Related papers: Learning Dissipative Chaotic Dynamics with Bounded…
This work provides a framework for nonlinear model-free control of systems with unknown input-output dynamics, but outputs that can be controlled by the inputs. This framework leads to real-time control of the system such that a feasible…
A dynamical systems approach to turbulence envisions the flow as a trajectory through a high-dimensional state space transiently visiting the neighbourhoods of unstable simple invariant solutions (E. Hopf, Commun. Appl. Maths 1, 303, 1948).…
Despite a cost-effective option in practical engineering, Reynolds-averaged Navier-Stokes simulations are facing the ever-growing demand for more accurate turbulence models. Recently, emerging machine learning techniques are making…
When training autoregressive models to forecast dynamical systems, a critical question arises: how far into the future should the model be trained to predict? Too short a horizon may miss long-term trends, while too long a horizon can…
Reservoir Computing (RC), a type of recurrent random neural network, is a powerful framework for modeling complex and chaotic dynamics. However, its autonomous (closed-loop) operation is often plagued by inherent instability. Moreover,…
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…
Extreme-event predictability in turbulence is strongly state dependent, yet event-by-event predictability horizons are difficult to quantify without access to governing equations or costly perturbation ensembles. Here we train an…
Recently, several complex network approaches to time series analysis have been developed and applied to study a wide range of model systems as well as real-world data, e.g., geophysical or financial time series. Among these techniques,…
In the framework of spatially extended dynamical systems, we present three examples in which the presence of walls lead to dynamic behavior qualitatively different from the one obtained in an infinite domain or under periodic boundary…
Recent research has demonstrated Reservoir Computing's capability to model various chaotic dynamical systems, yet its application to Hamiltonian systems remains relatively unexplored. This paper investigates the effectiveness of Reservoir…
High-dimensional dynamical systems projected onto a reduced-order model cease to be deterministic and are best described by probability distributions in state space. Their equations of motion map onto an evolution operator with a…
We use standard deep neural networks to classify univariate time series generated by discrete and continuous dynamical systems based on their chaotic or non-chaotic behaviour. Our approach to circumvent the lack of precise models for some…
The laminar-to-turbulent transition remains a fundamental and enduring challenge in fluid mechanics. Its complexity arises from the intrinsic nonlinearity and extreme sensitivity to external disturbances. This transition is critical in a…
Critical points separate distinct dynamical regimes of complex systems, often delimiting functional or macroscopic phases in which the system operates. However, the long-term prediction of critical regimes and behaviors is challenging given…
The task of modelling and forecasting a dynamical system is one of the oldest problems, and it remains challenging. Broadly, this task has two subtasks - extracting the full dynamical information from a partial observation; and then…
The past few years have witnessed an increased interest in learning Hamiltonian dynamics in deep learning frameworks. As an inductive bias based on physical laws, Hamiltonian dynamics endow neural networks with accurate long-term…
Model reduction of high-dimensional dynamical systems alleviates computational burdens faced in various tasks from design optimization to model predictive control. One popular model reduction approach is based on projecting the governing…
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…
In this paper we present a deep learning method to predict the temporal evolution of dissipative dynamic systems. We propose using both geometric and thermodynamic inductive biases to improve accuracy and generalization of the resulting…
High-fidelity numerical simulations of chaotic, high dimensional nonlinear dynamical systems are computationally expensive, necessitating the development of efficient surrogate models. Most surrogate models for such systems are…