Related papers: Efficient Multiscale Methods for Highly Heterogene…
This work develops a nonlinear multigrid method for diffusion problems discretized by cell-centered finite volume methods on general unstructured grids. The multigrid hierarchy is constructed algebraically using aggregation of degrees of…
In this paper, we construct and analyze a multiscale (finite element) method for parabolic problems with heterogeneous dynamic boundary conditions. As origin, we consider a reformulation of the system in order to decouple the discretization…
Developments in dynamical systems theory provides new support for the macroscale modelling of pdes and other microscale systems such as Lattice Boltzmann, Monte Carlo or Molecular Dynamics simulators. By systematically resolving subgrid…
Fiber network modeling can be used for studying mechanical properties of paper. The individual fibers and the bonds in-between constitute a detailed representation of the material. However, detailed microscale fiber network models must be…
In recent years, there has been a growing interest in using machine learning to overcome the high cost of numerical simulation, with some learned models achieving impressive speed-ups over classical solvers whilst maintaining accuracy.…
Choosing a deep neural network architecture is a fundamental problem in applications that require balancing performance and parameter efficiency. Standard approaches rely on ad-hoc engineering or computationally expensive validation on a…
Simulation in media with multiple continua where each continuum interacts with every other is often challenging due to multiple scales and high contrast. One needs some types of model reduction. One of the approaches is multi-continuum…
We introduce a new numerical strategy to solve a class of oscillatory transport PDE models which is able to captureaccurately the solutions without numerically resolving the high frequency oscillations {\em in both space and time}.Such PDE…
Monocular depth estimation (MDE) plays a pivotal role in various computer vision applications, such as robotics, augmented reality, and autonomous driving. Despite recent advancements, existing methods often fail to meet key requirements…
Hierarchical Bayesian models are increasingly used in large, inhomogeneous complex network dynamical systems by modeling parameters as draws from a hyperparameter-governed distribution. However, theoretical guarantees for these estimates as…
We present and analyze a preconditioned conjugate gradient method (PCG) for solving spatial network problems. Primarily, we consider diffusion and structural mechanics simulations for fiber based materials, but the methodology can be…
The described works have been carried out in the framework of a mid-term study initiated by the Centre Electronique de l'Armement, then by an advanced study launched by the Direction de la Recherche et des Etudes Technologiques in France in…
The hyperbolic random graph model (HRG) has proven useful in the analysis of scale-free networks, which are ubiquitous in many fields, from social network analysis to biology. However, working with this model is algorithmically and…
Many-query problems, arising from uncertainty quantification, Bayesian inversion, Bayesian optimal experimental design, and optimization under uncertainty-require numerous evaluations of a parameter-to-output map. These evaluations become…
Hierarchical spatial models are very flexible and popular for a vast array of applications in areas such as ecology, social science, public health, and atmospheric science. It is common to carry out Bayesian inference for these models via…
This work develops a computational framework that combines physics-informed neural networks with multi-patch isogeometric analysis to solve partial differential equations on complex computer-aided design geometries. The method utilizes…
A multiscale optimization framework for problems over a space of Lipschitz continuous functions is developed. The method solves a coarse-grid discretization followed by linear interpolation to warm-start project gradient descent on…
Neural ordinary differential equations (NODE) have garnered significant attention for their design of continuous-depth neural networks and the ability to learn data/feature dynamics. However, for high-dimensional systems, estimating…
It is of importance to develop statistical techniques to analyze high-dimensional data in the presence of both complex dependence and possible outliers in real-world applications such as imaging data analyses. We propose a new robust…
A new method to solve computationally challenging (random) parametric obstacle problems is developed and analyzed, where the parameters can influence the related partial differential equation (PDE) and determine the position and surface…