Related papers: Automatic Differentiation for the Direct Minimizat…

We prove the existence of solutions of the reduced Hartree-Fock equations at finite temperature for a periodic crystal with a small defect, and show total screening of the defect charge by the electrons. We also show the convergence of the…

A new method for stochastic control based on neural networks and using randomisation of discrete random variables is proposed and applied to optimal stopping time problems. The method models directly the policy and does not need the…

The essential difficulty of gradient-based bilevel optimization using implicit differentiation is to estimate the inverse Hessian vector product with respect to neural network parameters. This paper proposes to tackle this problem by the…

Coherent diffraction imaging methods enable imaging beyond lens-imposed resolution limits. In these methods, the object can be recovered by minimizing an error metric that quantifies the difference between diffraction patterns as observed,…

We enable the automatic construction of Hybrid Monte Carlo (HMC) forces in lattice gauge theory by performing reverse-mode automatic differentiation at the level of optimized LLVM intermediate representation, making the approach applicable…

Optimal prediction methods compensate for a lack of resolution in the numerical solution of time-dependent differential equations through the use of prior statistical information. We present a new derivation of the basic methodology, show…

We present two strategies for combining dynamical pruning with the multiconfiguration time-dependent Hartree method (DP-MCTDH), where dynamical pruning means on-the-fly selection of relevant basis functions. The first strategy prunes the…

We study a class of algorithms for solving bilevel optimization problems in both stochastic and deterministic settings when the inner-level objective is strongly convex. Specifically, we consider algorithms based on inexact implicit…

The density functional theory (DFT) in electronic structure calculations can be formulated as either a nonlinear eigenvalue or direct minimization problem. The most widely used approach for solving the former is the so-called…

In scientific computing and machine learning applications, matrices and more general multidimensional arrays (tensors) can often be approximated with the help of low-rank decompositions. Since matrices and tensors of fixed rank form smooth…

Automatic differentiation plays a prominent role in scientific computing and in modern machine learning, often in the context of powerful programming systems. The relation of the various embodiments of automatic differentiation to the…

This letter proposes a fast identification algorithm for Wiener-Hammerstein systems. The computational cost of separating the front and the back linear time invariant block dynamics is significantly improved by using discrete optimization.…

This paper considers unconstrained convex optimization problems with time-varying objective functions. We propose algorithms with a discrete time-sampling scheme to find and track the solution trajectory based on prediction and correction…

We study the Hartree-Fock model for pseudorelativistic atoms, that is, atoms where the kinetic energy of the electrons is given by the pseudorelativistic operator \sqrt{(pc)^2+(mc^2)^2}-mc^2. We prove the existence of a Hartree-Fock…

A simple and reliable finite difference approach is presented for solution of the Dirac equation eigenproblem for states confined in rotationally symmetric systems. The method sets the boundary condition for the spinor wave function…

Gradient-based inverse design in photonics has already achieved remarkable results in designing small-footprint, high-performance optical devices. The adjoint variable method, which allows for the efficient computation of gradients, has…

Solutions to fractional models inherently exhibit non-smooth behavior, which significantly deteriorates the accuracy and therefore efficiency of existing numerical methods. We develop a two-stage data-infused computational framework for…

Variational optimization of orbitals in time-independent density functional calculations of excited electronic states presents a significant challenge, as excited states typically correspond to saddle points on the electronic energy…

Model order reduction methods are a powerful tool to drastically reduce the computational effort of problems which need to be evaluated repeatedly, i.e., when computing the same system for various parameter values. When applying a reduced…

Derivative-based algorithms are ubiquitous in statistics, machine learning, and applied mathematics. Automatic differentiation offers an algorithmic way to efficiently evaluate these derivatives from computer programs that execute relevant…