Related papers: DySLIM: Dynamics Stable Learning by Invariant Meas…
Chaotic systems are notoriously challenging to predict because of their sensitivity to perturbations and errors due to time stepping. Despite this unpredictable behavior, for many dissipative systems the statistics of the long term…
Chaotic dynamics, commonly seen in weather systems and fluid turbulence, are characterized by their sensitivity to initial conditions, which makes accurate prediction challenging. Recent approaches have focused on developing data-driven…
Learning long-term behaviors in chaotic dynamical systems, such as turbulent flows and climate modelling, is challenging due to their inherent instability and unpredictability. These systems exhibit positive Lyapunov exponents, which…
Drawing on ergodic theory, we introduce a novel training method for machine learning based forecasting methods for chaotic dynamical systems. The training enforces dynamical invariants--such as the Lyapunov exponent spectrum and fractal…
Chaotic dynamical systems pose a fundamental challenge for Reinforcement Learning (RL): exponential sensitivity to initial conditions induces high-variance bootstrap targets and poorly conditioned gradient updates. Chaotic dynamics arise…
Invariance and stability are essential notions in dynamical systems study, and thus it is of great interest to learn a dynamics model with a stable invariant set. However, existing methods can only handle the stability of an equilibrium. In…
Chaotic systems make long-horizon forecasts difficult because small perturbations in initial conditions cause trajectories to diverge at an exponential rate. In this setting, neural operators trained to minimize squared error losses, while…
Learning complex trajectories from demonstrations in robotic tasks has been effectively addressed through the utilization of Dynamical Systems (DS). State-of-the-art DS learning methods ensure stability of the generated trajectories;…
Generating long-term trajectories of dissipative chaotic systems autoregressively is a highly challenging task. The inherent positive Lyapunov exponents amplify prediction errors over time. Many chaotic systems possess a crucial property -…
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…
We introduce new machine-learning techniques for analyzing chaotic dynamical systems. The primary objectives of the study include the development of a new and simple method for calculating the Lyapunov exponent using only two trajectory…
Consider an unknown nonlinear dynamical system that is known to be dissipative. The objective of this paper is to learn a neural dynamical model that approximates this system, while preserving the dissipativity property in the model. In…
Many safety-critical scientific and engineering systems evolve according to differential-algebraic equations (DAEs), where dynamical behavior is constrained by physical laws and admissibility conditions. In practice, these systems operate…
Multiscale stochastic dynamical systems have been widely adopted to a variety of scientific and engineering problems due to their capability of depicting complex phenomena in many real world applications. This work is devoted to…
Dynamical Systems (DS) are an effective and powerful means of shaping high-level policies for robotics control. They provide robust and reactive control while ensuring the stability of the driving vector field. The increasing complexity of…
As autonomous systems become more complex and integral in our society, the need to accurately model and safely control these systems has increased significantly. In the past decade, there has been tremendous success in using deep learning…
Inspired by the work of Tsiamis et al. \cite{tsiamis2022learning}, in this paper we study the statistical hardness of learning to stabilize linear time-invariant systems. Hardness is measured by the number of samples required to achieve a…
We propose a method for learning dynamical systems from high-dimensional empirical data that combines variational autoencoders and (spatio-)temporal attention within a framework designed to enforce certain scientifically-motivated…
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…
Linear dynamical systems are canonical models for learning-based control of plants with uncertain dynamics. The setting consists of a stochastic differential equation that captures the state evolution of the plant understudy, while the true…