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We study the automated abstraction-based synthesis of correct-by-construction control policies for stochastic dynamical systems with unknown dynamics. Our approach is to learn an abstraction from sampled data, which is represented in the…
We demonstrate a data-driven method to solve for the invariant probability density function of a randomly perturbed dynamical system. The key idea is to replace the boundary condition of numerical schemes by a least squares problem…
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…
An important class of spatio-temporal models is constructed by leveraging the hierarchical structure of dynamical (or, state-space) models. This paper proposes a new statistical dynamical model for spatio-temporal processes motivated by…
Incorporating the Hamiltonian structure of physical dynamics into deep learning models provides a powerful way to improve the interpretability and prediction accuracy. While previous works are mostly limited to the Euclidean spaces, their…
Analyzing signals arising from dynamical systems typically requires many modeling assumptions and parameter estimation. In high dimensions, this modeling is particularly difficult due to the "curse of dimensionality". In this paper, we…
The evolution of communities in dynamic (time-varying) network data is a prominent topic of interest. A popular approach to understanding these dynamic networks is to embed the dyadic relations into a latent metric space. While methods for…
Characterizing the long term behavior of dynamical systems given limited measurements is a common challenge throughout the physical and biological sciences. This is a challenging task due to the sparsity and noise inherent to empirical…
The position-based dynamics (PBD) algorithm is a popular and versatile technique for real-time simulation of deformable bodies, but is only applicable to forces that can be expressed as linearly compliant constraints. In this work, we…
Recently, many reinforcement learning techniques were shown to have provable guarantees in the simple case of linear dynamics, especially in problems like linear quadratic regulators. However, in practice, many reinforcement learning…
We present a data-driven framework for reachability analysis of nonlinear dynamical systems that requires no explicit model. A denoising diffusion probabilistic model learns the time-evolving state distribution of a dynamical system from…
Given a set of synchronous time series, each associated with a sensor-point in space and characterized by inter-series relationships, the problem of spatiotemporal forecasting consists of predicting future observations for each point.…
We develop a non-intrusive data-driven modeling framework for power network dynamics using the Lift and Learn approach of \cite{QianWillcox2020}. A lifting map is applied to the snapshot data obtained from the original nonlinear swing…
Inference on unknown quantities in dynamical systems via observational data is essential for providing meaningful insight, furnishing accurate predictions, enabling robust control, and establishing appropriate designs for future…
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…
We present a data-driven approach to construct entropy-based closures for the moment system from kinetic equations. The proposed closure learns the entropy function by fitting the map between the moments and the entropy of the moment…
In this work, we propose a non-parametric technique for online modeling of systems with unknown nonlinear Lipschitz dynamics. The key idea is to successively utilize measurements to approximate the graph of the state-update function using…
Trajectory optimization of a controlled dynamical system is an essential part of autonomy, however many trajectory optimization techniques are limited by the fidelity of the underlying parametric model. In the field of robotics, a lack of…
This study presents a method, along with its algorithmic and computational framework implementation, and performance verification for dynamical system identification. The approach incorporates insights from phase space structures, such as…
Autonomous motion planning under unknown nonlinear dynamics requires learning system properties while navigating toward a target. In this work, we develop a hierarchical planning-control framework that enables online motion synthesis with…