Towards Rapid Constitutive Model Discovery from Multi-Modal Data: Physics Augmented Finite Element Model Updating (paFEMU)

• URL: http://arxiv.org/abs/2604.07746v1
• Date: Thu, 09 Apr 2026 03:08:07 GMT
• Title: Towards Rapid Constitutive Model Discovery from Multi-Modal Data: Physics Augmented Finite Element Model Updating (paFEMU)
• Abstract summary: We introduce physics augmented finite element model updating (paFEMU), as a transfer learning approach that combines AI-enabled modeling, sparsification for interpretable model discovery, and finite element-based augmentation.<n>This is achieved by combining simple mechanical testing data, potentially from a distinct material, with digital image correlation-type full-field data acquisition.
• Score: 0.3199881502576702
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Recent progress in AI-enabled constitutive modeling has concentrated on moving from a purely data-driven paradigm to the enforcement of physical constraints and mechanistic principles, a concept referred to as physics augmentation. Classical phenomenological approaches rely on selecting a pre-defined model and calibrating its parameters, while machine learning methods often focus on discovery of the model itself. Sparse regression approaches lie in between, where large libraries of pre-defined models are probed during calibration. Sparsification in the aforementioned paradigm, but also in the context of neural network architecture, has been shown to enable interpretability, uncertainty quantification, but also heterogeneous software integration due to the low-dimensional nature of the resulting models. Most works in AI-enabled constitutive modeling have also focused on data from a single source, but in reality, materials modeling workflows can contain data from many different sources (multi-modal data), and also from testing other materials within the same materials class (multi-fidelity data). In this work, we introduce physics augmented finite element model updating (paFEMU), as a transfer learning approach that combines AI-enabled constitutive modeling, sparsification for interpretable model discovery, and finite element-based adjoint optimization utilizing multi-modal data. This is achieved by combining simple mechanical testing data, potentially from a distinct material, with digital image correlation-type full-field data acquisition to ultimately enable rapid constitutive modeling discovery. The simplicity of the sparse representation enables easy integration of neural constitutive models in existing finite element workflows, and also enables low-dimensional updating during transfer learning.

Related papers

• How Can AI Find My Model? A Model-Finding Experimental Study Considering Data Formats, Embeddings, and Retrieval Strategies [0.0]
  We present an experimental study investigating the impact of data representation, transformer-based embedding models, and retrieval strategies on the discovery of simulation models using natural language queries.<n>Results show that data representation matters, open-source embedding models can achieve high performance, and reranking methods are important, especially as query increases.
  arXiv  Detail & Related papers  (2026-06-29T19:23:32Z)
• Monotone Peridynamic Neural Operator for Nonlinear Material Modeling with Conditionally Unique Solutions [8.178003326156418]
  We introduce monotone peridynamic neural operator (MPNO), a novel data-driven nonlocal model learning approach based on neural operators.<n>MPNO learns a nonlocal kernel together with a nonlinear relation, while ensuring solution uniqueness through a monotone gradient network.<n>We show that MPNO exhibits superior generalization capabilities than the conventional neural networks.
  arXiv  Detail & Related papers  (2025-05-02T07:10:31Z)
• Generalized Factor Neural Network Model for High-dimensional Regression [50.554377879576066]
  We tackle the challenges of modeling high-dimensional data sets with latent low-dimensional structures hidden within complex, non-linear, and noisy relationships.<n>Our approach enables a seamless integration of concepts from non-parametric regression, factor models, and neural networks for high-dimensional regression.
  arXiv  Detail & Related papers  (2025-02-16T23:13:55Z)
• Discovering Interpretable Physical Models using Symbolic Regression and Discrete Exterior Calculus [55.2480439325792]
  We propose a framework that combines Symbolic Regression (SR) and Discrete Exterior Calculus (DEC) for the automated discovery of physical models. DEC provides building blocks for the discrete analogue of field theories, which are beyond the state-of-the-art applications of SR to physical problems. We prove the effectiveness of our methodology by re-discovering three models of Continuum Physics from synthetic experimental data.
  arXiv  Detail & Related papers  (2023-10-10T13:23:05Z)
• Learning Latent Dynamics via Invariant Decomposition and (Spatio-)Temporal Transformers [0.6767885381740952]
  We propose a method for learning dynamical systems from high-dimensional empirical data. We focus on the setting in which data are available from multiple different instances of a system. We study behaviour through simple theoretical analyses and extensive experiments on synthetic and real-world datasets.
  arXiv  Detail & Related papers  (2023-06-21T07:52:07Z)
• Dynamic Latent Separation for Deep Learning [67.62190501599176]
  A core problem in machine learning is to learn expressive latent variables for model prediction on complex data. Here, we develop an approach that improves expressiveness, provides partial interpretation, and is not restricted to specific applications.
  arXiv  Detail & Related papers  (2022-10-07T17:56:53Z)
• A Physics-Guided Neural Operator Learning Approach to Model Biological Tissues from Digital Image Correlation Measurements [3.65211252467094]
  We present a data-driven correlation to biological tissue modeling, which aims to predict the displacement field based on digital image correlation (DIC) measurements under unseen loading scenarios. A material database is constructed from the DIC displacement tracking measurements of multiple biaxial stretching protocols on a porcine tricuspid valve leaflet. The material response is modeled as a solution operator from the loading to the resultant displacement field, with the material properties learned implicitly from the data and naturally embedded in the network parameters.
  arXiv  Detail & Related papers  (2022-04-01T04:56:41Z)
• Learning Deep Implicit Fourier Neural Operators (IFNOs) with Applications to Heterogeneous Material Modeling [3.9181541460605116]
  We propose to use data-driven modeling to predict a material's response without using conventional models. The material response is modeled by learning the implicit mappings between loading conditions and the resultant displacement and/or damage fields. We demonstrate the performance of our proposed method for a number of examples, including hyperelastic, anisotropic and brittle materials.
  arXiv  Detail & Related papers  (2022-03-15T19:08:13Z)
• Model-agnostic multi-objective approach for the evolutionary discovery of mathematical models [55.41644538483948]
  In modern data science, it is more interesting to understand the properties of the model, which parts could be replaced to obtain better results. We use multi-objective evolutionary optimization for composite data-driven model learning to obtain the algorithm's desired properties.
  arXiv  Detail & Related papers  (2021-07-07T11:17:09Z)
• Closed-form Continuous-Depth Models [99.40335716948101]
  Continuous-depth neural models rely on advanced numerical differential equation solvers. We present a new family of models, termed Closed-form Continuous-depth (CfC) networks, that are simple to describe and at least one order of magnitude faster.
  arXiv  Detail & Related papers  (2021-06-25T22:08:51Z)
• Physics-Integrated Variational Autoencoders for Robust and Interpretable Generative Modeling [86.9726984929758]
  We focus on the integration of incomplete physics models into deep generative models. We propose a VAE architecture in which a part of the latent space is grounded by physics. We demonstrate generative performance improvements over a set of synthetic and real-world datasets.
  arXiv  Detail & Related papers  (2021-02-25T20:28:52Z)
• A machine learning based plasticity model using proper orthogonal decomposition [0.0]
  Data-driven material models have many advantages over classical numerical approaches. One approach to develop a data-driven material model is to use machine learning tools. A machine learning based material modelling framework is proposed for both elasticity and plasticity.
  arXiv  Detail & Related papers  (2020-01-07T15:46:16Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.