Related papers: Dynamically Optimal Projection onto Slow Spectral …

We introduce a method for constructing reduced-order models directly from videos of dynamical systems. The method uses a non-intrusive tracking to isolate the motion of a user-selected part in the video of an autonomous dynamical system. In…

Piecewise-linear nonlinear systems appear in many engineering disciplines. Prediction of the dynamic behavior of such systems is of great importance from practical and theoretical viewpoint. In this paper, a data-driven model order…

The main contribution of this paper is a novel method for planning globally optimal trajectories for dynamical systems subject to polygonal constraints. The proposed method is a hybrid trajectory planning approach, which combines graph…

The reduction of high-dimensional systems to effective models on a smaller set of variables is an essential task in many areas of science. For stochastic dynamics governed by diffusion processes, a general procedure to find effective…

We develop a Learning Direct Optimization (LiDO) method for the refinement of a latent variable model that describes input image x. Our goal is to explain a single image x with an interpretable 3D computer graphics model having scene graph…

A fully adaptive methodology is developed for reducing the complexity of large dissipative systems. This represents a significant step towards extracting essential physical knowledge from complex systems, by addressing the challenging…

Continuous-time primal-dual gradient dynamics (PDGD) is an ubiquitous approach for dynamically solving constrained distributed optimization problems. Yet, the distributed nature of the dynamics makes it prone to communication uncertainties,…

Problem of damping of an arbitrary number of linear oscillators under common bounded control is considered. We are looking for a feedback control steering the system to the equilibrium. The obtained control is asymptotically optimal: the…

Predictive simulations of complex systems are essential for applications ranging from weather forecasting to drug design. The veracity of these predictions hinges on their capacity to capture the effective system dynamics. Massively…

Dynamic mode decomposition (DMD) is an efficient tool for decomposing spatio-temporal data into a set of low-dimensional modes, yielding the oscillation frequencies and the growth rates of physically significant modes. In this paper, we…

Dynamics models learned from visual observations have shown to be effective in various robotic manipulation tasks. One of the key questions for learning such dynamics models is what scene representation to use. Prior works typically assume…

Though ubiquitous as first-principles models for conservative phenomena, Hamiltonian systems present numerous challenges for model reduction even in relatively simple, linear cases. Here, we present a method for the projection-based model…

We consider any dynamical system that starts from a given ensemble of configurations and evolves in time until the system reaches a certain fixed stopping criterion, with the mean first-passage time the quantity of interest. We present a…

This paper proposes a neural network hybrid modeling framework for dynamics learning to promote an interpretable, computationally efficient way of dynamics learning and system identification. First, a low-level model will be trained to…

Drawing upon the bursting mechanism in slow-fast systems, we propose indicators for the prediction of such rare extreme events which do not require a priori known slow and fast coordinates. The indicators are associated with functionals…

A novel approach to reduced-order modeling of high-dimensional time varying systems is proposed. It leverages the formalism of the Dynamic Mode Decomposition technique together with the concept of balanced realization. It is assumed that…

Prediction of the state evolution of complex high-dimensional nonlinear systems is challenging due to the nonlinear sensitivity of the evolution to small inaccuracies in the model. Data Assimilation (DA) techniques improve state estimates…

We consider many-body problems in classical mechanics where a wide range of time scales limits what can be computed. We apply the method of optimal prediction to obtain equations which are easier to solve numerically. We demonstrate by…

Legged robots offer several advantages when navigating unstructured environments, but they often fall short of the efficiency achieved by wheeled robots. One promising strategy to improve their energy economy is to leverage their natural…

In this paper, we introduce the concept of random time changes in dynamical systems. The sub- ordination principle may be applied to study the long time behavior of the random time systems. We show, under certain assumptions on the class of…