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About rectified sigmoid function for enhancing the accuracy of Physics-Informed Neural Networks

arXiv 2412.20851 ↗First posted 30 Dec 2024math.NA cs.AI cs.LGcited by 0

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Abstract (arXiv)

The article is devoted to the study of neural networks with one hidden layer and a modified activation function for solving physical problems. A rectified sigmoid activation function has been proposed to solve physical problems described by the ODE with neural networks. Algorithms for physics-informed data-driven initialization of a neural network and a neuron-by-neuron gradient-free fitting method have been presented for the neural network with this activation function. Numerical experiments demonstrate the superiority of neural networks with a rectified sigmoid function over neural networks with a sigmoid function in the accuracy of solving physical problems (harmonic oscillator, relativistic slingshot, and Lorentz system).

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References · 15

  1. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,305
  2. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 2,018
  3. 2022Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's nextcited by 608
  4. 2021Physics-informed neural networks (PINNs) for fluid mechanics: A reviewcited by 473
  5. 2017Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equationscited by 373
  6. 2020B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Datacited by 335
  7. 2020hp-VPINNs: Variational Physics-Informed Neural Networks With Domain Decompositioncited by 236
  8. 2022Respecting causality is all you need for training physics-informed neural networkscited by 156
  9. 2024PirateNets: Physics-informed Deep Learning with Residual Adaptive Networkscited by 72
  10. 2023AI-Aristotle: A Physics-Informed framework for Systems Biology Gray-Box Identificationcited by 29
  11. 2024Three Decades of Activations: A Comprehensive Survey of 400 Activation Functions for Neural Networkscited by 23
  12. 2023About optimal loss function for training physics-informed neural networks under respecting causalitycited by 6
3 more
  1. 2024Separable Physics-Informed Neural Networks for the solution of elasticity problemscited by 6
  2. 2024Element-wise Multiplication Based Deeper Physics-Informed Neural Networkscited by 3
  3. 2024Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks?cited by 3

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