Material modeling in the era of AI: From sparse regression to the language of material laws

Laura de Lorenzis

ETH Zurich

The lecture provides an overview of recent research conducted by the speaker's group and collaborators on the automated discovery of material models. This research advocates for a paradigm shift, moving away from the traditional approach of calibrating unknown parameters within a preselected material model towards a new objective of model discovery. This entails the simultaneous selection, generation, or encoding of the most suitable model to interpret given experimental data, along with the calibration of its unknown parameters. To achieve this goal, a variety of tools are employed, ranging from sparse regression [1-4] to Bayesian learning [5], and from formal grammars to symbolic regression [6]. Each of these tools possesses distinct features but shares the common aim of ensuring the fulfilment of physics constraints and interpretability of the discovered model(s). Initially developed to discover a specific model within a predetermined category (i.e. hyperelasticity [1,4], viscoelasticity [7] or plasticity [2]), the approach was more recently extended to the general case of a material belonging to an unknown class of constitutive behavior [3]. Additional relevant aspects such as the type of data, specimen design, and experimental validation are also discussed.

[1] Flaschel, M., S. Kumar, & L. De Lorenzis (2021). Unsupervised discovery of interpretable hyperelastic constitutive laws. Computer Methods in Applied Mechanics and Engineering 381, 113852.

[2] Flaschel, M., S. Kumar, & L. De Lorenzis (2022). Discovering plasticity models without stress data. npj Computational Materials 8, 91.

[3] Flaschel, M., S. Kumar, & L. De Lorenzis (2023). Automated discovery of generalized standard material models with EUCLID. Computer Methods in Applied Mechanics and Engineering 405, 115867.

[4] Flaschel, M., H. Yu, N. Reiter, J. Hinrichsen, S. Budday, P. Steinmann, S. Kumar, & L. De Lorenzis (2023). Automated discovery of interpretable hyperelastic material models for human brain tissue with EUCLID. Journal of the Mechanics and Physics of Solids 180, 105404.

[5] Joshi, A., P. Thakolkaran, Y. Zheng, M. Escande, M. Flaschel, L. De Lorenzis, & S. Kumar (2022). Bayesian-EUCLID: discovering hyperelastic material laws with uncertainties. Computer Methods in Applied Mechanics and Engineering 398, 115225.

[6] Kissas, G., S. Mishra, E. Chatzi, & L. De Lorenzis (2024). The language of hyperelastic materials. arXiv:2402.04263.

[7] Marino, E., M. Flaschel, S. Kumar, & L. De Lorenzis (2023). Automated identification of linear viscoelastic constitutive laws with EUCLID. Mechanics of Materials 181, 104643.