相关论文: Real-time operator evolution in two and three dime…

Operator learning offers a powerful paradigm for solving parametric partial differential equations (PDEs), but scaling probabilistic neural operators such as the recently proposed Gaussian Processes Operators (GPOs) to high-dimensional,…

We develop new efficient online algorithms for detecting transient sparse signals in TEM video sequences, by adopting the recently developed framework for sequential detection jointly with online convex optimization [1]. We cast the problem…

The Koopman operator, as a linear representation of a nonlinear dynamical system, has been attracting attention in many fields of science. Recently, Koopman operator theory has been combined with another concept that is popular in data…

We investigate learning the eigenfunctions of evolution operators for time-reversal invariant stochastic processes, a prime example being the Langevin equation used in molecular dynamics. Many physical or chemical processes described by…

A quantum Monte Carlo algorithm for the transverse Ising model with arbitrary short- or long-range interactions is presented. The algorithm is based on sampling the diagonal matrix elements of the power series expansion of the density…

In networked control systems, communication resource constraints often necessitate the use of \emph{sparse} control input vectors. A prototypical problem is how to ensure controllability of a linear dynamical system when only a limited…

In this paper, we study a class of convolution operators on the space of distributions that enlarge the well-studied class of passive operators. In this larger class, we are able to associate, to each operator, a holomorphic function in the…

Quantum dynamics for arbitrary system are traditionally realized by time evolutions of wave functions in Hilbert space and/or density operators in Liouville space. However, the traditional simulations may occasionally turn out to be…

Motivated by the modeling of three-dimensional fluid turbulence, we define and study a class of stochastic partial differential equations (SPDEs) that are randomly stirred by a spatially smooth and uncorrelated in time forcing term. To…

We consider random networks whose dynamics is described by a rate equation, with transition rates $w_{nm}$ that form a symmetric matrix. The long time evolution of the system is characterized by a diffusion coefficient $D$. In one dimension…

We consider a generalization of the projecting operators method for the case of Cauchy problem for systems of 1D evolution differential equations of first order with variable coefficients. It is supposed that the coefficients dependence on…

Sparsity is a ubiquitous feature of many real world signals such as natural images and neural spiking activities. Conventional compressed sensing utilizes sparsity to recover low dimensional signal structures in high ambient dimensions…

We show that a classical algorithm based on sparse Pauli dynamics can efficiently simulate quantum circuits studied in a recent experiment on 127 qubits of IBM's Eagle processor [Nature 618, 500 (2023)]. Our classical simulations on a…

Inducing-point-based sparse variational Gaussian processes have become the standard workhorse for scaling up GP models. Recent advances show that these methods can be improved by introducing a diagonal scaling matrix to the conditional…

We propose an effective and flexible scheme for reverse engineering of a Hamiltonian by designing the evolution operators to eliminate the terms of Hamiltonian which are hard to be realized in practice. Different from transitionless quantum…

The convolutional sparse model has recently gained increasing attention in the signal and image processing communities, and several methods have been proposed for solving the pursuit problem emerging from it -- in particular its convex…

This paper defines a novel Bayesian inverse problem to infer an infinite-dimensional uncertain operator appearing in a differential equation, whose action on an observable state variable affects its dynamics. Inference is made tractable by…

The quantitative formulation of evolution equations is the backbone for prediction, control, and understanding of dynamical systems across diverse scientific fields. Besides deriving differential equations for dynamical systems based on…

To meet the demands of instantaneous control of instabilities over long time horizons in plasma fusion, we design a dynamic feedback control strategy for the Vlasov-Poisson system by constructing an operator that maps state perturbations to…

We propose a novel framework for analyzing the dynamics of distribution shift in real-world systems that captures the feedback loop between learning algorithms and the distributions on which they are deployed. Prior work largely models…