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We propose a descent subgradient algorithm for minimizing a real function, assumed to be locally Lipschitz, but not necessarily smooth or convex. To find an effective descent direction, the Goldstein subdifferential is approximated through…
In a preceding paper, we have presented a general lattice formulation of the dynamic self-consistent field (DSCF) theory for inhomogeneous, unentangled homopolymer fluids. Here we apply the DSCF theory to study both transient and…
We consider scalar semilinear elliptic PDEs where the nonlinearity is strongly monotone, but only locally Lipschitz continuous. We formulate an adaptive iterative linearized finite element method (AILFEM) which steers the local mesh…
A space-filling curve (SFC) maps points in a multi-dimensional space to one-dimensional points by discretizing the multi-dimensional space into cells and imposing a linear order on the cells. This way, an SFC enables the indexing of…
The recently developed localized orbital scaling correction (LOSC) method shows the ability to systematically and size-consistently reduce the delocalization error existing in conventional density functional approximations (DFAs). Applying…
In this paper, we propose a scaled gradient modified non-monotone line search method for solving constrained minimization problems, and explore several specific properties of this method, namely, its convergence analysis. We discuss the…
We propose a high-speed and accurate hybrid dynamic density functional theory for the computer simulations of the phase separation processes of polymer melts and blends. The proposed theory is a combination of the dynamic self-consistent…
The so-called fast inertial relaxation engine is a first-order method for unconstrained smooth optimization problems. It updates the search direction by a linear combination of the past search direction, the current gradient and the…
We present an algorithm to solve the CASSCF linear response equations that is both simple and efficient. The algorithm makes use of the well established symmetric and antisymmetric combinations of trial vectors, but further orthogonalizes…
There has been an increasing interest in developing efficient immersed boundary method (IBM) based on Cartesian grids, recently in the context of high-order methods. IBM based on volume penalization is a robust and easy to implement method…
The dynamic slope scaling procedure is an approximation method successfully which solves the fixed charge network flow (FCNF) problem by iteratively linearizing the fixed cost. The parameterized dynamic slope scaling procedure adds an…
Tracking data lineage is important for data integrity, reproducibility, and debugging data science workflows. However, fine-grained lineage (i.e., at a cell level) is challenging to store, even for the smallest datasets. This paper…
Matched layers are commonly used in numerical simulations of wave propagation to model (semi-)infinite domains. Attenuation functions describe the damping in layers, and provide a matching of the wave impedance at the interface between the…
We re-adapt a spectral renormalization method, introduced in nonlinear optics, to solve the Kohn-Sham (KS) equations of density functional theory (DFT), with a focus on functionals based on the strictly-correlated electrons (SCE) regime,…
Static electric response properties of atoms and molecules are reported within the real-space Cartesian grid implementation of pseudopotential Kohn-Sham (KS) density functional theory (DFT). A detailed systematic investigation is made for a…
We design a self size-estimating feed-forward network (SSFN) using a joint optimization approach for estimation of number of layers, number of nodes and learning of weight matrices. The learning algorithm has a low computational complexity,…
Given a set of Kohn-Sham orbitals from an insulating system, we present a simple, robust, efficient and highly parallelizable method to construct a set of, optionally orthogonal, localized basis functions for the associated subspace. Our…
We study decentralized optimization over networks where agents cooperatively minimize a smooth (strongly) convex sum of local losses while communicating only with immediate neighbors. Prevailing decentralized methods require either…
The Kalman filter (KF) provides optimal recursive state estimates for linear-Gaussian systems and underpins applications in control, signal processing, and others. However, it is vulnerable to outliers in the measurements and process noise.…
We use a simplified self-consistent method to address nonlinear-optical cascading phenomena, which shows added microscopic cascading contributions in high-ordered nonlinear susceptibilities through fifth order. These cascading terms in the…