Finite Element-Based Material Learning via Automatic Differentiation: Learning constitutive neural network models from full-field deformation data

2026-06-06 · Source: cs.AI updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Computational Mechanics & Materials Science · Depth: Expert, short

Summary

FE-MAD, a Finite Element-Based Material learning via Automatic Differentiation framework, identifies constitutive neural network models from heterogeneous full-field deformation data. Submitted on May 22, 2026, this approach offers a robust alternative to traditional calibration methods, which often struggle with high-dimensional parameters, computational demands, noise sensitivity, or extensive data needs. FE-MAD integrates a constitutive neural network within a JAX-FEM nonlinear solver, optimizing parameters through gradient-based minimization of a measurement-mismatch loss. It leverages forward- and reverse-mode automatic differentiation for Newton tangent stiffness and loss gradients, removing the need for analytic adjoints. The framework was demonstrated with grey-box and white-box Constitutive Artificial Neural Networks (CANNs) on three experimental datasets, including full digital image correlation and a heterogeneous matrix-inclusion system, generalizing to twenty-two unseen samples.

Key takeaway

For research scientists developing advanced material models, FE-MAD offers a powerful approach to overcome limitations of traditional calibration. You should consider integrating differentiable finite element methods with neural networks to utilize full-field deformation data, significantly improving the robustness and efficiency of constitutive model identification. This framework eliminates the need for complex manual adjoints, accelerating your development of accurate and generalizable material laws.

Key insights

FE-MAD uses automatic differentiation within a JAX-FEM solver to learn constitutive neural network models from full-field deformation data.

Principles

• Full-field deformation data improves constitutive model identification.
• Automatic differentiation streamlines gradient-based material learning.

Method

FE-MAD integrates a constitutive neural network into a JAX-FEM solver, identifying parameters via gradient-based minimization of a measurement-mismatch loss, using forward- and reverse-mode automatic differentiation.

In practice

• Apply FE-MAD for hyperelastic material characterization.
• Utilize grey-box CANNs for flexible material modeling.
• Employ white-box CANNs for interpretable strain-energy terms.

Topics

• Finite Element Method
• Automatic Differentiation
• Constitutive Models
• Neural Networks
• Material Characterization
• Hyperelasticity
• Digital Image Correlation

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

Related on AIssential

• Mesh Graph Neural Network Framework for Accelerating Finite Element Simulation for Arbitrary Geometries — Mesh Graph Networks effectively generalize finite element analysis predictions across arbitrary structural geometries by encoding relative features.
• This Physics Breakthrough Looks Impossible — A novel communication protocol unifies disparate physics simulation methods, enabling complex, stable interactions between solids and fluids.
• MoSA: Motion-constrained Stress Adaptation for Mitigating Real-to-Sim Gap in Continuum Dynamics via Learning Residual Anisotropy — MoSA learns residual anisotropy and heterogeneity using physics priors to close the real-to-sim gap in continuum dynamics.
• Engineering Hybrid Physics-Informed Neural Networks for Next-Generation Electricity Systems: A State-of-the-Art Review — Physics-informed machine learning integrates domain physics into models, enhancing accuracy and efficiency for data-scarce electricity systems.
• Coupling Language Models with Physics-based Simulation for Synthesis of Inorganic Materials — Coupling LLMs with physics-based simulations offers more viable inorganic material synthesis routes than classical algorithms, leveraging LLMs' implicit priors.
• EPINN: Enhanced Physics-Informed Neural Network for Solving Continuous Integral Equations — EPINN offers a robust, scalable solution for high-dimensional integral equations by integrating physical principles into neural networks.

Open in AIssential →

Editorial summary, takeaway, and curation by AIssential. Original article published by cs.AI updates on arXiv.org.