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This paper presents a novel {\em Interpolated Factored Green Function} method (IFGF) for the accelerated evaluation of the integral operators in scattering theory and other areas. Like existing acceleration methods in these fields, the IFGF…
In this paper, we develop a class of high-order conservative methods for simulating non-equilibrium radiation diffusion problems. Numerically, this system poses significant challenges due to strong nonlinearity within the stiff source terms…
Albeit revealing impressive predictive performance for several computer vision tasks, deep neural networks (DNNs) are prone to making overconfident predictions. This limits the adoption and wider utilization of DNNs in many safety-critical…
Understanding the dynamics of nonequilibrium quantum many-body systems is an important research topic in a wide range of fields across condensed matter physics, quantum optics, and high-energy physics. However, numerical studies of…
Learned video compression (LVC) has witnessed remarkable advancements in recent years. Similar as the traditional video coding, LVC inherits motion estimation/compensation, residual coding and other modules, all of which are implemented…
The time evolution in quantum many-body systems after external excitations is attracting high interest in many fields. The theoretical modeling of these processes is challenging, and the only rigorous quantum-dynamics approach that can…
This letter presents a method to reduce the computational demands of including second-order dynamics sensitivity information into the Differential Dynamic Programming (DDP) trajectory optimization algorithm. An approach to DDP is developed…
We present a brief survey on the modern tensor numerical methods for multidimensional stationary and time-dependent partial differential equations (PDEs). The guiding principle of the tensor approach is the rank-structured separable…
We develop nonequilibribrium Green's function based transport theory, which includes effects of nonadiabatic nuclear motion in the calculation of the electric current in molecular junctions. Our approach is based on the separation of slow…
In this paper, we present details of the dual fermion (DF) method to study the non-local correction to single site DMFT. The DMFT two-particle Green's function is calculated using continuous time quantum monte carlo (CT-QMC) method. The…
Multi-way data arises in many applications such as electroencephalography (EEG) classification, face recognition, text mining and hyperspectral data analysis. Tensor decomposition has been commonly used to find the hidden factors and elicit…
The deep neural network multigrid solver (DNN-MG) combines a coarse-grid finite element simulation with a deep neural network that corrects the solution on finer grid levels, thereby improving the computational efficiency. In this work, we…
Data driven methods for time series forecasting that quantify uncertainty open new important possibilities for robot tasks with hard real time constraints, allowing the robot system to make decisions that trade off between reaction time and…
In this paper, we propose an efficient numerical method to solve high-dimensional nonlinear filtering (NLF) problems. Specifically, we use the tensor train decomposition method to solve the forward Kolmogorov equation (FKE) arising from the…
We present a simple and general approach to formulate the lattice BGK model for high speed compressible flows. The main point consists of two parts: an appropriate discrete equilibrium distribution function (DEDF) $\mathbf{f}^{eq}$ and a…
Time-dependent density functional theory (TDDFT) is a widely used method to investigate electron dynamics under external time-dependent perturbations such as laser fields. In this work, we present a machine learning approach to accelerate…
We present a quantum-inspired solver for the one-dimensional Gross-Pitaevskii equation in the Quantics Tensor-Train (QTT) representation. By evolving the system entirely within a low-rank tensor manifold, the method sidesteps the memory and…
We present a comprehensive study on the extraction of CFT data using tensor network methods, specially, from the fixed-point tensor of the linearized tensor renormalization group (lTRG) for the 2D classical Ising model near the critical…
We develop a nonperturbative dynamical theory (NDT) that is useful for treating nonequilibrium transport in a system with strong correlation. We apply our NDT to the single-impurity Anderson model in equilibrium to check its reliability by…
We study the discretization of a linear evolution partial differential equation when its Green function is known. We provide error estimates both for the spatial approximation and for the time stepping approximation. We show that, in fact,…