# A POD-TANN approach for the multiscale modeling of materials and macroelement derivation in geomechanics

arXiv: https://arxiv.org/abs/2408.07165 · HTML: https://mlsanity.com/paper/2408.07165/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 52 references that are in the map.
- First posted on arXiv 13 Aug 2024.

## Builds on (most cited first, 10 of 10)

- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [POD-DL-ROM: enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition](https://mlsanity.com/paper/2101.11845/) (2021)
- [Interfacing Finite Elements with Deep Neural Operators for Fast Multiscale Modeling of Mechanics Problems](https://mlsanity.com/paper/2203.00003/) (2022)
- [Automated discovery of generalized standard material models with EUCLID](https://mlsanity.com/paper/2211.04453/) (2022)
- [Reduced order modeling of parametrized systems through autoencoders and SINDy approach: continuation of periodic solutions](https://mlsanity.com/paper/2211.06786/) (2022)
- [Multiscale modeling of inelastic materials with Thermodynamics-based Artificial Neural Networks (TANN)](https://mlsanity.com/paper/2108.13137/) (2021)
- [Thermodynamically Consistent Machine-Learned Internal State Variable Approach for Data-Driven Modeling of Path-Dependent Materials](https://mlsanity.com/paper/2205.00578/) (2022)
- [Thermodynamics of learning physical phenomena](https://mlsanity.com/paper/2207.12749/) (2022)
- [Evolution TANN and the identification of internal variables and evolution equations in solid mechanics](https://mlsanity.com/paper/2209.13269/) (2022)
- [VENI, VINDy, VICI: a generative reduced-order modeling framework with uncertainty quantification](https://mlsanity.com/paper/2405.20905/) (2024)

## Built on by (most cited first, 1 of 1)

- [EPi-cKANs: Elasto-Plasticity Informed Kolmogorov-Arnold Networks Using Chebyshev Polynomials](https://mlsanity.com/paper/2410.10897/) (2024)

## Abstract (arXiv)

This paper introduces a novel approach that combines Proper Orthogonal Decomposition (POD) with Thermodynamics-based Artificial Neural Networks (TANN) to capture the macroscopic behavior of complex inelastic systems and derive macroelements in geomechanics. The methodology leverages POD to extract macroscopic Internal State Variables from microscopic state information, thereby enriching the macroscopic state description used to train an energy potential network within the TANN framework. The thermodynamic consistency provided by TANN, combined with the hierarchical nature of POD, allows to reproduce complex, non-linear inelastic material behaviors as well as macroscopic geomechanical systems responses. The approach is validated through applications of increasing complexity, demonstrating its capability to reproduce high-fidelity simulation data. The applications proposed include the homogenization of continuous inelastic representative unit cells and the derivation of a macroelement for a geotechnical system involving a monopile in a clay layer subjected to horizontal loading. Eventually, the projection operators directly obtained via POD, are exploit to easily reconstruct the microscopic fields. The results indicate that the POD-TANN approach not only offers accuracy in reproducing the studied constitutive responses, but also reduces computational costs, making it a practical tool for the multiscale modeling of heterogeneous inelastic geomechanical systems.