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A new fast multipole formulation for solving elliptic difference equations on unbounded domains and its parallel implementation are presented. These difference equations can arise directly in the description of physical systems, e.g.…
We propose a method to improve the computational and memory efficiency of numerical solvers for the nonequilibrium Dyson equation in the Keldysh formalism. It is based on the empirical observation that the nonequilibrium Green's functions…
The many-body Green's function provides access to electronic properties beyond density functional theory level in ab inito calculations. In this manuscript, we propose a deep learning framework for predicting the finite-temperature Green's…
We introduce a new method for simulating colloidal suspensions with spherical colloidal particles of dielectric constant different from the surrounding medium. The method uses exact calculation of the Green function to obtain the ion-ion…
With the emergence of mixed precision capabilities in hardware, iterative refinement schemes for solving linear systems $Ax=b$ have recently been revisited and reanalyzed in the context of three or more precisions. These new analyses show…
The combined source integral equation (CSIE) for the electric field on the surface of a perfect electrically conducting scatterer can be discretized very accurately with lowest-order Rao-Wilton-Glisson basis and testing functions if the…
A method for deriving quantum kinetic equations with initial correlations is developed on the basis of the nonequilibrium Green's function formalism. The method is applicable to a wide range of correlated initial states described by…
We present a new convergent iterative solution for the two lowest quantum wave functions $\psi_{ev}$ and $\psi_{od}$ of the Hamiltonian with a quartic double well potential $V$ in one dimension. By starting from a trial function, which is…
We generalize the interpolative separable density fitting (ISDF) method, used for compressing the four-index electron repulsion integral (ERI) tensor, to incorporate adaptive real space grids for potentially highly localized single-particle…
Continuous optimization is an important problem in many areas of AI, including vision, robotics, probabilistic inference, and machine learning. Unfortunately, most real-world optimization problems are nonconvex, causing standard convex…
With the recent study of deep learning in scientific computation, the Physics-Informed Neural Networks (PINNs) method has drawn widespread attention for solving Partial Differential Equations (PDEs). Compared to traditional methods, PINNs…
Maximum entropy inference and learning of graphical models are pivotal tasks in learning theory and optimization. This work extends algorithms for these problems, including generalized iterative scaling (GIS) and gradient descent (GD), to…
Combinatorial optimization is a promising area for achieving quantum speedup. Quantum approximate optimization algorithm (QAOA) is designed to search for low-energy states of the Ising model, which correspond to near-optimal solutions of…
In this work, we investigate the possibility of improving multireference-driven coupled cluster (CC) approaches with an algorithm that iteratively combines complete active space (CAS) calculations with tailored CC and externally corrected…
For the Poisson equation posed in a domain containing a large number of polygonal perforations, we propose a low-dimensional coarse approximation space based on a coarse polygonal partitioning of the domain. Similarly to other multiscale…
The inverse design of nonlocal metasurfaces requires the precise optimization of lattice geometry to engineer spatial dispersion and high-Q resonances. However, gradient-based optimization is frequently bottle-necked by the evaluation of…
In the present paper, we are interested in developing iterative Krylov subspace methods in tensor structure to solve a class of multilinear systems via Einstein product. In particular, we develop global variants of the GMRES and…
Due to non-linear structure, iterative Green's function methods can result in multiple different solutions even for simple molecular systems. In contrast to the wave-function methods, a detailed and careful analysis of such molecular…
A method is presented for calculating solutions to differential equations analytically for a variety of problems in physics. An iteration procedure based on the recently proposed BLUES (Beyond Linear Use of Equation Superposition) function…
In earlier work we have studied a method for discretization in time of a parabolic problem which consists in representing the exact solution as an integral in the complex plane and then applying a quadrature formula to this integral. In…