# Automatically Differentiable Model Updating (ADiMU): conventional, hybrid, and neural network material model discovery including history-dependency

arXiv: https://arxiv.org/abs/2505.07801 · HTML: https://mlsanity.com/paper/2505.07801/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 77 references that are in the map.
- First posted on arXiv 12 May 2025.

## Builds on (most cited first, 12 of 12)

- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [Input Convex Neural Networks](https://mlsanity.com/paper/1609.07152/) (2016)
- [MechAgents: Large language model multi-agent collaborations can solve mechanics problems, generate new data, and integrate knowledge](https://mlsanity.com/paper/2311.08166/) (2023)
- [A deep material network for multiscale topology learning and accelerated nonlinear modeling of heterogeneous materials](https://mlsanity.com/paper/1807.09829/) (2018)
- [NN-EUCLID: deep-learning hyperelasticity without stress data](https://mlsanity.com/paper/2205.06664/) (2022)
- [MeLM, a generative pretrained language modeling framework that solves forward and inverse mechanics problems](https://mlsanity.com/paper/2306.17525/) (2023)
- [Thermodynamically Consistent Machine-Learned Internal State Variable Approach for Data-Driven Modeling of Path-Dependent Materials](https://mlsanity.com/paper/2205.00578/) (2022)
- [A physics-informed deep neural network for surrogate modeling in classical elasto-plasticity](https://mlsanity.com/paper/2204.12088/) (2022)
- [Neural networks meet anisotropic hyperelasticity: A framework based on generalized structure tensors and isotropic tensor functions](https://mlsanity.com/paper/2410.03378/) (2024)
- [Cooperative data-driven modeling](https://mlsanity.com/paper/2211.12971/) (2022)
- [Consistent machine learning for topology optimization with microstructure-dependent neural network material models](https://mlsanity.com/paper/2408.13843/) (2024)
- [Calibration of Elastoplastic Constitutive Model Parameters from Full-field Data with Automatic Differentiation-based Sensitivities](https://mlsanity.com/paper/2010.03649/) (2020)

## Built on by (most cited first, 5 of 5)

- [Towards Rapid Constitutive Model Discovery from Multi-Modal Data: Physics Augmented Finite Element Model Updating (paFEMU)](https://mlsanity.com/paper/2604.07746/) (2026)
- [COMMET: orders-of-magnitude speed-up in finite element method via batch-vectorized neural constitutive updates](https://mlsanity.com/paper/2510.00884/) (2025)
- [Hyperelastic constitutive model discovery with differentiable finite elements and structure-preserving neural networks](https://mlsanity.com/paper/2603.26517/) (2026)
- [Single- to multi-fidelity history-dependent learning with uncertainty quantification and disentanglement: application to data-driven constitutive modeling](https://mlsanity.com/paper/2507.13416/) (2025)
- [Constitutive State-Space Modeling of Path-Dependent Plasticity: A Resolution-Consistent and Parallelizable Computational Framework](https://mlsanity.com/paper/2609.07294/) (2026)

## Abstract (arXiv)

We introduce the first Automatically Differentiable Model Updating (ADiMU) framework that finds any history-dependent material model from full-field displacement and global force data (global, indirect discovery) or from strain-stress data (local, direct discovery). We show that ADiMU can update conventional (physics-based), neural network (data-driven), and hybrid material models. Moreover, this framework requires no fine-tuning of hyperparameters or additional quantities beyond those inherent to the user-selected material model architecture and optimizer. The robustness and versatility of ADiMU is extensively exemplified by updating different models spanning tens to millions of parameters, in both local and global discovery settings. Relying on fully differentiable code, the algorithmic implementation leverages vectorizing maps that enable history-dependent automatic differentiation via efficient batched execution of shared computation graphs. This contribution also aims to facilitate the integration, evaluation and application of future material model architectures by openly supporting the research community. Therefore, ADiMU is released as an open-source computational tool, integrated into a carefully designed and documented software named HookeAI.