Scientific Machine Learning with Applications in Neuroscience

Abstract: The field of scientific machine learning seeks to extract interpretable and sparse models from often highly dimensional data. This is in contrast to deep learning neural networks, where the resulting weights are uninterpretable (black box). For example, a deep learning neural network (NN) that was taught to distinguish between cats and dogs cannot tell us what makes a cat a cat or a dog a dog. I will present our work on simulating brain circuit dynamics using Neuroblox, a software package written in the Julia language, in which we construct, simulate, and interrogate hierarchical dynamic circuits from biomimetic building blocks (Blox).   Here, we present our efforts to bridge scales by developing next-generation neural mass models to describe large collections of neurons accurately.  This is done by combining analytical mean-field approaches with scientific machine learning by first employing Universal Differential Equations (Systems of ODE combined with neural networks) and then interrogating these neural networks through symbolic regression.