Related papers: Implementation of the Linear Method for the optimi…
We show that the recently introduced iterative backflow renormalization can be interpreted as a general neural network in continuum space with non-linear functions in the hidden units. We use this wave function within Variational Monte…
A form of the conservation equations for fluid dynamics is presented, deduced using slightly less restrictive hypothesis than those necessary to obtain the Westervelt equation. This formulation accounts for full wave diffraction,…
The open-shell reference relativistic equation-of-motion coupled-cluster method within its four-component description is successfully implemented with the consideration of single- and double- excitation approximation. The one-body and…
Tools from control and dynamical systems have proven valuable for analyzing and developing optimization methods. In this paper, we establish rigorous theoretical foundations for using feedback linearization (FL) -- a well-established…
In this work we present a multilayer shallow model to approximate the Navier-Stokes equations with hydrostatic pressure and the $\mu(I)$-rheology. The main advantages of this approximation are (i) the low cost associated with the numerical…
We explore Riemannian optimization methods for Restricted-Open-shell Hartree-Fock (ROHF) and Complete Active Space Self-Consistent Field (CASSCF) methods. After showing that ROHF and CASSCF can be reformulated as optimization problems on…
We investigate modified steepest descent methods coupled with a loping Kaczmarz strategy for obtaining stable solutions of nonlinear systems of ill-posed operator equations. We show that the proposed method is a convergent regularization…
We study a nonlinear multimarginal optimal transport problem arising in risk management, where the objective is to maximize a spectral risk measure of the pushforward of a coupling by a cost function. Although this problem is inherently…
We show that Jastrow-Slater wave functions, in which a density-density Jastrow factor is applied onto an uncorrelated fermionic state, may possess long-range order even when all symmetries are preserved in the wave function. This fact is…
An iterative optimization approach that simultaneously minimizes the energy and optimizes the Lagrange multipliers enforcing desired constraints is presented. The method is tested on previously established benchmark systems and it is proved…
We study many-body correlations in the ground states of a general quantum system of bosons or fermions by including an additional Jastrow function in our ecently proposed variational coupled-cluster method. Our approach combines the…
We present an improved formalism for quantum Monte Carlo calculations of energy derivatives and properties (e.g. the interatomic forces), with a multideterminant Jastrow-Slater function. As a function of the number $N_e$ of Slater…
This paper presents a nonlinear reduced-order modeling (ROM) framework that leverages deep learning and manifold learning to predict compressible flow fields with complex nonlinear features, including shock waves. The proposed DeepManifold…
It is well known that the Johnson-Lindenstrauss dimensionality reduction method is optimal for worst case distortion. While in practice many other methods and heuristics are used, not much is known in terms of bounds on their performance.…
We have developed a flexible framework for constructing Jastrow factors which allows for the introduction of terms involving arbitrary numbers of particles. The use of various three- and four-body Jastrow terms in quantum Monte Carlo…
This paper proposes a finite element method that couples mixed and Lagrange finite elements to efficiently capture stress concentrations in elasticity problems. The method employs conforming mixed finite elements in regions with stress…
This paper provides a systematic investigation into the various nonlinear objective functions which can be used to explore the feasible space associated with the optimal power flow problem. A total of 40 nonlinear objective functions are…
Motivated by recent work on approximation of diffusion equations by deterministic interacting particle systems, we develop a nonlocal approximation for a range of linear and nonlinear diffusion equations and prove convergence of the method…
We demonstrate that a conditional wavefunction theory enables a unified and efficient treatment of the equilibrium structure and nonadiabatic dynamics of correlated electron-ion systems. The conditional decomposition of the many-body…
We introduce a novel method for the implementation of shape optimziation in fluid dynamics applications, where we propose to use the shape derivative to determine deformation fields with the help of the $p-$ Laplacian for $p > 2$. This…