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This paper introduces coordinate-independent methods for analysing multiscale dynamical systems using numerical techniques based on the transfer operator and its adjoint. In particular, we present a method for testing whether an arbitrary…

In observational studies, potential unobserved confounding is a major barrier in isolating the average causal effect (ACE). In these scenarios, two main approaches are often used: confounder adjustment for causality (CAC) and instrumental…

Pedestrian dynamics models have provided valuable insights into pedestrian interactions, collision avoidance, and self-organized crowd behavior using mathematical, computational, AI-based, and heuristic approaches. However, existing models…

This paper presents an active approach for part-based object detection, which optimizes the order of part filter evaluations and the time at which to stop and make a prediction. Statistics, describing the part responses, are learned from…

In this paper, we propose a variationally consistent technique for decreasing the maximum eigenfrequencies of structural dynamics related finite element formulations. Our approach is based on adding a symmetric positive-definite term to the…

A popular approach to analyze the dynamics of high-dimensional many-body systems, such as macromolecules, is to project the trajectories onto a space of slowly-varying collective variables, where subsequent analyses are made, such as…

The dynamical motion of mechanical systems possesses underlying geometric structures, and preserving these structures in numerical integration improves the qualitative accuracy and reduces the long-time error of the simulation. For a single…

This paper considers the problem of controlling a piecewise continuously differentiable system subject to time-varying uncertainties. The uncertainties are decomposed into a time-invariant, linearly-parameterized portion and a time-varying…

Independent component analysis (ICA) is now a widely used solution for the analysis of multi-subject functional magnetic resonance imaging (fMRI) data. Independent vector analysis (IVA) generalizes ICA to multiple datasets, i.e., to…

Online system identification algorithms are widely used for monitoring, diagnostics and control by continuously adapting to time-varying dynamics. Typically, these algorithms consider a model structure that lacks parsimony and offers…

This paper proposes a novel two-layer Volt/VAR control (VVC) framework to regulate the voltage profiles across an unbalanced active distribution system, which achieves both the efficient open-loop optimization and accurate closed-loop…

Unsupervised learning with functional data is an emerging paradigm of machine learning research with applications to computer vision, climate modeling and physical systems. A natural way of modeling functional data is by learning operators…

Variational inference is an alternative estimation technique for Bayesian models. Recent work shows that variational methods provide consistent estimation via efficient, deterministic algorithms. Other tools, such as model selection using…

We investigate the relationship between system identification and intervention design in dynamical systems. While previous research demonstrated how identifiable representation learning methods, such as Independent Component Analysis (ICA),…

We study existence and uniqueness of the fixed points solutions of a large class of non-linear variable discounted transfer operators associated to a sequential decision-making process. We establish regularity properties of these solutions,…

We introduce a new strategy for coupling the parallel in time (parareal) iterative methodology with multiscale integrators. Following the parareal framework, the algorithm computes a low-cost approximation of all slow variables in the…

The estimation of static parameters in dynamical systems and control theory has been extensively studied, with significant progress made in estimating varying parameters in specific system types. Suppose, in the general case, we have data…

Identifying causality behind complex systems plays a significant role in different domains, such as decision making, policy implementations, and management recommendations. However, existing causality studies on temporal event sequences…

We extend two methods of independent component analysis, fourth order blind identification and joint approximate diagonalization of eigen-matrices, to vector-valued functional data. Multivariate functional data occur naturally and…

The long-timescale behavior of complex dynamical systems can be described by linear Markov or Koopman models in a suitable latent space. Recent variational approaches allow the latent space representation and the linear dynamical model to…