mlsanityData to 7 Oct 2026

A Physics Informed Neural Network Approach to Solution and Identification of Biharmonic Equations of Elasticity

arXiv 2108.07243 ↗First posted 16 Aug 2021cs.LGcited by 12

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Abstract (arXiv)

We explore an application of the Physics Informed Neural Networks (PINNs) in conjunction with Airy stress functions and Fourier series to find optimal solutions to a few reference biharmonic problems of elasticity and elastic plate theory. Biharmonic relations are fourth-order partial differential equations (PDEs) that are challenging to solve using classical numerical methods, and have not been addressed using PINNs. Our work highlights a novel application of classical analytical methods to guide the construction of efficient neural networks with the minimal number of parameters that are very accurate and fast to evaluate. In particular, we find that enriching feature space using Airy stress functions can significantly improve the accuracy of PINN solutions for biharmonic PDEs.

Key facts. Cited by 12 papers in the map (data through 7 Oct 2026). Builds on 20 of its 71 references that are in the map. First posted on arXiv 16 Aug 2021.

Builds on

20 of 71 references.

References · 20

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8 more
  1. 2020Machine learning for metal additive manufacturing: Predicting temperature and melt pool fluid dynamics using physics-informed neural networkscited by 42
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Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 1; 2022: 4; 2023: 2; 2024: 1; 2025: 3; 2026: 1.

12 papers.

  1. 2021Physics informed neural networks for continuum micromechanicscited by 46
  2. 2022Physics-Guided, Physics-Informed, and Physics-Encoded Neural Networks in Scientific Computingcited by 24
  3. 2022A physics-informed deep neural network for surrogate modeling in classical elasto-plasticitycited by 14
  4. 2023Theory and implementation of inelastic Constitutive Artificial Neural Networkscited by 12
  5. 2022Physics Informed Neural Network for Dynamic Stress Predictioncited by 6
  6. 2022Reduced-PINN: An Integration-Based Physics-Informed Neural Networks for Stiff ODEscited by 3
  7. 2025Aligning Perception, Reasoning, Modeling and Interaction: A Survey on Physical AIcited by 3
  8. 2023Physics-aware deep learning framework for linear elasticitycited by 2
  9. 2024Stochastic Inference of Plate Bending from Heterogeneous Data: Physics-informed Gaussian Processes via Kirchhoff-Love Theorycited by 1
  10. 2025Collapsing Taylor Mode Automatic Differentiationcited by 1
  11. 2026A holomorphic neural network framework for 3D boundary value problems governed by harmonic potentialscited by 1
  12. 2025Breaking the Precision Ceiling in Physics-Informed Neural Networks: A Hybrid Fourier-Neural Architecture for Ultra-High Accuracycited by 0