2026-08-14 –, Room 6
The Weak-form Estimation of Non-linear Dynamics (WENDy) framework is a recently developed approach for parameter estimation and inference of systems of ordinary differential equations (ODEs). Prior work demonstrated WENDy to be robust, computationally efficient, and accurate. Prior work was limited to ODEs which are linear-in-parameters and utilized a less robust cost function. Our Julia package includes implementations of previously developed weak-form methods as well as novel extensions. Notably, WENDy.jl now accommodates systems of a more general class of ODEs that are nonlinear-in-parameters. This is made possible through the new WENDy-MLE which approximates the maximum likelihood estimator. Also, this code facilitates a Bayesian framework with custom objective priors through the new WENDy-MAP algorithms and maximum a posterior estimator respectively. Both estimators are computed via local non-convex optimization methods.
Our work is made possible by the availability of analytic expressions for the approximate weak-likelihood function and its first and second order derivatives. These algorithms have better accuracy, a substantially larger domain of convergence, and are often faster than other weak form methods and the conventional output error least squares method. Moreover, we extend the framework to accommodate data corrupted by multiplicative log-normal noise.
I am a PhD student at the University of Colorado Boulder. My research interests include statistics, optimization, and scientific computing. I have been working in Julia since 2018 when I learned the language while working for Numerica Corporation. I have a deep appreciation for code and mathematics, and I am very excited to have the opportunity to go to JuliaCon this year.