From Data to Equations: Weak Form Methods for Discovering Models from Noisy Data

Participants will explore the rapidly evolving field of weak form scientific machine learning (WSciML) – a robust, data-driven approach for discovering governing equations directly from real-world measurements. As equation learning becomes increasingly important across the sciences, weak form methods such as Weak-form Sparse Identification of Nonlinear Dynamics (WSINDy) offer a powerful advantage: they remain stable and accurate even when datasets are noisy, sparse, or experimentally constrained. In addition, weak‑form methods acknowledge the reality that the underlying processes being measured are often nonsmooth—exhibiting shocks, sharp gradients, or involving a stochastic microscale. By uniting analytical rigor with computational efficiency, the weak‑form framework has become indispensable for applied mathematicians and computational scientists seeking to advance data‑driven modeling, numerical analysis, and scientific machine learning. 

Through a combination of lectures, demonstrations, and extensive coding practice, attendees will work through example datasets and complete the full workflow of several inverse problems, including inferring governing differential equations and estimating parameters directly from raw data. Participants will leave with practical experience applying weak form methods to real datasets and a clear understanding of how to implement these approaches in their own work. Opportunities to connect with instructors and peers are integrated throughout the day.  

This Course Is for You If You: 

• Develop mathematical models as an applied mathematician or computational scientist 
• Want to apply scientific machine learning approaches, including weak-form methods (WSciML), to discover equations from complex, real-world data
• Are interested in dynamical systems, inverse problems, or data driven modeling 
• Work in the life sciences, epidemiology, ecology, atmospheric sciences, plasma physics, or other application areas and need tools that are robust to noise 
• Want to expand your research toolkit with modern model discovery methods 
• Are a graduate student or researcher looking for hands-on training in emerging WSciML methodologies 

In This Course You Will:

• Learn the foundations of weak form approaches and why they excel with noisy or incomplete data
• Understand and implement WSINDy
• Work through guided code exercises to perform rapid model discovery from provided datasets
• Solve inverse problems: discovering governing equations without knowing them in advance
• Explore applications across the sciences (life sciences, epidemiology, ecology, atmospheric and fluid models, computational plasma physics, and more)
• Gain confidence using MATLAB or Python to build, test, and validate discovered models 

Course Prerequisites:

To get the most out of the course, participants should have: 

• Familiarity with differential equations and linear algebra
• Basic coding ability in Python or MATLAB
• Access to MATLAB or Python 
• A personal laptop capable of running code exercises 

Cancellation Policy

Requests for registration refunds must be sent by email to customer service and will be issued in accordance with the following:

• Cancellation on or before June 8: $100 Cancellation Fee 
• After June 8: No Refund 

Hotel Reservations

SIAM is holding a block of rooms at the Hilton Cleveland Downtown for course participants. These rooms are being held on a first-come, first-served basis at the following discounted rates. Please be aware the room block fills quickly, so we suggest you make your hotel and travel plans early.

The group rate is guaranteed until 5:00 p.m. ET on June 8, 2026, or until the room block is full. If rooms are available after the cutoff date, they will be offered at the best available rate.  

Find more information about the hotel room block and reservations on the SIAM AN26 webpage.