Interval and fuzzy physics-augmented neural networks (iPANN and fPANN) for uncertainty quantification and propagation in constitutive modeling

2026-07-22 · Source: Machine Learning · Field: Science & Research — Artificial Intelligence & Machine Learning, Mathematics & Computational Sciences, Engineering & Applied Sciences · Depth: Expert, quick

Summary

The article introduces interval and fuzzy physics-augmented neural networks (iPANNs and fPANNs) to address uncertainty in hyperelastic constitutive modeling, particularly with sparse, noisy, or heterogeneous stress-deformation data. iPANNs learn distinct lower, mean, and upper free energy density branches. Stresses derived from these branches, using automatic differentiation, are designed to enclose noisy stress observations. fPANNs further embed these iPANN branches into a fuzzy-set representation via alpha-cut interpolation, generating a nested family of admissible responses. Both network types enforce mechanistic constraints such as objectivity, consistency, and polyconvexity, and employ smoothed L0 regularization for interpretable energy representations. The models are trained using a two-stage transfer-learning procedure. Evaluations on synthetic isotropic hyperelastic data, featuring heteroscedastic noise and varying magnitudes, confirmed that the learned bounds effectively enclose noisy stress observations and generalize to test sets. The framework also demonstrates uncertainty propagation in finite element simulations.

Key takeaway

For Machine Learning Engineers developing constitutive models with sparse or noisy data, iPANNs and fPANNs offer a robust approach to quantify and propagate uncertainty. You should consider integrating these physics-augmented neural networks to ensure your simulations account for aleatoric uncertainty in a distribution-free manner. This framework provides compact, physics-consistent bounds, improving the reliability of downstream finite element analyses.

Key insights

iPANNs and fPANNs provide physics-consistent, distribution-free uncertainty quantification in hyperelastic constitutive modeling.

Principles

• Constitutive models must preserve objectivity and consistency.
• Polyconvexity promotes robust energy representations.
• Transfer learning can refine initial mean responses.

Method

A two-stage transfer-learning procedure trains bound models. First, a sparse mean constitutive response is learned, then fine-tuned into lower and upper energy branches.

In practice

• Quantify aleatoric uncertainty in hyperelastic models.
• Propagate uncertainty into finite element simulations.
• Use smoothed L0 regularization for interpretability.

Topics

• Physics-Augmented Neural Networks
• Uncertainty Quantification
• Constitutive Modeling
• Hyperelasticity
• Finite Element Analysis
• Transfer Learning

Best for: AI Scientist, Research Scientist, Machine Learning Engineer

Related on AIssential

• Interval and fuzzy physics-augmented neural networks (iPANN and fPANN) for uncertainty quantification and propagation in constitutive modeling — iPANNs and fPANNs offer a physics-consistent, distribution-free approach for uncertainty quantification in hyperelastic constitutive modeling.
• A Unified Physics-Informed Neural Network for Modeling Coupled Electro- and Elastodynamic Wave Propagation Using Three-Stage Loss Optimization — PINNs can model coupled electro-elastodynamic systems, but face challenges with error propagation and time-dependent accuracy in multiphysics.
• Probabilistic Physics-Informed Neural Networks for Estimating Heterogeneous Elastic Properties from Low-Resolution and Noisy Displacement Data — PIE-PINN robustly estimates heterogeneous elastic properties from noisy, low-resolution data using a probabilistic physics-informed neural network with B-spline guidance.
• Finite Element-Based Material Learning via Automatic Differentiation: Learning constitutive neural network models from full-field deformation data — FE-MAD uses automatic differentiation within a JAX-FEM solver to learn constitutive neural network models from full-field deformation data.
• Extended pseudo-spectral physics-informed neural networks for phase-field models — ESPINN accurately infers phase-field model parameters and free-energy structure from limited transient data, even with noise.
• Mechanical Analysis of Parachute Suspension Line Deployment with Binding Tapes Using PINN — A PINN algorithm accurately and efficiently predicts parachute suspension line tension, surpassing traditional numerical methods.

See Counsel's argued verdicts on the open AI decisions leaders are weighing →

Open in AIssential →

Editorial summary, takeaway, and curation by AIssential. Original article published by Machine Learning.