Seth Minor, Department of Applied Mathematics, University of Colorado Boulder

Discovering Effective PDEs from Multiscale Data

The multiscale and turbulent nature of Earth's atmosphere has historically rendered accurate weather modeling a hard problem. Recently, there has been an explosion of interest surrounding data-driven approaches to weather modeling (e.g., GraphCast), which in many cases boasts both improved forecast accuracy and computational efficiency when compared to traditional methods. However, many of the new data-driven approaches employ highly parameterized neural networks, which often result in uninterpretable models and, in turn, a limited gain in scientific understanding. In this talk, we address a current research direction that addresses the interpretability problem in data-driven weather and climate modeling, with applications in ecology. In particular, we cover a data-driven approach for explicitly discovering the governing PDEs symbolically, thus identifying mathematical models with direct physical interpretations. In particular, we use a weak-form sparse regression method dubbed the Weak Sparse Identification of Nonlinear Dynamics (WSINDy) algorithm to learn models from simulated and assimilated climate data.

Noah Parks, Department of Applied Mathematics, University of Colorado Boulder

Stroboscopic effects in delayed neural fields

Neural fields are integrodifferential equations whose kernels describe the spatial structure of neural coupling. Delayed coupling models the finite time needed for signals to travel along axons connecting distant populations. These delays can have essential impacts on sensory processing. We study the dynamics of a delay-coupled neural field model, aiming to characterize both accurate and illusory percepts of object motion.