mlsanityData to 7 Oct 2026

Energy-based error bound of physics-informed neural network solutions in elasticity

arXiv 2010.09088 ↗First posted 18 Oct 2020math.NA cs.LG cs.NAcited by 15

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Abstract (arXiv)

An energy-based a posteriori error bound is proposed for the physics-informed neural network solutions of elasticity problems. An admissible displacement-stress solution pair is obtained from a mixed form of physics-informed neural networks, and the proposed error bound is formulated as the constitutive relation error defined by the solution pair. Such an error estimator provides an upper bound of the global error of neural network discretization. The bounding property, as well as the asymptotic behavior of the physics-informed neural network solutions, are studied in a demonstrating example.

Key facts. Cited by 15 papers in the map (data through 7 Oct 2026). First posted on arXiv 18 Oct 2020.

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Citing papers per year: 2021: 4; 2022: 2; 2023: 1; 2024: 5; 2025: 2; 2026: 1.

15 papers.

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  1. 2021Physics informed neural networks for continuum micromechanicscited by 46
  2. 2022A mixed formulation for physics-informed neural networks as a potential solver for engineering problems in heterogeneous domains: comparison with finite element methodcited by 33
  3. 2021Physics-informed neural network simulation of multiphase poroelasticity using stress-split sequential trainingcited by 26
  4. 2022Constitutive model characterization and discovery using physics-informed deep learningcited by 17
  5. 2021A Physics Informed Neural Network Approach to Solution and Identification of Biharmonic Equations of Elasticitycited by 12
  6. 2024Preconditioning for Physics-Informed Neural Networkscited by 12
  7. 2021Non-intrusive reduced order modeling of poroelasticity of heterogeneous media based on a discontinuous Galerkin approximationcited by 6
  8. 2025Improved Uncertainty Quantification in Physics-Informed Neural Networks Using Error Bounds and Solution Bundlescited by 3
  9. 2023Physics-aware deep learning framework for linear elasticitycited by 2
  10. 2024Stochastic Inference of Plate Bending from Heterogeneous Data: Physics-informed Gaussian Processes via Kirchhoff-Love Theorycited by 1
  11. 2024Astral: training physics-informed neural networks with error majorantscited by 1
  12. 2024Parsimonious Universal Function Approximator for Elastic and Elasto-Plastic Cavity Expansion Problemscited by 1
3 more
  1. 2024Geometry-aware framework for deep energy method: an application to structural mechanics with hyperelastic materialscited by 0
  2. 2025A decomposition-based robust training of physics-informed neural networks for nearly incompressible linear elasticitycited by 0
  3. 2026Reliable Error Estimation for PINNs: Lower and Upper A Posteriori Boundscited by 0