mlsanityData to 14 Oct 2026

Complex Physics-Informed Neural Network

arXiv 2502.04917 ↗First posted 7 Feb 2025cs.LG cs.AIcited by 7

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Abstract (arXiv)

We propose compleX-PINN, a novel physics-informed neural network (PINN) architecture incorporating a learnable activation function inspired by the Cauchy integral theorem. By optimizing the activation parameters, compleX-PINN achieves high accuracy with just a single hidden layer. Empirically, we demonstrate that compleX-PINN solves high-dimensional problems that pose significant challenges for PINNs. Our results show that compleX-PINN consistently achieves substantially greater precision, often improving accuracy by an order of magnitude, on these complex tasks.

Key facts. Cited by 7 papers in the map (data through 14 Oct 2026). Builds on 31 of its 57 references that are in the map. First posted on arXiv 7 Feb 2025.

Builds on

31 of 57 references.

References · 31

  1. 2024KAN: Kolmogorov-Arnold Networkscited by 649
  2. 2021Characterizing possible failure modes in physics-informed neural networkscited by 643
  3. 2020When and why PINNs fail to train: A neural tangent kernel perspectivecited by 634
  4. 2019DeepXDE: A deep learning library for solving differential equationscited by 619
  5. 2021Physics-informed neural networks (PINNs) for fluid mechanics: A reviewcited by 473
  6. 2020B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Datacited by 335
  7. 2020On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networkscited by 284
  8. 2022A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networkscited by 236
  9. 2020Self-Adaptive Physics-Informed Neural Networks using a Soft Attention Mechanismcited by 233
  10. 2021Gradient-enhanced physics-informed neural networks for forward and inverse PDE problemscited by 222
  11. 2018Physics-Informed Generative Adversarial Networks for Stochastic Differential Equationscited by 135
  12. 2018Adversarial Uncertainty Quantification in Physics-Informed Neural Networkscited by 120
19 more
  1. 2021Parallel Physics-Informed Neural Networks via Domain Decompositioncited by 112
  2. 2024A comprehensive and FAIR comparison between MLP and KAN representations for differential equations and operator networkscited by 104
  3. 2023Tackling the Curse of Dimensionality with Physics-Informed Neural Networkscited by 79
  4. 2022Physics-informed neural networks for inverse problems in supersonic flowscited by 76
  5. 2022Mitigating Propagation Failures in Physics-informed Neural Networks using Retain-Resample-Release (R3) Samplingcited by 73
  6. 2023Residual-based attention in physics-informed neural networkscited by 72
  7. 2024PirateNets: Physics-informed Deep Learning with Residual Adaptive Networkscited by 72
  8. 2024Kolmogorov Arnold Informed neural network: A physics-informed deep learning framework for solving forward and inverse problems based on Kolmogorov Arnold Networkscited by 67
  9. 2022Failure-informed adaptive sampling for PINNscited by 64
  10. 2023PINNsFormer: A Transformer-Based Framework For Physics-Informed Neural Networkscited by 64
  11. 2022Augmented Physics-Informed Neural Networks (APINNs): A gating network-based soft domain decomposition methodologycited by 44
  12. 2022Enhanced Physics-Informed Neural Networks with Augmented Lagrangian Relaxation Method (AL-PINNs)cited by 35
  13. 2022How important are activation functions in regression and classification? A survey, performance comparison, and future directionscited by 29
  14. 2021Stochastic Physics-Informed Neural Ordinary Differential Equationscited by 19
  15. 2024Initialization-enhanced Physics-Informed Neural Network with Domain Decomposition (IDPINN)cited by 9
  16. 2024Binary structured physics-informed neural networks for solving equations with rapidly changing solutionscited by 8
  17. 2024Cauchy activation function and XNetcited by 5
  18. 2024Quantifying Training Difficulty and Accelerating Convergence in Neural Network-Based PDE Solverscited by 4
  19. 2024Two-stage initial-value iterative physics-informed neural networks for simulating solitary waves of nonlinear wave equationscited by 2

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 3; 2026: 4.

7 papers.

  1. 2025Convolution-weighting method for the physics-informed neural network: A Primal-Dual Optimization Perspectivecited by 6
  2. 2025Kolmogorov-Arnold Representation for Symplectic Learning: Advancing Hamiltonian Neural Networkscited by 0
  3. 2025AutoBalance: An Automatic Balancing Framework for Training Physics-Informed Neural Networkscited by 0
  4. 2026Trainable Spline Representations for Physics-Informed Learningcited by 0
  5. 2026From Non-Convex Self-Concordant Regularization to Scalable Quasi-Newton Training of PINNscited by 0
  6. 2026Alternating Levenberg-Marquardt Training of Physics-Informed Neural Networks with Fourier-Enhanced Featurescited by 0
  7. 2026Hierarchical rank-evolving representation for physics-informed neural networkscited by 0