Current Projects

DARPA SCEPTER (with BAE Systems)

Principal Investigators: Dr. Maria Fonoberova, Dr. Allan Avila, Dr. Ryan Mohr

DARPA EC (with BAE Systems)

U-PrECISE – Uncertainty Propagation via (dynamical) Evolution of Information from Complex Signals/Sensors and Environments

With the growing ubiquity of using machine learning systems for critical tasks, it is imperative that the level of confidence for ML-based decisions is properly quantified. This project uses Koopman operator theory, along with statistical methods, to generate confidence intervals for the outputs of machine learning systems. These context-sensitive Koopman models allow for contextual adaptation and quantitative analyses of the underlying dynamics of ML systems – two important steps towards the third wave of artificial intelligence.

Principal Investigator: Dr. Maria Fonoberova; co-PI: Dean Huang


Koopman Operator Theoretic Methods for Efficient Training and Analysis of Deep Neural Networks

The past decade has seen a tremendous increase in the capability of deep neural networks, as models have become increasingly large and intricate. However, such improvements have come at the cost of requiring significant computational resources and time. This proposal leverages Koopman operator theory to make deep neural network training and deployment more efficient, interpretable, and generalizable.

Principal Investigator: Dr. Maria Fonoberova;  co-PIs: William Redman and Dr. Ryan Mohr

DARPA MINC (with BAE Systems, UCSB, Apogee Electronics, RAM Laboratories)

Battlespace-Enabling Data Dissemination through Orchestrated Control and Koopman (BEDROCK)

Principal Investigator: Dr. Allan Avila

DARPA ACTM (with BAE Systems)

Hybrid AI Integrating Koopman Units (HAIKU)

The HAIKU project leverages Koopman Operator methods to enhance existing state-of-the-art climate models for long-term predictions through the use of AI. The Koopman-based climate models offer improved predictions by modeling physics not accounted for in the climate models while exhibiting a speed-up of over a million times. These models allow climatologists to efficiently run simulations under different scenarios to improve the understanding of our planet’s weather system.

Principal Investigator: Dr. Maria Fonoberova


Koopman Operator-Based Forecasting for Nonstationary Processes from Near-Term, Limited Observational Data

We are developing 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. 

Principal Investigator: Dr. Maria Fonoberova



Computational Advances in Operator Theoretic Approach to Dynamical Systems, with Application to Data Assimilation

In this project, we are planning to bring theoretical and numerical advances to the data assimilation methods by pursuing them in the operator-theoretic, probabilistic, and numerical linear algebra frameworks.

Principal Investigator: Dr. Maria Fonoberova

Network Security with MixMode  

Koopman Mode Analysis

AIMdyn has developed an AI system for use in network security. Koopman operator models of streams of data are used to provide generative models of the dynamics, based on which anomalous behavior on the network is detected. Such anomalous behavior is correlated using AI to provide the analyst with detailed information of malicious behavior on their network, enabling them to mitigate the threat


Recently Completed Projects


Koopman Mode Analysis of Spatially Extended Dynamical Systems with Applications to Agent-Based Models

This project focuses on extending the Koopman operator framework for AI to model spatially extended dynamical systems that possess a changing network topology. The optimization of neural networks has long been appreciated as being a dynamical system, but the complex way in which the architecture, data, and activation function affects the dynamics has made it difficult to study from such a perspective. Using advances in Koopman operator theory, we build data-driven, but theoretically backed, models that allow us to optimize, design, and analyze neural networks.

Principal Investigator: Dr. Maria Fonoberova

DARPA DITTO (with BAE Systems and Synopsys)

Fast Accurate Surrogate Implementation, Modeling, and Integrated Learning Environment (FACSIMILE)

This project uses the Koopman operator framework for AI 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.

Principal Investigator: Dr. Ryan Mohr

DARPA Combat (with BAE Systems 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 simulated game AI’s for real-time strategy games such as Starcraft. These AI’s can be played against to test and evaluate new player strategies, allowing us a vast data collection of different approaches to real-world battle.

Principal Investigator: Dr. Maria Fonoberova

DARPA Gamebreaker (with BAE Systems 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.

Principal Investigator: Dr. Maria Fonoberova