This work develops a general approach to data-driven material modeling adapted to “standard” history-dependent materials within the Thermodynamics of Irreversible Processes framework. This approach is based on the so-called global Constitutive Relation Error (CRE) defined in the time-space domain. The presentation aims to highlight the fundamental aspects, the numerical treatment of the regression and interpolation problems involved, for which machine learning tools, particularly deep neural networks, may complement more conventional tools. The data relates to the family of tested structures; it consists of measurements of the displacement and tensile fields on the boundary of the tested structures. In our data-driven modeling approach, this data is taken into account exactly. In addition, we use Materials Science to define the most general mathematical model possible with hidden internal state variables for the material; of course, these hidden state variables are part of the model unknowns. All the information is considered in a global CRE for the family of tested structures. It is minimized to give the calculated material model based on the data, and in particular its involved hidden state variables. The final value of the CRE characterizes the quality of the calculated material model. The extension to noisy measurements has also been carried out. We emphasize that for “standard” elasto-(visco-)plastic materials, we need to numerically solve a high-dimensional convex regression problem for which additional information is required today, such as microstructure information. REFERENCES [1] Ladevèze P, Chamoin L, The Constitutive Relation Error and Data Assimilation (book to appear) [2] Ladevèze P, Chamoin L, Data-driven material modeling based on the Constitutive Relation Error, submitted in AMSES [3] Ladevèze P, Néron D, Gerbaud PW, Data-driven computation for history-dependent materials, Comptes Rendus, Mécanique, 347(11):831-844 (2019) [4] Gerbaud PW, Néron D, Ladevèze P, Data-driven elasto-(visco-)plasticity involving hidden state variables, CMAME, 402:115394 (2022) [5] Benady A, Baranger E, Chamoin L, NN-mCRE: Unsupervised learning of history-dependent constitutive material laws with thermodynamically-consistent neural networks in the modified Constitutive Relation Error framework, CMAME, 425:116967 (2024)