# Adaptivity for clustering-based reduced-order modeling of localized history-dependent phenomena

arXiv: https://arxiv.org/abs/2109.11897 · HTML: https://mlsanity.com/paper/2109.11897/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 0 of its 108 references that are in the map.
- First posted on arXiv 24 Sep 2021.

## Built on by (most cited first, 3 of 3)

- [An Introduction to Kernel and Operator Learning Methods for Homogenization by Self-consistent Clustering Analysis](https://mlsanity.com/paper/2212.00802/) (2022)
- [Practical multi-fidelity machine learning: fusion of deterministic and Bayesian models](https://mlsanity.com/paper/2407.15110/) (2024)
- [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)

## Abstract (arXiv)

This paper proposes a novel Adaptive Clustering-based Reduced-Order Modeling (ACROM) framework to significantly improve and extend the recent family of clustering-based reduced-order models (CROMs). This adaptive framework enables the clustering-based domain decomposition to evolve dynamically throughout the problem solution, ensuring optimum refinement in regions where the relevant fields present steeper gradients. It offers a new route to fast and accurate material modeling of history-dependent nonlinear problems involving highly localized plasticity and damage phenomena. The overall approach is composed of three main building blocks: target clusters selection criterion, adaptive cluster analysis, and computation of cluster interaction tensors. In addition, an adaptive clustering solution rewinding procedure and a dynamic adaptivity split factor strategy are suggested to further enhance the adaptive process. The coined Adaptive Self-Consistent Clustering Analysis (ASCA) is shown to perform better than its static counterpart when capturing the multi-scale elasto-plastic behavior of a particle-matrix composite and predicting the associated fracture and toughness. Given the encouraging results shown in this paper, the ACROM framework sets the stage and opens new avenues to explore adaptivity in the context of CROMs.