Related papers: Data-driven construction of stochastic reduced dyn…
The information encoded into an open quantum system that evolves under a Markovian dynamics is always monotonically non-increasing. Nonetheless, for a given quantifier of the information contained in the system, it is in general not clear…
Latent dynamics discovery is challenging in extracting complex dynamics from high-dimensional noisy neural data. Many dimensionality reduction methods have been widely adopted to extract low-dimensional, smooth and time-evolving latent…
The equations of classical mechanics can be used to model the time evolution of countless physical systems, from the astrophysical to the atomic scale. Accurate numerical integration requires small time steps, which limits the computational…
Modal synthesis methods are a long-standing approach for modelling distributed musical systems. In some cases extensions are possible in order to handle geometric nonlinearities. One such case is the high-amplitude vibration of a string,…
Increasing effort is put into the development of methods for learning mechanistic models from data. This task entails not only the accurate estimation of parameters but also a suitable model structure. Recent work on the discovery of…
We develop a data-driven framework for identifying non-Markovian dynamical equations of motion for open quantum systems. Starting from the Nakajima--Zwanzig formalism, we vectorize the reduced density matrix into a four-dimensional state…
A data-efficient learning-based control design method is proposed in this paper. It is based on learning a system dynamics model that is then leveraged in a two-level procedure. On the higher level, a simple but powerful optimization…
Bridging the sim-to-real gap remains a fundamental challenge in robotics, as accurate dynamic parameter estimation is essential for reliable model-based control, realistic simulation, and safe deployment of manipulators. Traditional…
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…
Markedly increased computational power and data acquisition have led to growing interest in data-driven inverse dynamics problems. These seek to answer a fundamental question: What can we learn from time series measurements of a complex…
Slow Feature Analysis is a unsupervised representation learning method that extracts slowly varying features from temporal data and can be used as a basis for subsequent reinforcement learning. Often, the behavior that generates the data on…
This article introduces a new data-driven approach that leverages a manifold embedding generated by the invertible neural network to improve the robustness, efficiency, and accuracy of the constitutive-law-free simulations with limited…
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…
Detecting anomalies and discovering driving signals is an essential component of scientific research and industrial practice. Often the underlying mechanism is highly complex, involving hidden evolving nonlinear dynamics and noise…
We define non-Markovian quantum dynamics as evolution in which the current state depends on all past states, and completely characterize its structure under the assumptions of complete positivity and non-signalling. The resulting…
Understanding and simulating non-Markovian quantum dynamics remains an important challenge in open quantum system theory. A key advance in this endeavour would be to develop a unified mathematical description of non-Markovian dynamics, and…
Non-affine parametric dependencies, nonlinearities and advection-dominated regimes of the model of interest can result in a slow Kolmogorov n-width decay, which precludes the realization of efficient reduced-order models based on linear…
We present a data-driven method for separating complex, multiscale systems into their constituent time-scale components using a recursive implementation of dynamic mode decomposition (DMD). Local linear models are built from windowed…
Living systems are open nonequilibrium systems that continuously exchange energy, matter, and information with their environments, leading to stochastic dynamics with memory and active fluctuations. In this study, we develop a non-Markovian…
We characterize a class of Markovian dynamics using the concept of divisible dynamical map. Moreover we provide a family of criteria which can distinguish Markovian and non-Markovian dynamics. These Markovianity criteria are based on a…