相关论文: Surrogate models for quantum spin systems based on…

The radiative transfer equation (RTE) is a fundamental mathematical model to describe physical phenomena involving the propagation of radiation and its interactions with the host medium. Deterministic methods can produce accurate solutions…

Reduced order models are computationally inexpensive approximations that capture the important dynamical characteristics of large, high-fidelity computer models of physical systems. This paper applies machine learning techniques to improve…

Quantum state tomography (QST) is essential for validating quantum devices but suffers from exponential scaling in system size. Neural-network quantum states, such as Restricted Boltzmann Machines (RBMs), can efficiently parameterize…

In this work, we propose to use the Reduced-Basis Method (RBM) as a model order reduction approach to solve Maxwell's equations in electromagnetic (EM) scatterers based on plasma to build a metasurface, taking into account a parameter,…

The numerical treatment of fluid-particle systems is a very challenging problem because of the complex coupling phenomena occurring between the two phases. Although accurate mathematical modelling is available to address this kind of…

Random Batch Methods (RBM) for mean-field interacting particle systems enable the reduction of the quadratic computational cost associated with particle interactions to a near-linear cost. The essence of these algorithms lies in the random…

Sliced-basis DMRG(sb-DMRG) is used to simulate a chain of hydrogen atoms and to construct low-energy effective Hubbard-like models. The downfolding procedure first involves a change of basis to a set of atom-centered Wannier functions…

Designing quantum circuits for ground state preparation is a fundamental task in quantum information science. However, standard Variational Quantum Algorithms (VQAs) are often constrained by limited ansatz expressivity and difficult…

This work introduces a reduced order modeling (ROM) framework for the solution of parameterized second-order linear elliptic partial differential equations formulated on unfitted geometries. The goal is to construct efficient…

We investigate Riemannian gradient flows for preparing ground states of a desired Hamiltonian on a quantum device. We show that the number of steps of the corresponding Riemannian gradient descent (RGD) algorithm that prepares a ground…

Due to quasicrystals having long-range orientational order but without translational symmetry, traditional numerical methods usually suffer when applied as is. In the past decade, the projection method has emerged as a prominent solver for…

Reduced modeling of a computationally demanding dynamical system aims at approximating its trajectories, while optimizing the trade-off between accuracy and computational complexity. In this work, we propose to achieve such an approximation…

Simulation of quantum dynamics is a grand challenge of computational physics. In this work we investigate methods for reducing the demands of such simulation by identifying reduced-order models for dynamics generated by parameterized…

We propose and test the first Reduced Radial Basis Function Method (R$^2$BFM) for solving parametric partial differential equations on irregular domains. The two major ingredients are a stable Radial Basis Function (RBF) solver that has an…

Rapid improvement in quantum hardware has opened the door to complex problems, but the precise characterization of quantum systems itself remains a challenge. To address this obstacle, novel tomography schemes have been developed that…

We propose a snapshots-based method to compute reduction subspaces for physics-based simulations. Our method is applicable to any mesh with some artistic prior knowledge of the solution and only requires a record of existing solutions…

A methodology for using random sketching in the context of model order reduction for high-dimensional parameter-dependent systems of equations was introduced in [Balabanov and Nouy 2019, Part I]. Following this framework, we here construct…

Mechanical systems are often characterized only by their response to certain loads known from experiments or simulations. The obtained data can be used for various purposes: system analysis, design of mathematical models, or construction of…

We consider fully discrete embedded finite element approximations for a shallow water hyperbolic problem and its reduced-order model. Our approach is based on a fixed background mesh and an embedded reduced basis. The Shifted Boundary…

Predictive modeling involving simulation and sensor data at the same time, is a growing challenge in computational science. Even with large-scale finite element models, a mismatch to the sensor data often remains, which can be attributed to…