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Modeling dynamical systems plays a crucial role in capturing and understanding complex physical phenomena. When physical models are not sufficiently accurate or hardly describable by analytical formulas, one can use generic function…

Discovering the underlying dynamics of complex systems from data is an important practical topic. Constrained optimization algorithms are widely utilized and lead to many successes. Yet, such purely data-driven methods may bring about…

Modeling dynamical systems is important in many disciplines, e.g., control, robotics, or neurotechnology. Commonly the state of these systems is not directly observed, but only available through noisy and potentially high-dimensional…

We study the problem of stabilizing an unknown partially observable linear time-invariant (LTI) system. For fully observable systems, leveraging an unstable/stable subspace decomposition approach, state-of-art sample complexity is…

Complex and nonlinear dynamical systems often involve parameters that change with time, accurate tracking of which is essential to tasks such as state estimation, prediction, and control. Existing machine-learning methods require full state…

We consider the problem of learning the link parameters as well as the structure of a binary-valued pairwise Markov model. Under sparsity assumption, we propose a method based on $l_1$- regularized logistic regression, which estimate…

Many systems in physics, engineering, and biology exhibit multiscale stochastic dynamics, where low-dimensional slow variables evolve under the influence of high-dimensional fast processes. In practice, observations are often limited to a…

Stochastic processes offer a flexible mathematical formalism to model and reason about systems. Most analysis tools, however, start from the premises that models are fully specified, so that any parameters controlling the system's dynamics…

This paper considers the problem of system identification (ID) of linear and nonlinear non-autonomous systems from noisy and sparse data. We propose and analyze an objective function derived from a Bayesian formulation for learning a hidden…

We study the problem of learning a mixture of multiple linear dynamical systems (LDSs) from unlabeled short sample trajectories, each generated by one of the LDS models. Despite the wide applicability of mixture models for time-series data,…

Recently there has been substantial interest in spectral methods for learning dynamical systems. These methods are popular since they often offer a good tradeoff between computational and statistical efficiency. Unfortunately, they can be…

Learning from Demonstration (LfD) techniques enable robots to learn and generalize tasks from user demonstrations, eliminating the need for coding expertise among end-users. One established technique to implement LfD in robots is to encode…

In this paper, we investigate when system identification is statistically easy or hard, in the finite sample regime. Statistically easy to learn linear system classes have sample complexity that is polynomial with the system dimension. Most…

Partial Observability -- where agents can only observe partial information about the true underlying state of the system -- is ubiquitous in real-world applications of Reinforcement Learning (RL). Theoretically, learning a near-optimal…

System identification is a key step for model-based control, estimator design, and output prediction. This work considers the offline identification of partially observed nonlinear systems. We empirically show that the certainty-equivalent…

Estimation of Markov Random Field and covariance models from high-dimensional data represents a canonical problem that has received a lot of attention in the literature. A key assumption, widely employed, is that of {\em sparsity} of the…

Many real-world systems, such as moving planets, can be considered as multi-agent dynamic systems, where objects interact with each other and co-evolve along with the time. Such dynamics is usually difficult to capture, and understanding…

We derive a finite-sample probabilistic bound on the parameter estimation error of a system identification algorithm for Linear Switched Systems. The algorithm estimates Markov parameters from a single trajectory and applies a variant of…

Sparse linear regression -- finding an unknown vector from linear measurements -- is now known to be possible with fewer samples than variables, via methods like the LASSO. We consider the multiple sparse linear regression problem, where…

Identifying dynamical systems from experimental data is a notably difficult task. Prior knowledge generally helps, but the extent of this knowledge varies with the application, and customized models are often needed. Neural ordinary…