BIDS Machine Learning and Science Forum
Date: Monday, April 19, 2021
Time: 11:00 AM - 12:00 PM Pacific Time
Location: Participate remotely using this Zoom link
Improving neural network based equations solvers
Speaker: Akshunna Shaurya Dogra, UC Berkeley
Abstract: Neural Networks (NNs) have ushered in new methods of constructing solution approximations to complex mathematical equations. However, especially in the context of Differential Equations (DEs), such approximations are often reliant on external methods/solutions to reliably estimate the errors associated with them. This occurs because cost functions are seldom explicitly dependent on the difference between the true solution and the NN based approximation. Thus, NN DE solvers retain an element of ambiguity vis a vis the fitness of their approximations that cannot seemingly be resolved without prior knowledge of an external solution - severely limiting their practicality and trustworthiness. We show how simple mathematical transformations upon the cost functions at hand can help address this issue, by creating explicit relationships between them and the error associated with the NN based approximations. We further show how such relationships allow for the construction of efficient error correction schemes.
The BIDS Machine Learning and Science Forum meets biweekly to discuss current applications across a wide variety of research domains in the physical sciences and beyond. These active sessions bring together domain scientists, statisticians, and computer scientists who are either developing state-of-the-art methods or are interested in applying these methods in their research. This Forum is organized by BIDS Faculty Affiliate Uroš Seljak (professor of Physics at UC Berkeley), BIDS Research Affiliate Ben Nachman (Physicist at Lawrence Berkeley National Laboratory), Vanessa Böhm and Ben Erichson. All interested members of the UC Berkeley and Berkeley Lab communities are welcome and encouraged to attend. To receive email notifications about upcoming meetings, or to request more information, please contact email@example.com.