Related papers: Nonlinear reduced basis using mixture Wasserstein …

Partial differential equations can be used to model many problems in several fields of application including, e.g., fluid mechanics, heat and mass transfer, and electromagnetism. Accurate discretization methods (e.g., finite element or…

We focus here on a class of fourth-order parabolic equations that can be written as a system of second-order equations by introducing an auxiliary variable. We design a novel second-order fully discrete mixed finite element method to…

The implementation of the orbital minimization method (OMM) for solving the self-consistent Kohn-Sham (KS) problem for electronic structure calculations in a basis of non-orthogonal numerical atomic orbitals of finite-range is reported. We…

Reduced models for the (defocusing) nonlinear Schr\"odinger equation are developed. In particular, we develop reduced models that only involve the low-frequency modes given noisy observations of these modes. The ansatz of the reduced…

The Wasserstein barycenter (WB) is an important tool for summarizing sets of probability measures. It finds applications in applied probability, clustering, image processing, etc. When the measures' supports are finite, computing a…

A new efficient numerical algorithm for interacting fermion systems is proposed and examined in detail. The ground state is expressed approximately by a linear combination of numerically chosen basis states in a truncated Hilbert space. Two…

In analyzing and assessing the condition of dynamical systems, it is necessary to account for nonlinearity. Recent advances in computation have rendered previously computationally infeasible analyses readily executable on common computer…

In this manuscript, we introduce the tensor-train reduced basis method, a novel projection-based reduced-order model designed for the efficient solution of parameterized partial differential equations. While reduced-order models are widely…

This work presents a new methodology for computing ground states of Bose-Einstein condensates based on finite element discretizations on two different scales of numerical resolution. In a pre-processing step, a low-dimensional (coarse)…

In this article we apply reduced order techniques for the approximation of parametric eigenvalue problems. The effect of the choice of sampling points is investigated. Here we use the standard proper orthogonal decomposition technique to…

Computing the ground state of interacting quantum matter is a long-standing challenge, especially for complex two-dimensional systems. Recent developments have highlighted the potential of neural quantum states to solve the quantum…

This contribution presents a model order reduction framework for real-time efficient solution of trimmed, multi-patch isogeometric Kirchhoff-Love shells. In several scenarios, such as design and shape optimization, multiple simulations need…

We propose an efficient method for simultaneously optimizing both the structure and parameter values of quantum circuits with only a small computational overhead. Shallow circuits that use structure optimization perform significantly better…

In order to optimally design materials, it is crucial to understand the structure-property relations in the material by analyzing the effect of microstructure parameters on the macroscopic properties. In computational homogenization, the…

In this work we propose reduced order methods as a reliable strategy to efficiently solve parametrized optimal control problems governed by shallow waters equations in a solution tracking setting. The physical parametrized model we deal…

We investigate a projection-based reduced-order model of the steady incompressible Navier-Stokes equations for moderate Reynolds numbers. In particular, we construct an "embedded" reduced basis space, by applying proper orthogonal…

We propose a probabilistic way for reducing the cost of classical projection-based model order reduction methods for parameter-dependent linear equations. A reduced order model is here approximated from its random sketch, which is a set of…

We develop a unified framework for the design and analysis of high-order nonconforming virtual element methods for nonlinear fourth-order reaction--diffusion problems in two dimensions, with emphasis on clamped, Navier, and…

We develop and analyze a nonlinear reduced basis (RB) method for parametrized elliptic partial differential equations based on a binary-tree partition of the parameter domain into tensor-product structured subdomains. Each subdomain is…

We propose a modification of the Variational Quantum Eigensolver algorithm for electronic structure optimization using quantum computers, named non-unitary Variational Quantum Eigensolver (nu-VQE), in which a non-unitary operator is…