Related papers: Systematic Derivation of Order Parameters through …
We consider the reduction of parametric families of linear dynamical systems having an affine parameter dependence that differ from one another by a low-rank variation in the state matrix. Usual approaches for parametric model reduction…
The density-matrix renormalization-group (DMRG) algorithm is extended to treat time-dependent problems. The method provides a systematic and robust tool to explore out-of-equilibrium phenomena in quantum many-body systems. We illustrate the…
We introduce a simple method to estimate the system parameters in continuous dynamical systems from the time series. In this method, we construct a modified system by introducing some constants (controlling constants) into the given…
We demonstrate the power of a first principle-based and practicable method that allows for the perturbative computation of reduced density matrix elements of an open quantum system without making use of any master equations. The approach is…
We present a method of parameter estimation for large class of nonlinear systems, namely those in which the state consists of output derivatives and the flow is linear in the parameter. The method, which solves for the unknown parameter by…
This paper presents a novel theoretical framework for reducing the computational complexity of multi-model adaptive control/estimation systems through systematic transformation to controllable canonical form. While traditional multi-model…
We investigate circuit complexity to characterize chaos in multiparticle quantum systems. In the process, we take a stride to analyze open quantum systems by using complexity. We propose a new diagnostic of quantum chaos from complexity…
We propose a multiscale approach for an elliptic multiscale setting with general unstructured diffusion coefficients that is able to achieve high-order convergence rates with respect to the mesh parameter and the polynomial degree. The…
In this paper, we consider the problem of model reduction of large scale systems, such as those obtained through the discretization of PDEs. We propose a randomized proper orthogonal decomposition (RPOD) technique to obtain the reduced…
We provide a constructive algorithm to find the best separable approximation to an arbitrary density matrix of a composite quantum system of finite dimensions. The method leads to a condition of separability and to a measure of…
An application of an effective numerical algorithm for solving eigenvalue problems which arise in modelling electronic properties of quantum disordered systems is considered. We study the electron states at the localization-delocalization…
Dynamical systems describe the changes in processes that arise naturally from their underlying physical principles, such as the laws of motion or the conservation of mass, energy or momentum. These models facilitate a causal explanation for…
While the equilibrium properties, states, and phase transitions of interacting systems are well described by statistical mechanics, the lack of suitable state parameters has hindered the understanding of non-equilibrium phenomena in diverse…
Quantum state tomography, the ability to deduce the density matrix of a quantum system from measured data, is of fundamental importance for the verification of present and future quantum devices. It has been realized in systems with few…
Practical measures of electronic decoherence, called distilled purities, that are applicable to many-body systems are introduced. While usual measures of electronic decoherence such as the purity employ the full $N$-particle density matrix…
Latent ODE models provide flexible descriptions of dynamic systems, but they can struggle with extrapolation and predicting complicated non-linear dynamics. The latent ODE approach implicitly relies on encoders to identify unknown system…
A methodology grounded in model reduction is presented for accelerating the gradient-based solution of a family of linear or nonlinear constrained optimization problems where the constraints include at least one linear Partial Differential…
Data-driven methods for the identification of the governing equations of dynamical systems or the computation of reduced surrogate models play an increasingly important role in many application areas such as physics, chemistry, biology, and…
Simulations of complex physical systems are typically realized by discretizing partial differential equations (PDEs) on unstructured meshes. While neural networks have recently been explored for surrogate and reduced order modeling of PDE…
We review a novel approach to evaluate the ground-state properties of many-body lattice systems based on an exact probabilistic representation of the dynamics and its long time approximation via a central limit theorem. The choice of the…