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'Active Mechanical Metamaterials (AMMs), also known as intelligent mechanical metamaterials, combine the architecture of mechanical metamaterials with active control provided by stimuli-responsive materials [1-3]. They have been the subject of extensive research over the last decades. An active mechanical metamaterial can be defined as a material whose microstructure can transform between different configurations when subjected to external stimuli (light, temperature, mechanical or electrical loading, etc.). The mechanisms driving these transformations include phase transitions, strain incompatibilities, and mechanical instabilities [1-3], making AMMs programmable and suitable for numerous applications.

Most AMMs rely on the integration of multiple materials: elastic materials form the primary load-bearing structure, while stimuli-responsive materials provide sensing and actuation functions. Several major challenges in the study of AMMs still require urgent advancement, such as improving the properties of stimuli-responsive materials and achieving coordinated design with the supporting elastic materials.

In recent years, the introduction of machine learning into metamaterial design has become a major research trend, significantly reducing human effort and experimental costs compared to classical trial-and-error approaches [4-7]. Once trained on experimental and simulation data, these models can capture the relationships between input parameters (e.g., material types, micro-architectures) and output parameters (e.g., stiffness, flexibility, compressibility). However, current generative AI models are data-intensive, require lengthy training and hyperparameter optimization, lack interpretability, and often violate thermodynamic principles [4-7].

This project aims to develop an interpretable and thermodynamically consistent generative AI framework for active metamaterials, based on Kolmogorov–Arnold Networks (KANs). With KANs, model responses become interpretable because each physical relationship between inputs and outputs is represented by a trainable mathematical function [7]. In this project, the two fundamental laws of thermodynamics will be integrated into the KAN architecture by leveraging automatic differentiation to calculate the network's numerical derivatives with respect to its inputs [6].

In doing so, the derivatives of free energy, dissipation rate, and their relationships with stresses and internal state variables will be directly integrated into the THErmodynamics-based GEnerative KAN (TheGeKAN) architecture. Consequently, TheGeKAN will not need to learn thermodynamic laws from the data, thereby reducing the required dataset size. Training becomes more efficient and robust, and predictions more accurate and broadly interpretable. Most importantly, the predictions remain thermodynamically consistent, even in the presence of noisy and/or unseen data.

Thanks to these capabilities, TheGeKANs will serve as the foundation for the inverse, data-driven, and physics-informed design of active metamaterials using interpretable neural networks. TheGeKANs will be validated using existing datasets of active mechanical metamaterials made from well-known elasto-plastic materials, experimental data from USTH and Imperial College London, as well as finite element simulations from LMPS at ENS Paris-Saclay.

Skills required

Civil, Mechanical engineering, bioengineering, AI and Computer sciences curriculum or related fields. The student should have taken at least a course in Finite element Method and Numerical Methods and entry-level courses in physics and materials. Large computations will be developed, and notions of elementary programming are preferred.

Bibliography

[1] J. Qi et al., “Recent Progress in Active Mechanical Metamaterials and Construction Principles,” Advanced Science, vol. 9, no. 1, p. 2102662, 2022, doi: 10.1002/advs.202102662.

[2] Chen Liu, Minh-Son Pham. Spatially Programmable Architected Materials Inspired by the Metallurgical Phase Engineering. Advanced Materials, 2024

[3] W. (Wayne) Chen, R. Sun, D. Lee, C. M. Portela, and W. Chen, “Generative Inverse Design of Metamaterials with Functional Responses by Interpretable Learning,” Advanced Intelligent Systems, vol. 7, no. 6, p. 2400611, 2025, doi: 10.1002/aisy.202400611.

[3] F. Masi, I. Stefanou, P. Vannucci, and V. Maffi-Berthier, “Thermodynamics-based Artificial Neural Networks for constitutive modeling,” Journal of the Mechanics and Physics of Solids, vol. 147, p. 104277, Feb. 2021, doi: 10.1016/j.jmps.2020.104277.

[4] Le-Duc, T., Nguyen, Q. H., Lee, J., & Nguyen-Xuan, H. (2022). Strengthening gradient descent by sequential motion optimization for deep neural networks. IEEE Transactions on Evolutionary Computation, 27(3), 565-579.

[5] Cuong Ha-Minh, Quoc-Hoan Pham, Tien-Long Chu, Quyet-Tien Le. Prediction of the nonlinear transversal compression behavior of high performance fibers using machine learning. The 14th International Conference of Computational Methods (ICCM2023), Aug 2023, Ho Chi Minh City, Vietnam

[6] Quyet Tien Le, Cuong Ha-Minh, Quoc Hoan Pham, Chu Tuan Long. Optimizing the Identification of Transversal Compression Behavior of a High-Strength Synthetic Fiber Using Advanced Machine Learning Algorithms. 16th World Congress on Computational Mechanics and 4th Pan American Congress on Computational Mechanics (WCCM-PANAM 2024), Jul 2024, Vancouver (BC), Canada.

[7] Z. Liu et al., “KAN: Kolmogorov-Arnold Networks,” June 16, 2024, arXiv: arXiv:2404.19756. doi: 10.48550/arXiv.2404.19756.

Keywords

Generative AI, Active Mechanical Metamaterials, Kolmogorov–Arnold Networks (KANs), Thermodynamics, Mechanical Behavior Transformation