Koopman Operator-Based Forecasting for Nonstationary Processes from Near-Term, Limited Observational Data
We develop a forecasting methodology that can be used with small amounts of data from possibly non-stationary sources, as opposed to traditional methodologies that require large data sets from stationary processes. The developed method can adapt to changes in the underlying process that generates the data. COVID-19 data is used as a test case for the methodology. We combine this forecasting technique with a control framework that makes recommendations on resource and patient distribution.
Koopman Mode Analysis of Spatially Extended Dynamical Systems with Applications to Agent-Based Models
This project focuses on extending Koopman operator theory to model spatially extended dynamical systems that possess a changing network topology.
DARPA DITTO (with BAE and Synopsys)
Fast Accurate Surrogate Implementation, Modeling, and Integrated Learning Environment (FACSIMILE)
This project uses Koopman operator methods to surrogate functional ECUs. This is done so that these ECUs do not need to be fully simulated when testing new components under design. The Koopman surrogates allow faster simulation of these ECUs leading to a speed up during the design and testing of a new component.
DARPA Gamebreaker (with BAE and UCSB)
Scale Tipping Automated by Close-loop Koopman Estimates and Reinforcement Learning (STACKER)
When designing games for fun, the game is designed to be balanced; i.e., that one side isn’t inherently superior so that winning the game comes down to the skill of the player. Balancing a game is often an iterative, intuitive process on the part of game designers. This project aims to automatically determine the “game-balance equation” as a function of game parameters and its sensitivity to each. This allows us to know how each parameter affects the game and if need be “break” the game toward one side or another.
DARPA Combat (with BAE and UCSB)
Brigade AIs for TTP Learning and Evaluation via Behavioral Optimization of Tactics and Strategies (BATTLE BOTS)
We use Koopman operator theory to develop game AI’s for real-time strategy games. These AI’s can be played against to test and evaluate new player strategies.
Computational Advances in Operator Theoretic Approach to Dynamical Systems, with Application to Data Assimilation
In this project, we plan to bring theoretical and numerical advances to the data assimilation methods by pursuing them in the operator-theoretic, probabilistic, and numerical linear algebra frameworks.