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Topology learning of networked dynamical systems is an important problem with implications to optimal control, decision-making over networks, cybersecurity and safety. The majority of prior work in consistent topology estimation relies on…
Natural systems are typically nonlinear and complex, and it is of great interest to be able to reconstruct a system in order to understand its mechanism, which can not only recover nonlinear behaviors but also predict future dynamics. Due…
Sequential modelling of high-dimensional data is an important problem that appears in many domains including model-based reinforcement learning and dynamics identification for control. Latent variable models applied to sequential data…
We present a numerical method for learning the dynamics of slow components of unknown multiscale stochastic dynamical systems. While the governing equations of the systems are unknown, bursts of observation data of the slow variables are…
Regression trees and their ensemble methods are popular methods for nonparametric regression: they combine strong predictive performance with interpretable estimators. To improve their utility for locally smooth response surfaces, we study…
Many, if not most, systems of interest in science are naturally described as nonlinear dynamical systems. Empirically, we commonly access these systems through time series measurements. Often such time series may consist of discrete random…
Deep networks are commonly used to model dynamical systems, predicting how the state of a system will evolve over time (either autonomously or in response to control inputs). Despite the predictive power of these systems, it has been…
We study the modeling and prediction of dynamical systems based on conventional models derived from measurements. Such algorithms are highly desirable in situations where the underlying dynamics are hard to model from physical principles or…
Model predictive control (MPC) is an effective approach to control multivariable dynamic systems with constraints. Most real dynamic models are however affected by plant-model mismatch and process uncertainties, which can lead to…
We focus on improving the accuracy of an approximate model of a multiscale dynamical system that uses a set of parameter-dependent terms to account for the effects of unresolved or neglected dynamics on resolved scales. We start by…
The demand of probabilistic time series forecasting has been recently raised in various dynamic system scenarios, for example, system identification and prognostic and health management of machines. To this end, we combine the advances in…
Probabilistic graphical models (PGMs) are widely used to discover latent structure in data, but their success hinges on selecting an appropriate model design. In practice, model specification is difficult and often requires iterative…
This paper presents a novel theoretical framework for reducing the computational complexity of multi-model adaptive control/estimation systems through systematic transformation to controllable canonical form. While traditional multi-model…
By linking conceptual theories with observed data, generative models can support reasoning in complex situations. They have come to play a central role both within and beyond statistics, providing the basis for power analysis in molecular…
Simulating transition dynamics between metastable states is a fundamental challenge in dynamical systems and stochastic processes with wide real-world applications in understanding protein folding, chemical reactions and neural activities.…
Tree-based models have been successfully applied to a wide variety of tasks, including time series forecasting. They are increasingly in demand and widely accepted because of their comparatively high level of interpretability. However, many…
Many real-world systems can be described by mathematical models that are human-comprehensible, easy to analyze and help explain the system's behavior. Symbolic regression is a method that can automatically generate such models from data.…
The mathematical models used to capture features of complex, biological systems are typically non-linear, meaning that there are no generally valid simple relationships between their outputs and the data that might be used to validate them.…
Mathematical descriptions of dynamical systems are deeply rooted in topological spaces defined by non-Euclidean geometry. This paper proposes leveraging structure-rich geometric spaces for machine learning to achieve structural…
Many current challenges involve understanding the complex dynamical interplay between the constituents of systems. Typically, the number of such constituents is high, but only limited data sources on them are available. Conventional…