Hayden Schaeffer
Hayden Schaeffer is a Professor of Mathematics at the University of California, Los Angeles. His research is in mathematical machine learning, differential equations, randomization, and physical modeling.
Office:
Mathematical Sciences Building 7931
Email:
hayden at math dot ucla another dot edu
Below are highlights of some of my group's recent results, which were supported by grants from AFOSR and NSF.
You can find an up-to-date list of my papers on my Google Scholar Page.
Multi-Operator Learning and Equation Generation
The PROSE algorithm (Predicting Operators and Symbolic Expressions) trains a map from multimodal inputs to multimodal outputs. It is capable of forcasting future states of a dynamic system and "writing" the underlying differential equation that describes the data.
See
Operator Learning and Multi-Scale Physics
High-contrast and multi-scale phenomena are challenging to capture with standard ML and deep networks. We work on operator learning approaches to handle challenges for stationary solutions and dynamic multi-scale problems.
See our recent paper: https://arxiv.org/abs/2308.14188
Machine Learning Theory
We are developing theoretical understanding of AI by studying the accuracy, stability, and reliability of neural networks and randomized methods. This includes providing theoretical guarantees, conditioning, and generalization of learning algorithms.
See our recent work on randomized feature analysis:
https://arxiv.org/pdf/2110.11477
https://www.sciencedirect.com/science/article/pii/S1063520322000653
Learning Models and Equations from Observational Data
An important scientific task is to be able to write an equation/model for a given physical phenomena. Our work tries to automate this process by developing algorithms and approaches for obtaining governing equations or surrogate models directly from data. This includes high-dimensional chaotic systems, turbulence, combustion, and nonlocal dynamics.
See our recent work on learning interacting systems:
https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.2022.0835
