Related papers: Data-driven construction of stochastic reduced dyn…
In spatially extended systems, it is common to find latent variables that are hard, or even impossible, to measure with acceptable precision, but are crucially important for the proper description of the dynamics. This substantially…
We study the Langevin dynamics of a physical system with manifold structure $\mathcal{M}\subset\mathbb{R}^p$ based on collected sample points $\{\mathsf{x}_i\}_{i=1}^n \subset \mathcal{M}$ that probe the unknown manifold $\mathcal{M}$.…
Embedding non-Markovian open quantum dynamics into an enlarged Markovian space offers a powerful route to nonperturbative simulations, where the dynamics of the extended space can be governed by multiple distinct Markovian equations. We…
Finding the dynamical law of observable quantities lies at the core of physics. Within the particular field of statistical mechanics, the generalized Langevin equation (GLE) comprises a general model for the evolution of observables…
A key challenge to nonlocal models is the analytical complexity of deriving them from first principles, and frequently their use is justified a posteriori. In this work we extract nonlocal models from data, circumventing these challenges…
Recently, a large class of quantum non-Markovian piecewise dynamics for an open quantum system obeying closed evolution equations has been introduced [B. Vacchini, Phys. Rev. Lett. 117, 230401 (2016)]. These dynamics have been defined in…
The dynamical behavior of open quantum systems plays a key role in many applications of quantum mechanics, examples ranging from fundamental problems, such as the environment-induced decay of quantum coherence and relaxation in many-body…
We examine the challenging problem of constructing reduced models for the long time prediction of systems where there is no timescale separation between the resolved and unresolved variables. In previous work we focused on the case where…
We study data-driven learning of robust stochastic control for infinite-horizon systems with potentially continuous state and action spaces. In many managerial settings--supply chains, finance, manufacturing, services, and dynamic…
In the wild, we often encounter collections of sequential data such as electrocardiograms, motion capture, genomes, and natural language, and sequences may be multichannel or symbolic with nonlinear dynamics. We introduce a new method to…
Computing reduced-order models using non-intrusive methods is particularly attractive for systems that are simulated using black-box solvers. However, obtaining accurate data-driven models can be challenging, especially if the underlying…
Quantum information processing relies on how dynamics unfold in open quantum systems. In this work, we study the non-Markovian dynamics in the single mode spin-boson model at strong couplings. In order to apply perturbation theory, we…
We present a novel method for learning reduced-order models of dynamical systems using nonlinear manifolds. First, we learn the manifold by identifying nonlinear structure in the data through a general representation learning problem. The…
The developing field of stochastic thermodynamics extends concepts of macroscopic thermodynamics such as entropy production and work to the microscopic level of individual trajectories taken by a system through phase space. The scheme…
Model order reduction techniques simplify high-dimensional dynamical systems by deriving lower-dimensional models that retain essential system characteristics. These techniques are crucial for the controller design of complex systems while…
A central challenge in neuroscience is understanding how neural system implements computation through its dynamics. We propose a nonlinear time series model aimed at characterizing interpretable dynamics from neural trajectories. Our model…
The use of machine learning algorithms to predict behaviors of complex systems is booming. However, the key to an effective use of machine learning tools in multi-physics problems, including combustion, is to couple them to physical and…
This article presents a general framework for recovering missing dynamical systems using available data and machine learning techniques. The proposed framework reformulates the prediction problem as a supervised learning problem to…
We construct a continuous-time, positively divisible non-Markovian process with memory of the initial state that satisfies the differential Chapman--Kolmogorov equation. In the stationary state, the correlation function exhibits exponential…
Data-driven modeling techniques have been explored in the spatial-temporal modeling of complex dynamical systems for many engineering applications. However, a systematic approach is still lacking to leverage the information from different…