Related papers: Modeling Latent Non-Linear Dynamical System over T…

Many complex systems operating far from the equilibrium exhibit stochastic dynamics that can be described by a Langevin equation. Inferring Langevin equations from data can reveal how transient dynamics of such systems give rise to their…

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…

The prediction of behavior in dynamical systems, is frequently subject to the design of models. When a time series obtained from observing the system is available, the task can be performed by designing the model from these observations…

Nonlinear systems with model uncertainty are often described by stochastic differential equations. Some techniques from random dynamical systems are discussed. They are relevant to better understanding of solution processes of stochastic…

Many real-world complex systems, such as epidemic spreading networks and ecosystems, can be modeled as networked dynamical systems that produce multivariate time series. Learning the intrinsic dynamics from observational data is pivotal for…

Deep learning has shown impressive results in a variety of time series forecasting tasks, where modeling the conditional distribution of the future given the past is the essence. However, when this conditional distribution is…

A low-dimensional dynamical system is observed in an experiment as a high-dimensional signal; for example, a video of a chaotic pendulums system. Assuming that we know the dynamical model up to some unknown parameters, can we estimate the…

Dynamical systems describe the changes in processes that arise naturally from their underlying physical principles, such as the laws of motion or the conservation of mass, energy or momentum. These models facilitate a causal explanation for…

This paper addresses the data-driven identification of latent dynamical representations of partially-observed systems, i.e., dynamical systems for which some components are never observed, with an emphasis on forecasting applications,…

Data-driven methods for modeling dynamic systems have received considerable attention as they provide a mechanism for control synthesis directly from the observed time-series data. In the absence of prior assumptions on how the time-series…

Many natural systems, such as neurons firing in the brain or basketball teams traversing a court, give rise to time series data with complex, nonlinear dynamics. We can gain insight into these systems by decomposing the data into segments…

Linear dynamical systems are the foundational statistical model upon which control theory is built. Both the celebrated Kalman filter and the linear quadratic regulator require knowledge of the system dynamics to provide analytic…

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…

When intelligent spacecraft or space robots perform tasks in a complex environment, the controllable variables are usually not directly available and have to be inferred from high-dimensional observable variables, such as outputs of neural…

We consider the problem of parameter estimation using weakly supervised datasets, where a training sample consists of the input and a partially specified annotation, which we refer to as the output. The missing information in the annotation…

Nonequilibrium statistical mechanics exhibit a variety of complex phenomena far from equilibrium. It inherits challenges of equilibrium, including accurately describing the joint distribution of a large number of configurations, and also…

The condition of parameter identifiability is essential for the consistency of all estimators and is often challenging to prove. As a consequence, this condition is often assumed for simplicity although this may not be straightforward to…

Linear dynamical systems are a fundamental and powerful parametric model class. However, identifying the parameters of a linear dynamical system is a venerable task, permitting provably efficient solutions only in special cases. This work…

We propose a recurrent neural network for a "model-free" simulation of a dynamical system with unknown parameters without prior knowledge. The deep learning model aims to jointly learn the nonlinear time marching operator and the effects of…

Mathematical models of interacting populations are often constructed as systems of differential equations, which describe how populations change with time. Below we study one such model connected to the nonlinear dynamics of a system of…