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            <title xml:lang="en">Material Modeling via Thermodynamics-Based Artificial Neural Networks</title>
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                <forename type="first">Filippo</forename>
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            <funder>European Research Council, ERC; Horizon 2020: 757848</funder>
            <funder>Acknowledgements. The author I.S. would like to acknowledge the support of the European Research Council (ERC) under the European Union Horizon 2020 research and innovation program (Grant agreement ID 757848 CoQuake).</funder>
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            <idno type="halRefHtml">&lt;i&gt;Workshop on Joint Structures and Common Foundations of Statistical Physics, Information Geometry and Inference for Learning, SPIGL 2020&lt;/i&gt;, 2020, Les Houches, France. pp.308-329, &lt;a target="_blank" href="https://dx.doi.org/10.1007/978-3-030-77957-3_16"&gt;&amp;#x27E8;10.1007/978-3-030-77957-3_16&amp;#x27E9;&lt;/a&gt;</idno>
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                  <country key="FR">France</country>
                </meeting>
                <editor>Barbaresco F.Nielsen F.</editor>
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              <p>Machine Learning methods and, in particular, Artificial Neural Networks (ANNs) have demonstrated promising capabilities in material constitutive modeling. One of the main drawbacks of such approaches is the lack of a rigorous frame based on the laws of physics. Here we propose a new class of data-driven, physics-based, neural networks for constitutive modeling of strain-rate independent processes at the material point level, which we define as Thermodynamics-based Artificial Neural Networks (TANNs). Relying on automatic differentiation, derivatives of the free-energy, the dissipation rate and their relation with the stress and internal state variables are hardwired in the network. The proposed network does not have to identify the underlying pattern of thermodynamic laws during training, reducing the need of large data-sets, improving the robustness and the performance of predictions. Finally and more important, the predictions remain thermodynamically consistent, even for unseen data. TANNs are herein used to model history-dependent materials, with kinematic softening. While the motivating examples considered may be rather simple, we emphasize that the proposed class of ANN can be successfully applied (without any modification) to materials with different or more complex behavior. Based on these features, TANNs are a starting point for data-driven, physics-based constitutive modeling with neural networks.</p>
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