Related papers: Learning non-Markovian Dynamical Systems with Sign…
Path signatures have been proposed as a powerful representation of paths that efficiently captures the path's analytic and geometric characteristics, having useful algebraic properties including fast concatenation of paths through tensor…
Quantum trajectory techniques have been used in the theory of open systems as a starting point for numerical computations and to describe the monitoring of a quantum system in continuous time. Here we extend this technique and use it to…
Many real-world problems can be naturally described by mathematical formulas. The task of finding formulas from a set of observed inputs and outputs is called symbolic regression. Recently, neural networks have been applied to symbolic…
We present a long-term intrinsically motivated structure learning method for modeling transition dynamics during controlled interactions between a robot and semi-permanent structures in the world. In particular, we discuss how…
The high numerical demands for simulating non-Markovian open quantum systems motivate a line of research where short-time dynamical maps are extrapolated to predict long-time behavior. The transfer tensor method (TTM) has emerged as a…
Neural population activity often exhibits regime-dependent non-stationarity in the form of switching dynamics. Learning accurate switching dynamical system models can reveal how behavior is encoded in neural activity. Existing switching…
Nonlinear state-space identification for dynamical systems is most often performed by minimizing the simulation error to reduce the effect of model errors. This optimization problem becomes computationally expensive for large datasets.…
Recurrent Neural Networks (RNNs) can encode rich dynamics which makes them suitable for modeling dynamic systems. To train an RNN for multi-step prediction of dynamic systems, it is crucial to efficiently address the state initialization…
We study Boundary time crystals (BTCs) in the presence of non-Markovian dynamics. In contrast to BTCs observed in earlier works in the Markovian regime, we show that non-Markovian dynamics can be highly beneficial for stabilizing BTCs over…
Understanding how complex systems respond to perturbations, such as whether they will remain stable or what their most sensitive patterns are, is a fundamental challenge across science and engineering. Traditional stability and receptivity…
Complex time-varying systems are often studied by abstracting away from the dynamics of individual components to build a model of the population-level dynamics from the start. However, when building a population-level description, it can be…
Cross-Correlation random matrices have emerged as a promising indicator of phase transitions in spin systems. The core concept is that the evolution of magnetization encapsulates thermodynamic information [R. da Silva, Int. J. Mod. Phys. C,…
We study discrete time crystals (DTCs) in periodically driven quantum systems, in the presence of non-Markovian dissipation. In contrast to DTCs observed in earlier works in the presence of Markovian dynamics, using the open Dicke model in…
Variational auto-encoder frameworks have demonstrated success in reducing complex nonlinear dynamics in molecular simulation to a single non-linear embedding. In this work, we illustrate how this non-linear latent embedding can be used as a…
Neural ordinary differential equations (NODEs) are an effective approach for data-driven modeling of dynamical systems arising from simulations and experiments. One of the major shortcomings of NODEs, especially when coupled with explicit…
We propose a system identification method, Non-Markovian Optimization-based Modeling for Approximate Dynamics with Spatially-homogeneous memory (NOMADS), for identifying linear dynamical systems from a set of multi-dimensional time-series…
We characterize the dynamical behavior of continuous-time, Markovian quantum systems with respect to a subsystem of interest. Markovian dynamics describes a wide class of open quantum systems of relevance to quantum information processing,…
This work integrates the physics-informed neural network (PINN) approach into the neural quantum state framework to simulate open quantum system dynamics, to circumvent the computationally expensive time-dependent variational principle…
Building a predictive model that rapidly adapts to real-time condition monitoring (CM) signals is critical for engineering systems/units. Unfortunately, many current methods suffer from a trade-off between representation power and agility…
One of the most important topics in the study of the dynamics of open quantum system is information exchange between system and environment. Based on the features of a back-flow information from an environment to a system, an approach is…