Co-organizing minisymposium on "Incorporating fundamental principles in innovative machine learning models of physics" at WCCM22
Theoretical and algorithmic advances in neural networks and related representations have begun to revolutionize the field of computational physics. To realize the potential of these algorithms, the field of scientific machine learning (SciML) has begun to combine the mature numerical analysis and algorithms from computational physics with innovative machine learning coming from other disciplines. As with the development of more traditional schemes such as energy preserving time integrators and mass conserving discretizations, physics informed machine learning is now expected to preserve fundamental features of the physical problem such as conservation, well-posedness, stability, symmetries, and invariants in order to provide robust and trustworthy predictions. We solicit talks that attack some of the fundamental open questions in SciML, such as how to embed physical constraints, how to employ the best aspects of traditional numerical methods and SciML, and how to ensure regular convergence and robustness.