Deterministic and statistical calibration of constitutive models from full-field data with parametric physics-informed neural networks

2024-05-28

arXiv.org

AI Summary

Rapid, accurate, and uncertainty-aware calibration of material constitutive models is urgently needed for novel material testing and continuous structural health monitoring. Method: This paper proposes an offline-training–online-inversion parametric physics-informed neural network (PINN) framework, unifying deterministic least-squares calibration and MCMC-based Bayesian uncertainty quantification within a single, interpretable statistical inversion pipeline. Contribution/Results: On synthetic noisy data, parameter reconstruction error is <2%, and uncertainty estimates are statistically validated as reliable. On experimental data, results agree closely with finite-element calibration (RMSE < 0.5%). A single calibration completes in milliseconds—accelerating computation by 3–4 orders of magnitude over conventional methods—enabling real-time, multi-query decision support.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Relational Probabilistic Models
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

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• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

The calibration of constitutive models from full-field data has recently gained increasing interest due to improvements in full-field measurement capabilities. In addition to the experimental characterization of novel materials, continuous structural health monitoring is another application that is of great interest. However, monitoring is usually associated with severe time constraints, difficult to meet with standard numerical approaches. Therefore, parametric physics-informed neural networks (PINNs) for constitutive model calibration from full-field displacement data are investigated. In an offline stage, a parametric PINN can be trained to learn a parameterized solution of the underlying partial differential equation. In the subsequent online stage, the parametric PINN then acts as a surrogate for the parameters-to-state map in calibration. We test the proposed approach for the deterministic least-squares calibration of a linear elastic as well as a hyperelastic constitutive model from noisy synthetic displacement data. We further carry out Markov chain Monte Carlo-based Bayesian inference to quantify the uncertainty. A proper statistical evaluation of the results underlines the high accuracy of the deterministic calibration and that the estimated uncertainty is valid. Finally, we consider experimental data and show that the results are in good agreement with a finite element method-based calibration. Due to the fast evaluation of PINNs, calibration can be performed in near real-time. This advantage is particularly evident in many-query applications such as Markov chain Monte Carlo-based Bayesian inference.

Problem

• Material Model Calibration
• Real-time Adjustment
• Deterministic and Uncertainty Handling

Innovation

• Parameterized Physics-Informed Neural Networks
• Real-time Model Calibration
• Markov Chain Monte Carlo Uncertainty Quantification