Related papers: Data-driven construction of stochastic reduced dyn…

We present a unified framework for the data-driven construction of stochastic reduced models with state-dependent memory for high-dimensional Hamiltonian systems. The method addresses two key challenges: (\rmnum{1}) accurately modeling…

We introduce a new method to accurately and efficiently estimate the effective dynamics of collective variables in molecular simulations. Such reduced dynamics play an essential role in the study of a broad class of processes, ranging from…

This work introduces a method for learning low-dimensional models from data of high-dimensional black-box dynamical systems. The novelty is that the learned models are exactly the reduced models that are traditionally constructed with model…

Machine learning methods have proved to be useful for the recognition of patterns in statistical data. The measurement outcomes are intrinsically random in quantum physics, however, they do have a pattern when the measurements are performed…

A precise understanding of the influence of a quantum system's environment on its dynamics, which is at the heart of the theory of open quantum systems, is crucial for further progress in the development of controllable large-scale quantum…

We present a data-driven method to learn stochastic reduced models of complex systems that retain a state-dependent memory beyond the standard generalized Langevin equation (GLE) with a homogeneous kernel. The constructed model naturally…

Modeling complex dynamical systems under varying conditions is computationally intensive, often rendering high-fidelity simulations intractable. Although reduced-order models (ROMs) offer a promising solution, current methods often struggle…

Leveraging recent work on data-driven methods for constructing a finite state space Markov process from dynamical systems, we address two problems for obtaining further reduced statistical representations. The first problem is to extract…

We present a numerical method to compute non-equilibrium memory kernels based on experimental data or molecular dynamics simulations. The procedure uses a recasting of the non-stationary generalized Langevin equation, in which we expand the…

This work introduces a non-intrusive model reduction approach for learning reduced models from partially observed state trajectories of high-dimensional dynamical systems. The proposed approach compensates for the loss of information due to…

For a quantum system undergoing non-Markovian open quantum dynamics, we demonstrate a tomography algorithm based on multi-time measurements of the system, which reconstructs a minimal environment coupled to the system, such that the system…

Providing efficient and accurate parametrizations for model reduction is a key goal in many areas of science and technology. Here we present a strong link between data-driven and theoretical approaches to achieving this goal. Formal…

Fault-tolerant quantum computing requires extremely precise knowledge and control of qubit dynamics during the application of a gate. We develop a data-driven learning protocol for characterizing quantum gates that builds off previous work…

Complex chaotic dynamics, seen in natural and industrial systems like turbulent flows and weather patterns, often span vast spatial domains with interactions across scales. Accurately capturing these features requires a high-dimensional…

We present a numerical method for learning the dynamics of slow components of unknown multiscale stochastic dynamical systems. While the governing equations of the systems are unknown, bursts of observation data of the slow variables are…

Featuring memory of past inputs is a fundamental requirement for machine learning models processing time-dependent data. In quantum reservoir computing, all architectures proposed so far rely on Markovian dynamics, which, as we prove,…

Data-driven modeling of non-Markovian dynamics is a recent topic of research with applications in many fields such as climate research, molecular dynamics, biophysics, or wind power modeling. In the frequently used standard Langevin…

Multiple time scale stochastic dynamical systems are ubiquitous in science and engineering, and the reduction of such systems and their models to only their slow components is often essential for scientific computation and further analysis.…

This paper focuses on the construction of accurate and predictive data-driven reduced models of large-scale numerical simulations with complex dynamics and sparse training datasets. In these settings, standard, single-domain approaches may…

The complexity of molecular dynamics simulations necessitates dimension reduction and coarse-graining techniques to enable tractable computation. The generalized Langevin equation (GLE) describes coarse-grained dynamics in reduced…