“WEAK FORM ESTIMATION OF NONLINEAR DYNAMICS” Jack Krebsbach ‘24, PhD candidate CU-Boulder

Parameter inference for dynamical systems governed by ordinary differential equations (ODEs) is a central problem across many areas of science and engineering. Traditional approaches often rely on forward solvers combined with nonlinear least-squares optimization, which can be computationally expensive and sensitive to noise. Weak-form Estimation of Nonlinear Dynamics (WENDy) addresses these challenges by exploiting the weak formulation of the governing ODE, which includes multiplying the equation by compactly supported test functions and integrating over the domain. With this approach derivatives of the state variables can be transferred to the test functions through integration by parts, avoiding the need to estimate derivatives from noisy data. In addition, using an appropriate set of test functions can naturally smooth over moderate noise in the observations. In this talk, I
provide an overview of WENDy and demonstrate its computational efficiency and accuracy through several examples.

Jack Krebsbach is a second-year PhD student in Applied Mathematics at the University of Colorado Boulder. He graduated from Hope College in 2024 with a B.S. in Mathematics. His research interests lie in data-driven methods for dynamical systems. In his free time, he enjoys traveling, exploring the mountains of Colorado, and playing music.