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Existing methods for optimal control struggle to deal with the complexity commonly encountered in real-world systems, including dimensionality, process error, model bias and data heterogeneity. Instead of tackling these system complexities…

Large Language Model (LLM) image recognition is a powerful tool for extracting data from images, but accuracy depends on providing sufficient cues in the prompt - requiring a domain expert for specialized tasks. We introduce Cue Learning…

The adoption of detailed mechanisms for chemical kinetics often poses two types of severe challenges: First, the number of degrees of freedom is large; and second, the dynamics is characterized by widely disparate time scales. As a result,…

Recent work [Ran22] formulated a class of optimal control problems involving positive linear systems, linear stage costs, and elementwise constraints on control. It was shown that the problem admits linear optimal cost and the associated…

Continual learning (CL) is crucial for evaluating adaptability in learning solutions to retain knowledge. Our research addresses the challenge of catastrophic forgetting, where models lose proficiency in previously learned tasks as they…

With the advent of the big data era, generative models of complex networks are becoming elusive from direct computational simulation. We present an exact, linear-algebraic reduction scheme of generative models of networks. By exploiting the…

Dimensionality reduction and clustering techniques are frequently used to analyze complex data sets, but their results are often not easy to interpret. We consider how to support users in interpreting apparent cluster structure on scatter…

The energy demand of vehicles, particularly in unsteady drive cycles, is affected by complex dynamics internal to the engine and other powertrain components. Yet, in many applications, particularly macroscopic traffic flow modeling and…

Conservation laws are an inherent feature in many systems modeling real world phenomena, in particular, those modeling biological and chemical systems. If the form of the underlying dynamical system is known, linear algebra and algebraic…

Transformer models exhibit remarkable in-context learning (ICL), adapting to novel tasks from examples within their context, yet the underlying mechanisms remain largely mysterious. Here, we provide an exact analytical characterization of…

We present an algorithm for the simulation of the exact real-time dynamics of classical many-body systems with discrete energy levels. In the same spirit of kinetic Monte Carlo methods, a stochastic solution of the master equation is found,…

This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…

Deep learning recommendation systems at scale have provided remarkable gains through increasing model capacity (i.e. wider and deeper neural networks), but it comes at significant training cost and infrastructure cost. Model pruning is an…

Deleting data from a trained machine learning (ML) model is a critical task in many applications. For example, we may want to remove the influence of training points that might be out of date or outliers. Regulations such as EU's General…

The dynamics of many-body systems can often be captured in terms of only a few relevant variables. Mathematical and numerical approaches exist to identify these variables by exploiting a separation of time scales between slow relevant and…

Dynamical systems theory has long provided a foundation for understanding evolving phenomena across scientific domains. Yet, the application of this theory to complex real-world systems remains challenging due to issues in mathematical…

This work focuses on the problem of exact model reduction of positive linear systems, by leveraging minimal realization theory. While determining the existence of a positive reachable realization remains in general an open problem, we are…

We develop a linear-algebraic framework for dimensional analysis in systems with constraints, particularly when variables are numerous or related by implicit relations so that direct elimination is impractical. By expressing both…

Trajectory following is one of the complicated control problems when its dynamics are nonlinear, stochastic and include a large number of parameters. The problem has significant difficulties including a large number of trials required for…

Scientists often use observational time series data to study complex natural processes, but regression analyses often assume simplistic dynamics. Recent advances in deep learning have yielded startling improvements to the performance of…