Related papers: Three-Dimensional Data-Driven Magnetostatic Field …
In this paper we explore the possibility for solving the 3D Maxwell's equations in the presence of nonlinear and/or inhomogeneous material response. We propose using a hybrid approach which combines a bound- ary integral representation with…
Power systems solvers are vital tools in planning, operating, and optimizing electrical distribution networks. The current generation of solvers employ computationally expensive iterative methods to compute sequential solutions. To…
Domain-Driven Solver (DDS) is a MATLAB-based software package for convex optimization problems in Domain-Driven form [Karimi and Tun\c{c}el, arXiv:1804.06925]. The current version of DDS accepts every combination of the following…
Computing reduced-order models using non-intrusive methods is particularly attractive for systems that are simulated using black-box solvers. However, obtaining accurate data-driven models can be challenging, especially if the underlying…
Data-driven techniques are increasingly used to replace electronic-structure calculations of matter. In this context, a relevant question is whether machine learning (ML) should be applied directly to predict the desired properties or be…
Scientific computations or measurements may result in huge volumes of data. Often these can be thought of representing a real-valued function on a high-dimensional domain, and can be conceptually arranged in the format of a tensor of high…
We study, from an empirical standpoint, the efficacy of synthetic data in real-world scenarios. Leveraging synthetic data for training perception models has become a key strategy embraced by the community due to its efficiency, scalability,…
We investigate an optimization problem that arises when working within the paradigm of Data-Driven Computational Mechanics. In the context of the diffusion-reaction problem, such an optimization problem seeks for the continuous primal…
We develop a new, efficient, and accurate method to simulate frequency-domain borehole electromagnetic (EM) measurements acquired in the presence of three-dimensional (3D) variations of the anisotropic subsurface conductivity. The method is…
A hybrid spectral/finite-element code is developed to numerically solve the resistive finite-pressure magnetohydrodynamic equilibria without the necessity of postulating nested magnetic flux surfaces in the non-axisymmetric toroidal…
We establish a time-stepping learning algorithm and apply it to predict the solution of the partial differential equation of motion in micromagnetism as a dynamical system depending on the external field as parameter. The data-driven…
We extend to finite elasticity the Data-Driven formulation of geometrically linear elasticity presented in Conti, M\"uller, Ortiz, Arch.\ Ration.\ Mech.\ Anal.\ 229, 79-123, 2018. The main focus of this paper concerns the formulation of a…
Magnetohydrodynamics is an important tool to study the dynamics of plasma Space Physics. In this context, we introduce a three-dimensional magnetohydrodynamic solver with divergence-cleaning in the adaptive multiresolution CARMEN code. The…
Modern computational methods, involving highly sophisticated mathematical formulations, enable several tasks like modeling complex physical phenomenon, predicting key properties and design optimization. The higher fidelity in these computer…
A finite element approach for approximating the solution of a mathematical model for the response of a penetrable, bounded object (obstacle) to the excitation by an external electromagnetic field is presented and investigated. The model…
A new dimension reduction (DR) method for data sets is proposed by autonomous deforming of data manifolds. The deformation is guided by the proposed deforming vector field, which is defined by two kinds of virtual interactions between data…
We propose a method for efficiently coupling the finite element method with atomistic simulations, while using molecular dynamics or kinetic Monte Carlo techniques. Our method can dynamically build an optimized unstructured mesh that…
In spatially extended systems, it is common to find latent variables that are hard, or even impossible, to measure with acceptable precision, but are crucially important for the proper description of the dynamics. This substantially…
In this paper we study finite element method for three-dimensional incompressible resistive magnetohydrodynamic equations, in which the velocity, the current density, and the magnetic induction are divergence-free. It is desirable that the…
Analysis and processing of data is a vital part of our modern society and requires vast amounts of computational resources. To reduce the computational burden, compressing and approximating data has become a central topic. We consider the…