APPM Researchers Invited to Lead SIAM 2026 Tutorial on Equation Discovery from Noisy Data
Researchers from Applied Mathematics will lead an invited tutorial this summer at the 2026 Society for Industrial and Applied Mathematics (SIAM) Annual Meeting, introducing participants to emerging techniques in scientific machine learning that allow researchers to uncover governing equations directly from noisy data.
The one-day workshop,Ìý, will be taught by Professor David Bortz and Dr. Daniel Messenger, a 2022 Ph.D. graduate of APPM and current Director’s Postdoctoral Fellow at Los Alamos National Laboratory.Ìý
Modern science increasingly relies on massive observational and experimental datasets, spanning fields from epidemiology and ecology to atmospheric science and plasma physics. Yet despite the abundance of data, the underlying mathematical rules governing these systems are often incomplete or unknown. Bortz and Messenger’s tutorial focuses on a growing area of scientific machine learning aimed at discovering the equations behind complex systems directly from data.Ìý
Central to this course are mathematical approaches known as weak from scientific machine learning (WSciML). This family of methods was developed here in APPM, arising out of work in Dr. Messenger’s PhD dissertation and then expanded significantly by Prof. Bortz, Prof. Vanja Dukic, and Dr. Messenger.Ìý The core of the approach combines mathematical modeling, computation, and data-driven methods to infer governing differential equations even when measurements are noisy, sparse, or experimentally constrained. Unlike many traditional techniques, weak form methods remain most robust when systems exhibit sharp gradients, irregular behavior, or stochastic effects common in real-world applications.Ìý
The tutorial will introduce participants to methods such as Weak-form Sparse Identification of Nonlinear Dynamics (WSINDy), while guiding attendees through hands-on coding exercises in MATLAB and Python. Participants will work through complete inverse problems, learning how to estimate parameters and recover governing equations directly from raw datasets.
Rather than focusing solely on theory, the course is designed to provide researchers with practical tools they can immediately apply in their own work.
The invitation to lead the tutorial reflects growing interest in weak form approaches across the applied mathematics and computational sciences communities. Over the past several years, researchers in the field have increasingly turned toward scientific machine learning techniques capable of combining physical insight with modern data analysis.
The WSciML group here (jointly led by Bortz and Dukic) has contributed extensively to the development of weak form methods with applications spanning biological systems, disease ecology, atmospheric fluid dynamics, and computational plasma physics. Messenger, whose doctoral research in APPM focused on weak form equation discovery from noisy measurements, has continued advancing these methods through work in multiscale modeling and dynamical systems at Los Alamos.
The course will take place July 5, 2026, at the SIAM Annual Meeting in Cleveland, Ohio, bringing together graduate students, researchers, and computational scientists interested in expanding their scientific machine learning toolkit.Ìý