# Model-Free Data-Driven Methods in Mechanics: Material Data Identification and Solvers

arXiv: https://arxiv.org/abs/1903.07983 · HTML: https://mlsanity.com/paper/1903.07983/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Mar 2019.

## Built on by (most cited first, 7 of 7)

- [Learning Deep Implicit Fourier Neural Operators (IFNOs) with Applications to Heterogeneous Material Modeling](https://mlsanity.com/paper/2203.08205/) (2022)
- [A review on data-driven constitutive laws for solids](https://mlsanity.com/paper/2405.03658/) (2024)
- [Recent Advances and Applications of Machine Learning in Experimental Solid Mechanics: A Review](https://mlsanity.com/paper/2303.07647/) (2023)
- [Deep autoencoders for physics-constrained data-driven nonlinear materials modeling](https://mlsanity.com/paper/2209.04416/) (2022)
- [Stress representations for tensor basis neural networks: alternative formulations to Finger-Rivlin-Ericksen](https://mlsanity.com/paper/2308.11080/) (2023)
- [A Complement to Neural Networks for Anisotropic Inelasticity at Finite Strains](https://mlsanity.com/paper/2510.04187/) (2025)
- [Hyperelastic constitutive model discovery with differentiable finite elements and structure-preserving neural networks](https://mlsanity.com/paper/2603.26517/) (2026)

## Abstract (arXiv)

This paper presents an integrated model-free data-driven approach to solid mechanics, allowing to perform numerical simulations on structures on the basis of measures of displacement fields on representative samples, without postulating a specific constitutive model. A material data identification procedure, allowing to infer strain-stress pairs from displacement fields and boundary conditions, is used to build a material database from a set of mutiaxial tests on a non-conventional sample. This database is in turn used by a data-driven solver, based on an algorithm minimizing the distance between manifolds of compatible and balanced mechanical states and the given database, to predict the response of structures of the same material, with arbitrary geometry and boundary conditions. Examples illustrate this modelling cycle and demonstrate how the data-driven identification method allows importance sampling of the material state space, yielding faster convergence of simulation results with increasing database size, when compared to synthetic material databases with regular sampling patterns.