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

2026-07-22 · Source: Takara TLDR - Daily AI Papers · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Computational Mechanics · Depth: Expert, quick

Summary

Interval and fuzzy physics-augmented neural networks (iPANNs and fPANNs) address the challenge of constitutive modeling under uncertainty, particularly with sparse, noisy, or heterogeneous stress-deformation data. iPANNs learn sparse lower, mean, and upper free energy density branches whose automatically differentiated stresses enclose noisy observations. fPANNs extend this by embedding iPANN branches into a fuzzy-set representation via alpha-cut interpolation, creating a nested family of admissible responses. Both frameworks encode mechanistic constraints like objectivity, consistency, and polyconvexity, using smoothed L0 regularization for interpretable energy. Trained through a two-stage transfer-learning procedure, these models were evaluated on synthetic isotropic hyperelastic data with various noise conditions, demonstrating that learned bounds enclose noisy stress observations and generalize well. The framework also propagates uncertainty through finite element simulations, offering a compact, physics-consistent route for distribution-free aleatoric uncertainty quantification.

Key takeaway

For research scientists and engineers developing constitutive models or performing mechanics simulations with uncertain data, iPANNs and fPANNs provide a robust solution. If you are dealing with sparse, noisy stress-deformation data, this framework offers a physics-consistent, distribution-free method to quantify and propagate aleatoric uncertainty. Consider integrating these networks to enhance the reliability and interpretability of your hyperelastic material simulations, ensuring more robust predictions under real-world variability.

Key insights

iPANNs and fPANNs offer a physics-consistent, distribution-free approach for uncertainty quantification in hyperelastic constitutive modeling.

Principles

• Mechanistic constraints (objectivity, consistency, polyconvexity) are crucial for model reliability.
• Smoothed L0 regularization promotes interpretable energy representations.
• Two-stage transfer-learning effectively trains bound models.

Method

iPANNs learn lower, mean, and upper free energy density branches. fPANNs embed iPANNs into fuzzy-set representations via alpha-cut interpolation. Automatic differentiation obtains stresses from learned energy densities.

In practice

• Apply iPANNs for uncertainty-aware hyperelastic constitutive modeling.
• Use fPANNs to generate a nested family of admissible responses.
• Integrate learned bounds into finite element simulations for uncertainty propagation.

Topics

• Constitutive Modeling
• Uncertainty Quantification
• Physics-Augmented Neural Networks
• Hyperelasticity
• Finite Element Analysis
• Fuzzy Set Theory
• Interval Analysis

Best for: AI Scientist, Research Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by Takara TLDR - Daily AI Papers.