相关论文: Stochastic Adaptive Single-Site Time-Dependent Var…

We present a new temporal discretization paradigm for developing energy-production-rate preserving numerical approximations to thermodynamically consistent partial differential equation systems, called the supplementary variable method. The…

Stochastic differential equations (SDEs), which models uncertain phenomena as the time evolution of random variables, are exploited in various fields of natural and social sciences such as finance. Since SDEs rarely admit analytical…

The increasing deployment of distribution-level phasor measurement units (PMUs) calls for dynamic distribution state estimation (DDSE) approaches that tap into high-rate measurements to maintain a comprehensive view of the…

We propose a data-driven method to learn the time-dependent probability density of a multivariate stochastic process from sample paths, assuming that the initial probability density is known and can be evaluated. Our method uses a novel…

Time-dependent density-functional theory (TDDFT) is a central tool for studying the dynamical electronic structure of molecules and solids, yet aspects of its mathematical foundations remain insufficiently understood. In this work, we…

We revisit macroeconomic time-varying parameter vector autoregressions (TVP-VARs), whose persistent coefficients may adapt too slowly to large, abrupt shifts such as those during major crises. We explore the performance of an…

A dynamical formulation of coupled cluster theory is derived using a variational principle. By allowing time-dependent single-particle functions, a high degree of adaptivity is introduced, allowing complex systems to be simulated with high…

Color images and video sequences can be modeled as three-way tensors, which admit low tubal-rank approximations via convex surrogate minimization. This optimization problem is efficiently addressed by tensor singular value thresholding…

Stochastic nonlinear dynamical systems can undergo rapid transitions relative to the change in their forcing, for example due to the occurrence of multiple equilibrium solutions for a specific interval of parameters. In this paper, we…

The most widely used approach for simulating the dynamics of time-dependent Hamiltonians via quantum computation depends on the quantum-classical hybrid variational quantum time evolution algorithm, in which ordinary differential equations…

We introduce time-dependent variational principles to study the non-unitary dynamics of open quantum many-body systems, including dynamics described by the full Lindblad master equation, the non-Hermitian dynamics corresponding to the…

Motivated by applications in risk-sensitive reinforcement learning, we study mean-variance optimization in a discounted reward Markov Decision Process (MDP). Specifically, we analyze a Temporal Difference (TD) learning algorithm with linear…

Static disorder plays a crucial role in the electronic dynamics and spectroscopy of complex molecular systems. Traditionally, obtaining observables averaged over static disorder requires thousands of realizations via direct sampling of the…

In this paper, we introduce proximal gradient temporal difference learning, which provides a principled way of designing and analyzing true stochastic gradient temporal difference learning algorithms. We show how gradient TD (GTD)…

We present a new paradigm for the dynamical simulation of interacting many-boson open quantum systems. The method relies on a variational ansatz for the $n$-boson density matrix, in terms of a superposition of photon-added coherent states.…

In this paper, we proved moderate deviation principles for a fully coupled two-time-scale stochastic systems, where the slow process is given by stochastic differential equations with small noise, while the fast process is a rapidly…

With the rapid development of machine learning applications on time-series data, accurately assessing the value of training samples has become essential for data selection, noise detection, and model optimization. However, traditional data…

We present a scheme to perform an iterative variational optimization with infinite projected entangled-pair states (iPEPS), a tensor network ansatz for a two-dimensional wave function in the thermodynamic limit, to compute the ground state…

A matrix product state formulation of the multiconfiguration time-dependent Hartree (MPS-MCTDH) theory is presented. The Hilbert space that is spanned by the direct products of the phonon degree of freedoms, which is linearly parameterized…

The real-time electronic dynamics on material surfaces is critically important to a variety of applications. However, their simulations have remained challenging for conventional methods such as the time-dependent density-functional theory…