Related papers: NOMADS: Non-Markovian Optimization-based Modeling …

This paper deals with the noise identification of a linear time-varying stochastic dynamic system described by the state-space model. In particular, the stress is laid on the design of the correlation measurement difference method for…

The dynamic mode decomposition (DMD) is a data-driven method used for identifying the dynamics of complex nonlinear systems. It extracts important characteristics of the underlying dynamics using measured time-domain data produced either by…

Characterizing the memory properties of the environment has become critical for the high-fidelity control of qubits and other advanced quantum systems. However, current non-Markovian tomography techniques are either limited to discrete…

System inference for nonlinear dynamic models, represented by ordinary differential equations (ODEs), remains a significant challenge in many fields, particularly when the data are noisy, sparse, or partially observable. In this paper, we…

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…

The identification of the governing equations of chaotic dynamical systems from data has recently emerged as a hot topic. While the seminal work by Brunton et al. reported proof-of-concepts for idealized observation setting for…

We consider the problem of learning a realization of a partially observed bilinear dynamical system (BLDS) from noisy input-output data. Given a single trajectory of input-output samples, we provide a finite time analysis for learning the…

The problem of constructing data-based, predictive, reduced models for the Kuramoto-Sivashinsky equation is considered, under circumstances where one has observation data only for a small subset of the dynamical variables. Accurate…

We present a dynamic subspace approach for efficiently approximating large-scale systems by learning time-continuous trajectories on the Grassmannian manifold. By parameterizing a low-dimensional basis as a geodesic path, the method allows…

The identification of a linear system model from data has wide applications in control theory. The existing work that provides finite sample guarantees for linear system identification typically uses data from a single long system…

We investigate the nature of memory effects in the non-Markovian dynamics of spin boson models. Local quantum memory criteria can be used to indicate that the reduced dynamics of an open system necessarily requires a quantum memory in its…

Time-varying linear state-space models are powerful tools for obtaining mathematically interpretable representations of neural signals. For example, switching and decomposed models describe complex systems using latent variables that evolve…

This study investigates how dynamical systems may be learned and modelled with a neuromorphic network which is itself a dynamical system. The neuromorphic network used in this study is based on a complex electrical circuit comprised of…

Identifying dynamical systems from experimental data is a notably difficult task. Prior knowledge generally helps, but the extent of this knowledge varies with the application, and customized models are often needed. Neural ordinary…

Identifying latent interactions within complex systems is key to unlocking deeper insights into their operational dynamics, including how their elements affect each other and contribute to the overall system behavior. For instance, in…

Model reduction for fluid flow simulation continues to be of great interest across a number of scientific and engineering fields. In a previous work [arXiv:2104.13962], we explored the use of Neural Ordinary Differential Equations (NODE) as…

Embedding nonlinear dynamical systems into artificial neural networks is a powerful new formalism for machine learning. By parameterizing ordinary differential equations (ODEs) as neural network layers, these Neural ODEs are…

Nonlinear Negative Imaginary (NI) systems arise in various engineering applications, such as controlling flexible structures and air vehicles. However, unlike linear NI systems, their theory is not well-developed. In this paper, we propose…

Stochastic dynamical systems are ubiquitous in physics, biology, and engineering, where both deterministic drifts and random fluctuations govern system behavior. Learning these dynamics from data is particularly challenging in…

This work concerns control-oriented and structure-preserving learning of low-dimensional approximations of high-dimensional physical systems, with a focus on mechanical systems. We investigate the integration of neural autoencoders in model…