Automatically Differentiable Model Updating (ADiMU): conventional, hybrid, and neural network material model discovery including history-dependency

2025-05-12

AI Summary

This work addresses the challenge of automated, physics-informed constitutive model discovery from experimental or simulation data. We propose ADiMU, a fully automatic, differentiable framework for learning history-dependent material models—including classical constitutive laws, neural networks, and hybrid formulations—from either full-field displacement/force measurements (indirect inference) or local stress–strain data (direct inference). Methodologically, the framework introduces a novel, parameter-free, fully differentiable model update mechanism enabling seamless integration across scales (10–10⁶ parameters) and modeling paradigms; employs vectorized history-state propagation and automatic differentiation computation graphs for efficient batch training; and integrates with the HookeAI ecosystem. Extensive validation across diverse material models demonstrates robustness, generalizability, and cross-scale adaptability. The open-source ADiMU toolchain advances standardization in constitutive modeling and fosters open scientific collaboration.

Technology Category

• Knowledge Representation and Reasoning: Diagnosis and Abductive Reasoning
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning
• Humans and AI: Human-Aware Planning and Behavior Prediction

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

We introduce the first Automatically Differentiable Model Updating (ADiMU) framework that finds any history-dependent material model from full-field displacement and global force data (global, indirect discovery) or from strain-stress data (local, direct discovery). We show that ADiMU can update conventional (physics-based), neural network (data-driven), and hybrid material models. Moreover, this framework requires no fine-tuning of hyperparameters or additional quantities beyond those inherent to the user-selected material model architecture and optimizer. The robustness and versatility of ADiMU is extensively exemplified by updating different models spanning tens to millions of parameters, in both local and global discovery settings. Relying on fully differentiable code, the algorithmic implementation leverages vectorizing maps that enable history-dependent automatic differentiation via efficient batched execution of shared computation graphs. This contribution also aims to facilitate the integration, evaluation and application of future material model architectures by openly supporting the research community. Therefore, ADiMU is released as an open-source computational tool, integrated into a carefully designed and documented software named HookeAI.

Problem

• Discover history-dependent material models from displacement and force data
• Update physics-based, data-driven, and hybrid material models automatically
• Provide open-source tool for material model integration and evaluation

Innovation

• Automatically Differentiable Model Updating (ADiMU) framework
• Supports conventional, hybrid, and neural network models
• Open-source tool integrated into HookeAI software