CMSA New Technologies in Mathematics: Towards AI for mathematical modeling of complex biological systems: Machine-learned model reduction, spatial graph dynamics, and symbolic mathematics


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November 11, 2020 3:00 pm - 4:00 pm
via Zoom Video Conferencing

Eric Mjolsness - University of California

The complexity of biological systems (among others) makes demands on the complexity of the mathematical modeling enterprise that could be satisfied with mathematical artificial intelligence of both symbolic and numerical flavors. Technologies that I think will be fruitful in this regard include (1) the use of machine learning to bridge spatiotemporal scales, which I will illustrate with the “Dynamic Boltzmann Distribution” method for learning model reduction of stochastic spatial biochemical networks and the “Graph Prolongation Convolutional Network” approach to course-graining the biophysics of microtubules; (2) a meta-language for stochastic spatial graph dynamics, “Dynamical Graph Grammars”, that can represent structure-changing processes including microtubule dynamics and that has an underlying combinatorial theory related to operator algebras; and (3) an integrative conceptual architecture of typed symbolic modeling languages and structure-preserving maps between them, including model reduction and implementation maps.