mlsanityData to 7 Oct 2026

Separable Physics-Informed Neural Networks for the solution of elasticity problems

arXiv 2401.13486 ↗First posted 24 Jan 2024math.NA cs.AI cs.LGcited by 5

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Abstract (arXiv)

A method for solving elasticity problems based on separable physics-informed neural networks (SPINN) in conjunction with the deep energy method (DEM) is presented. Numerical experiments have been carried out for a number of problems showing that this method has a significantly higher convergence rate and accuracy than the vanilla physics-informed neural networks (PINN) and even SPINN based on a system of partial differential equations (PDEs). In addition, using the SPINN in the framework of DEM approach it is possible to solve problems of the linear theory of elasticity on complex geometries, which is unachievable with the help of PINNs in frames of partial differential equations. Considered problems are very close to the industrial problems in terms of geometry, loading, and material parameters.

Key facts. Cited by 5 papers in the map (data through 7 Oct 2026). Builds on 22 of its 55 references that are in the map. First posted on arXiv 24 Jan 2024.

Builds on

22 of 55 references.

References · 22

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10 more
  1. 2022Respecting causality is all you need for training physics-informed neural networkscited by 154
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Cited by year

Citing papers per year: 2024: 3; 2025: 2.

5 papers.

  1. 2024Separable Operator Networkscited by 4
  2. 2024Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks?cited by 3
  3. 2025Heterogeneous Graph Representation of Stiffened Panels with Non-Uniform Boundary Conditions and Loadscited by 2
  4. 2024About rectified sigmoid function for enhancing the accuracy of Physics-Informed Neural Networkscited by 0
  5. 2025A decomposition-based robust training of physics-informed neural networks for nearly incompressible linear elasticitycited by 0