mlsanityData to 7 Oct 2026

Feature Mapping in Physics-Informed Neural Networks (PINNs)

arXiv 2402.06955 ↗First posted 10 Feb 2024cs.LG cs.AI cs.CEcited by 2

Not on the map. Why?

Abstract (arXiv)

In this paper, the training dynamics of PINNs with a feature mapping layer via the limiting Conjugate Kernel and Neural Tangent Kernel is investigated, shedding light on the convergence of PINNs; Although the commonly used Fourier-based feature mapping has achieved great success, we show its inadequacy in some physics scenarios. Via these two scopes, we propose conditionally positive definite Radial Basis Function as a better alternative. Lastly, we explore the feature mapping numerically in wide neural networks. Our empirical results reveal the efficacy of our method in diverse forward and inverse problem sets. Composing feature functions is found to be a practical way to address the expressivity and generalisability trade-off, viz., tuning the bandwidth of the kernels and the surjectivity of the feature mapping function. This simple technique can be implemented for coordinate inputs and benefits the broader PINNs research.

Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Builds on 39 of its 64 references that are in the map. First posted on arXiv 10 Feb 2024.

Builds on

39 of 64 references.

References · 39

  1. 2018Neural Tangent Kernel: Convergence and Generalization in Neural Networkscited by 2,597
  2. 2020Implicit Neural Representations with Periodic Activation Functionscited by 2,214
  3. 2020Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domainscited by 2,170
  4. 2018On the Spectral Bias of Neural Networkscited by 1,321
  5. 2019Wide Neural Networks of Any Depth Evolve as Linear Models Under Gradient Descentcited by 732
  6. 2021Characterizing possible failure modes in physics-informed neural networkscited by 632
  7. 2020When and why PINNs fail to train: A neural tangent kernel perspectivecited by 629
  8. 2019DeepXDE: A deep learning library for solving differential equationscited by 617
  9. 2022Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's nextcited by 603
  10. 2021Neural Fields in Visual Computing and Beyondcited by 539
  11. 2018Gaussian Process Behaviour in Wide Deep Neural Networkscited by 314
  12. 2020On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networkscited by 279
27 more
  1. 2020hp-VPINNs: Variational Physics-Informed Neural Networks With Domain Decompositioncited by 236
  2. 2022A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networkscited by 233
  3. 2021Gradient-enhanced physics-informed neural networks for forward and inverse PDE problemscited by 220
  4. 2023WIRE: Wavelet Implicit Neural Representationscited by 220
  5. 2022Respecting causality is all you need for training physics-informed neural networkscited by 154
  6. 2021Finite Basis Physics-Informed Neural Networks (FBPINNs): a scalable domain decomposition approach for solving differential equationscited by 142
  7. 2021Beyond Periodicity: Towards a Unifying Framework for Activations in Coordinate-MLPscited by 134
  8. 2023An Expert's Guide to Training Physics-informed Neural Networkscited by 119
  9. 2021Efficient training of physics-informed neural networks via importance samplingcited by 109
  10. 2023PINNacle: A Comprehensive Benchmark of Physics-Informed Neural Networks for Solving PDEscited by 84
  11. 2020Spectra of the Conjugate Kernel and Neural Tangent Kernel for linear-width neural networkscited by 76
  12. 2022Mitigating Propagation Failures in Physics-informed Neural Networks using Retain-Resample-Release (R3) Samplingcited by 71
  13. 2023PINNsFormer: A Transformer-Based Framework For Physics-Informed Neural Networkscited by 62
  14. 2021Learning in Sinusoidal Spaces with Physics-Informed Neural Networkscited by 61
  15. 2021Meta-learning PINN loss functionscited by 51
  16. 2021Spline-PINN: Approaching PDEs without Data using Fast, Physics-Informed Hermite-Spline CNNscited by 38
  17. 2023Lie Point Symmetry and Physics Informed Networkscited by 24
  18. 2022Is L2 Physics-Informed Loss Always Suitable for Training Physics-Informed Neural Network?cited by 23
  19. 2022Unravelling the Performance of Physics-informed Graph Neural Networks for Dynamical Systemscited by 23
  20. 2021PhysGNN: A Physics-Driven Graph Neural Network Based Model for Predicting Soft Tissue Deformation in Image-Guided Neurosurgerycited by 22
  21. 2022NTFields: Neural Time Fields for Physics-Informed Robot Motion Planningcited by 22
  22. 2021Spline Positional Encoding for Learning 3D Implicit Signed Distance Fieldscited by 21
  23. 2022Trading Positional Complexity vs. Deepness in Coordinate Networkscited by 16
  24. 2022State-of-the-Art Review of Design of Experiments for Physics-Informed Deep Learningcited by 12
  25. 2021Learning Positional Embeddings for Coordinate-MLPscited by 7
  26. 2022Meta Learning of Interface Conditions for Multi-Domain Physics-Informed Neural Networkscited by 6
  27. 2021Physics-Aware Downsampling with Deep Learning for Scalable Flood Modelingcited by 4

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 1; 2025: 0; 2026: 1.

2 papers.

  1. 2024Functional Tensor Decompositions for Physics-Informed Neural Networkscited by 11
  2. 2026High-Fidelity Modeling of Stochastic Chemical Dynamics on Complex Manifolds: A Multi-Scale SIREN-PINN Framework for the Curvature-Perturbed Ginzburg-Landau Equationcited by 0