Related papers: Computing time-dependent reduced models for classi…
Nonlinear dynamical systems are ubiquitous in nature and they are hard to forecast. Not only they may be sensitive to small perturbations in their initial conditions, but they are often composed of processes acting at multiple scales.…
In the context of data-driven control of nonlinear systems, many approaches lack of rigorous guarantees, call for nonconvex optimization, or require knowledge of a function basis containing the system dynamics. To tackle these drawbacks, we…
In this paper, we present a proof-of-concept quantum algorithm for simulating time-dependent Hamiltonian evolution by reducing the problem to simulating a time-independent Hamiltonian in a larger space using a discrete clock Hamiltonian…
Projection-based reduced order models are effective at approximating parameter-dependent differential equations that are parametrically separable. When parametric separability is not satisfied, which occurs in both linear and nonlinear…
Controllability and observability energy functions play a fundamental role in model order reduction and are inherently connected to optimal control problems. For linear dynamical systems the energy functions are known to be quadratic…
The letter proposes an adaptive model reduction approach based on tensor decomposition to speed up time-domain power system simulation. Taylor series expansion of a power system dynamic model is calculated around multiple equilibria…
This paper presents a trajectory generation method that optimizes a quadratic cost functional with respect to linear system dynamics and to linear input and state constraints. The method is based on continuous-time flatness-based trajectory…
Compared with time independent Hamiltonians, the dynamics of generic quantum Hamiltonians $H(t)$ are complicated by the presence of time ordering in the evolution operator. In the context of digital quantum simulation, this difficulty…
Simulating the dynamics of complex quantum systems is a central application of quantum devices. Here, we propose leveraging the power of measurements to simulate short-time quantum dynamics of physically prepared quantum states in classical…
Low-rank approximation is a technique to approximate a tensor or a matrix with a reduced rank to reduce the memory required and computational cost for simulation. Its broad applications include dimension reduction, signal processing,…
We present a low-space overhead simulation algorithm based on the truncated Dyson series for time-dependent quantum dynamics. This algorithm is applied to simulating time-independent Hamiltonians by transitioning to the interaction picture,…
We show that one can approximate the least fixed point solution for a multivariate system of monotone probabilistic polynomial equations in time polynomial in both the encoding size of the system of equations and in log(1/\epsilon), where…
We develop a new algorithm based on the time-dependent variational principle applied to matrix product states to efficiently simulate the real- and imaginary time dynamics for infinite one-dimensional quantum lattice systems. This…
Simulation of quantum dynamics is a grand challenge of computational physics. In this work we investigate methods for reducing the demands of such simulation by identifying reduced-order models for dynamics generated by parameterized…
We propose a projection-based model order reduction method for the solution of parameter-dependent dynamical systems. The proposed method relies on the construction of time-dependent reduced spaces generated from evaluations of the solution…
In this communication we demonstrate that a deep artificial neural network based on a transformer architecture with self-attention layers can predict the long-time population dynamics of a quantum system coupled to a dissipative environment…
Capturing the temporal evolution of Gaussian properties such as position, rotation, and scale is a challenging task due to the vast number of time-varying parameters and the limited photometric data available, which generally results in…
Imaginary-time evolution is fundamental for analyzing quantum many-body systems, yet classical simulation requires exponentially growing resources in both system size and evolution time. While quantum approaches reduce the system-size…
A classical reduced order model for dynamical problems involves spatial reduction of the problem size. However, temporal reduction accompanied by the spatial reduction can further reduce the problem size without losing accuracy much, which…
In autoregressive modeling for tensor-valued time series, Tucker decomposition, when applied to the coefficient tensor, provides a clear interpretation of supervised factor modeling but loses its efficiency rapidly with increasing tensor…