Beatriz Moya (CNRS@CREATE), Exploring the role of geometric and learning biases in Model Order Reduction and Data-Driven simulation
This talk highlights the practical application and synergistic use of geometric and learning biases in interpretable and consistent deep learning for complex problems. We propose the use of Geometric Deep Learning for Model Order Reduction. Its high generalizability, even with limited data, facilitates real-time evaluation of partial differential equations (PDEs) for complex behaviors and changing domains. Additionally, we showcase the application of Thermodynamics-Informed Machine Learning as an alternative when the physics of the system under study is not fully known. This algorithm results in a cognitive digital twin capable of self-correction for adapting to changing environments when only partial evaluations of the dynamical state are available. Finally, the integration of Geometric Deep Learning and Thermodynamics-Informed Machine Learning produces an enhanced combined effect with high applicability in real-world domains.
