# Deep autoencoders for physics-constrained data-driven nonlinear materials modeling

arXiv: https://arxiv.org/abs/2209.04416 · HTML: https://mlsanity.com/paper/2209.04416/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 64 references that are in the map.
- First posted on arXiv 3 Sep 2022.

## Builds on (most cited first, 7 of 7)

- [A deep material network for multiscale topology learning and accelerated nonlinear modeling of heterogeneous materials](https://mlsanity.com/paper/1807.09829/) (2018)
- [Model-Free Data-Driven Inelasticity](https://mlsanity.com/paper/1808.10859/) (2018)
- [Diffusion Nets](https://mlsanity.com/paper/1506.07840/) (2015)
- [A Physics-Constrained Data-Driven Approach Based on Locally Convex Reconstruction for Noisy Database](https://mlsanity.com/paper/1907.12651/) (2019)
- [Exploring the 3D architectures of deep material network in data-driven multiscale mechanics](https://mlsanity.com/paper/1901.04832/) (2019)
- [Model-Free Data-Driven Methods in Mechanics: Material Data Identification and Solvers](https://mlsanity.com/paper/1903.07983/) (2019)
- [Model-free Data-Driven Computational Mechanics Enhanced by Tensor Voting](https://mlsanity.com/paper/2004.02503/) (2020)

## Built on by (most cited first, 13 of 13)

- [A review on data-driven constitutive laws for solids](https://mlsanity.com/paper/2405.03658/) (2024)
- [MeLM, a generative pretrained language modeling framework that solves forward and inverse mechanics problems](https://mlsanity.com/paper/2306.17525/) (2023)
- [Solving engineering eigenvalue problems with neural networks using the Rayleigh quotient](https://mlsanity.com/paper/2506.04375/) (2025)
- [LS-DYNA Machine Learning-based Multiscale Method for Nonlinear Modeling of Short Fiber-Reinforced Composites](https://mlsanity.com/paper/2301.02738/) (2023)
- [A Multi-Resolution Physics-Informed Recurrent Neural Network: Formulation and Application to Musculoskeletal Systems](https://mlsanity.com/paper/2305.16593/) (2023)
- [History-Aware Neural Operator: Robust Data-Driven Constitutive Modeling of Path-Dependent Materials](https://mlsanity.com/paper/2506.10352/) (2025)
- [A Neural Network-Based Enrichment of Reproducing Kernel Approximation for Modeling Brittle Fracture](https://mlsanity.com/paper/2307.01937/) (2023)
- [Neural-Integrated Meshfree (NIM) Method: A differentiable programming-based hybrid solver for computational mechanics](https://mlsanity.com/paper/2311.12915/) (2023)
- [RefreshNet: Learning Multiscale Dynamics through Hierarchical Refreshing](https://mlsanity.com/paper/2401.13282/) (2024)
- [N-Adaptive Ritz Method: A Neural Network Enriched Partition of Unity for Boundary Value Problems](https://mlsanity.com/paper/2401.08544/) (2024)
- [Data-Driven Modeling of an Unsaturated Bentonite Buffer Model Test Under High Temperatures Using an Enhanced Axisymmetric Reproducing Kernel Particle Method](https://mlsanity.com/paper/2309.13519/) (2023)
- [A thermodynamically consistent physics-informed deep learning material model for short fiber/polymer nanocomposites](https://mlsanity.com/paper/2403.18310/) (2024)
- [Systematic Performance Assessment of Deep Material Networks for Multiscale Material Modeling](https://mlsanity.com/paper/2602.07192/) (2026)

## Abstract (arXiv)

Physics-constrained data-driven computing is an emerging computational paradigm that allows simulation of complex materials directly based on material database and bypass the classical constitutive model construction. However, it remains difficult to deal with high-dimensional applications and extrapolative generalization. This paper introduces deep learning techniques under the data-driven framework to address these fundamental issues in nonlinear materials modeling. To this end, an autoencoder neural network architecture is introduced to learn the underlying low-dimensional representation (embedding) of the given material database. The offline trained autoencoder and the discovered embedding space are then incorporated in the online data-driven computation such that the search of optimal material state from database can be performed on a low-dimensional space, aiming to enhance the robustness and predictability with projected material data. To ensure numerical stability and representative constitutive manifold, a convexity-preserving interpolation scheme tailored to the proposed autoencoder-based data-driven solver is proposed for constructing the material state. In this study, the applicability of the proposed approach is demonstrated by modeling nonlinear biological tissues. A parametric study on data noise, data size and sparsity, training initialization, and model architectures, is also conducted to examine the robustness and convergence property of the proposed approach.