Towards a mathematical architecture for more flexible scientific modeling

In developmental biology we find modeling problems that stretch the boundaries of traditional computational science: complex local information-processing, regulation of dynamically changing neighborhood relations, reticulated geometric structures of multiple dimensionalities, highly heterogeneous laws of motion, and a rich multiscale structure. It may be advantageous to enlist automation in the form of mathematical AI (artificial intelligence, both symbolic and machine learning) to help manage this essential model complexity. Machine learning (ML) naturally applies to the problem of finding scale changes in mathematical models, as we will show. But a new kind of mathematical AI/ML may be required overall, in order to create such an “intelligent” architecture for multiscale scientific modeling. To that end I suggest desiderata, consider useful new and existing mathematical ingredients, and propose an overall structure for such an architecture.Non UBCUnreviewedAuthor affiliation: University of California, IrvineFacult