Related papers: Nonlinear reduced basis using mixture Wasserstein …
In this paper, an $\mathscr{H}_2$ norm-based model reduction method for linear quantum systems is presented, which can obtain a physically realizable model with a reduced order for closely approximating the original system. The model…
Considering recent advancements and successes in the development of efficient quantum algorithms for electronic structure calculations --- alongside impressive results using machine learning techniques for computation --- hybridizing…
We propose an efficient reduced-order technique for electronic structure calculations of semiconductor nanostructures, suited for inclusion in full-band quantum transport simulators. The model is based on the linear combination of bulk…
The combined effectiveness of model reduction and the quasilinear approximation for the reproduction of the low-order statistics of oceanic surface boundary-layer turbulence is investigated. Idealized horizontally homogeneous problems of…
This paper introduces a new nonlinear dictionary learning method for histograms in the probability simplex. The method leverages optimal transport theory, in the sense that our aim is to reconstruct histograms using so-called displacement…
Nonlinear balanced truncation is a model order reduction technique that reduces the dimension of nonlinear systems in a manner that accounts for either open- or closed-loop observability and controllability aspects of the system. Two…
Quasi two-dimensional pattern forming systems with spontaneously broken isotropy represent a novel symmetry class, that is experimentally accessible in electroconvection of homeotropically aligned liquid crystals. We present a weakly…
Monitoring the integrity of elastic structures using ultrasonic waves requires the efficient identification of material parameters from measured surface displacements. The displacement field is governed by Cauchy's equation of motion, i.e.,…
The reduction of computational costs in the numerical solution of nonstationary problems is achieved through splitting schemes. In this case, solving a set of less computationally complex problems provides the transition to a new level in…
A refined a priori error analysis of the lowest order (linear) nonconforming Virtual Element Method (VEM) for approximating a model Poisson problem is developed in both 2D and 3D. A set of new geometric assumptions is proposed on shape…
We present a methodology to investigate phase-diagrams of quantum models based on the principle of the reduced basis method (RBM). The RBM is built from a few ground-state snapshots, i.e., lowest eigenvectors of the full system Hamiltonian…
The simulation of strongly correlated many-electron systems is one of the most promising applications for near-term quantum devices. Here we use a class of eigenvalue solvers (presented in Phys. Rev. Lett. 126, 070504 (2021)) in which a…
We present a new adaptive method for electronic structure calculations based on novel fast algorithms for reduction of multivariate mixtures. In our calculations, spatial orbitals are maintained as Gaussian mixtures whose terms are selected…
The last several decades have seen significant advances in the theoretical modeling of materials within the fields of solid-state physics and materials science, but many methods commonly applied to this problem struggle to capture strong…
Standard variational methods tend to obtain upper bounds on the ground state energy of quantum many-body systems. Here we study a complementary method that determines lower bounds on the ground state energy in a systematic fashion, scales…
In a recent work, we proposed a graph-based manifold learning scheme for the nonlinear Galerkin-reduction of quasi-static solid mechanical problems [1]. The resulting nonlinear approximation spaces can closely and flexibly represent…
State estimation is key to both analyzing physical mechanisms and enabling real-time control of fluid flows. A common estimation approach is to relate sensor measurements to a reduced state governed by a reduced-order model (ROM). (When…
In this paper, we propose a certified reduced basis (RB) method for quasilinear elliptic problems together with its application to nonlinear magnetostatics equations, where the later model permanent magnet synchronous motors (PMSM). The…
The Kolmogorov $n$-width is an established benchmark to judge the performance of reduced basis and similar methods that produce linear reduced spaces. Although immensely successful in the elliptic regime, this width, shows unsatisfactory…
Computing the Wasserstein barycenter of a set of probability measures under the optimal transport metric can quickly become prohibitive for traditional second-order algorithms, such as interior-point methods, as the support size of the…