mlsanityData to 7 Oct 2026

ST-PINN: A Self-Training Physics-Informed Neural Network for Partial Differential Equations

arXiv 2306.09389 ↗First posted 15 Jun 2023cs.LG cs.AI physics.comp-phcited by 6

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Abstract (arXiv)

Partial differential equations (PDEs) are an essential computational kernel in physics and engineering. With the advance of deep learning, physics-informed neural networks (PINNs), as a mesh-free method, have shown great potential for fast PDE solving in various applications. To address the issue of low accuracy and convergence problems of existing PINNs, we propose a self-training physics-informed neural network, ST-PINN. Specifically, ST-PINN introduces a pseudo label based self-learning algorithm during training. It employs governing equation as the pseudo-labeled evaluation index and selects the highest confidence examples from the sample points to attach the pseudo labels. To our best knowledge, we are the first to incorporate a self-training mechanism into physics-informed learning. We conduct experiments on five PDE problems in different fields and scenarios. The results demonstrate that the proposed method allows the network to learn more physical information and benefit convergence. The ST-PINN outperforms existing physics-informed neural network methods and improves the accuracy by a factor of 1.33x-2.54x. The code of ST-PINN is available at GitHub: https://github.com/junjun-yan/ST-PINN.

Key facts. Cited by 6 papers in the map (data through 7 Oct 2026). Builds on 15 of its 33 references that are in the map. First posted on arXiv 15 Jun 2023.

Builds on

15 of 33 references.

References · 15

  1. 2020When and why PINNs fail to train: A neural tangent kernel perspectivecited by 629
  2. 2019DeepXDE: A deep learning library for solving differential equationscited by 617
  3. 2021Physics-informed neural networks (PINNs) for fluid mechanics: A reviewcited by 470
  4. 2021Semi-Supervised Semantic Segmentation with Cross Pseudo Supervisioncited by 462
  5. 2022PDEBENCH: An Extensive Benchmark for Scientific Machine Learningcited by 396
  6. 2020Rethinking Pre-training and Self-trainingcited by 352
  7. 2020B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Datacited by 329
  8. 2022A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networkscited by 233
  9. 2021Gradient-enhanced physics-informed neural networks for forward and inverse PDE problemscited by 220
  10. 2020Estimates on the generalization error of Physics Informed Neural Networks (PINNs) for approximating a class of inverse problems for PDEscited by 101
  11. 2022Generic bounds on the approximation error for physics-informed (and) operator learningcited by 65
  12. 2020On the convergence of physics informed neural networks for linear second-order elliptic and parabolic type PDEscited by 31
3 more
  1. 2020Teaching the Incompressible Navier-Stokes Equations to Fast Neural Surrogate Models in 3Dcited by 26
  2. 2021Physics-informed Spline Learning for Nonlinear Dynamics Discoverycited by 18
  3. 2020Physics-aware Spatiotemporal Modules with Auxiliary Tasks for Meta-Learningcited by 7

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 3; 2024: 0; 2025: 2; 2026: 1.

6 papers.

  1. 2023Auxiliary-Tasks Learning for Physics-Informed Neural Network-Based Partial Differential Equations Solvingcited by 2
  2. 2025Gradient Enhanced Self-Training Physics-Informed Neural Network (gST-PINN) for Solving Nonlinear Partial Differential Equationscited by 1
  3. 2025PHANTOM: Physics-Aware Adversarial Attacks against Federated Learning-Coordinated EV Charging Management Systemcited by 1
  4. 2023Enhancing Convergence Speed with Feature-Enforcing Physics-Informed Neural Networks: Utilizing Boundary Conditions as Prior Knowledge for Faster Convergencecited by 0
  5. 2023Can Physics Informed Neural Operators Self Improve?cited by 0
  6. 2026Physics and Data Driven Transformer-Mamba Framework for Flow Fieldcited by 0