the Mechanism of Continuous Representation Full-Waveform Inversion: A Wave Based Neural Tangent Kernel Frameworkcited by 1
  3. 2025Objective Value Change and Shape-Based Accelerated Optimization for the Neural Network Approximationcited by 0
  4. 2026Pseudo-differential-enhanced physics-informed neural networkscited by 0
  5. 2026Deciphering Neural Reparameterized Full-Waveform Inversion with Neural Sensitivity Kernel and Wave Tangent Kernelcited by 0