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

arXiv: https://arxiv.org/abs/2401.13486 · HTML: https://mlsanity.com/paper/2401.13486/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 55 references that are in the map.
- First posted on arXiv 24 Jan 2024.

## Builds on (most cited first, 22 of 22)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Zero-Shot Text-to-Image Generation](https://mlsanity.com/paper/2102.12092/) (2021)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Mastering Atari, Go, Chess and Shogi by Planning with a Learned Model](https://mlsanity.com/paper/1911.08265/) (2019)
- [Transformers in Vision: A Survey](https://mlsanity.com/paper/2101.01169/) (2021)
- [When and why PINNs fail to train: A neural tangent kernel perspective](https://mlsanity.com/paper/2007.14527/) (2020)
- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [Physics-informed neural networks (PINNs) for fluid mechanics: A review](https://mlsanity.com/paper/2105.09506/) (2021)
- [Fourier Neural Operator with Learned Deformations for PDEs on General Geometries](https://mlsanity.com/paper/2207.05209/) (2022)
- [B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Data](https://mlsanity.com/paper/2003.06097/) (2020)
- [Learning Deep Transformer Models for Machine Translation](https://mlsanity.com/paper/1906.01787/) (2019)
- [hp-VPINNs: Variational Physics-Informed Neural Networks With Domain Decomposition](https://mlsanity.com/paper/2003.05385/) (2020)
- [Respecting causality is all you need for training physics-informed neural networks](https://mlsanity.com/paper/2203.07404/) (2022)
- [An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applications](https://mlsanity.com/paper/1908.10407/) (2019)
- [Estimates on the generalization error of Physics Informed Neural Networks (PINNs) for approximating a class of inverse problems for PDEs](https://mlsanity.com/paper/2007.01138/) (2020)
- [Tensor2Tensor for Neural Machine Translation](https://mlsanity.com/paper/1803.07416/) (2018)
- [Physics-Informed Neural Networks for Multiphysics Data Assimilation with Application to Subsurface Transport](https://mlsanity.com/paper/1912.02968/) (2019)
- [Adversarial Text-to-Image Synthesis: A Review](https://mlsanity.com/paper/2101.09983/) (2021)
- [nPINNs: nonlocal Physics-Informed Neural Networks for a parametrized nonlocal universal Laplacian operator. Algorithms and Applications](https://mlsanity.com/paper/2004.04276/) (2020)
- [ViTO: Vision Transformer-Operator](https://mlsanity.com/paper/2303.08891/) (2023)
- [Mixed formulation of physics-informed neural networks for thermo-mechanically coupled systems and heterogeneous domains](https://mlsanity.com/paper/2302.04954/) (2023)
- [About optimal loss function for training physics-informed neural networks under respecting causality](https://mlsanity.com/paper/2304.02282/) (2023)

## Built on by (most cited first, 6 of 6)

- [Separable Operator Networks](https://mlsanity.com/paper/2407.11253/) (2024)
- [Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks?](https://mlsanity.com/paper/2412.19235/) (2024)
- [Heterogeneous Graph Representation of Stiffened Panels with Non-Uniform Boundary Conditions and Loads](https://mlsanity.com/paper/2510.02472/) (2025)
- [About rectified sigmoid function for enhancing the accuracy of Physics-Informed Neural Networks](https://mlsanity.com/paper/2412.20851/) (2024)
- [A decomposition-based robust training of physics-informed neural networks for nearly incompressible linear elasticity](https://mlsanity.com/paper/2505.21994/) (2025)
- [S2-PINN: Stochastic Separable Physics-Informed Neural Networks](https://mlsanity.com/paper/2610.03303/) (2026)

## 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.