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Geometry is central to PDE-governed systems, motivating shape optimization and inversion. Classical pipelines conduct costly forward simulation with geometry processing, requiring substantial expert effort. Neural surrogates accelerate…
Green's function provides an inherent connection between theoretical analysis and numerical methods for elliptic partial differential equations, and general absence of its closed-form expression necessitates surrogate modeling to guide the…
We develop a numerical homogenization method for fourth-order singular perturbation problems within the framework of heterogeneous multiscale method. These problems arise from heterogeneous strain gradient elasticity and elasticity models…
Iterative methods are widely used for solving partial differential equations (PDEs). However, the difficulty in eliminating global low-frequency errors significantly limits their convergence speed. In recent years, neural networks have…
In view of the problems that existing salient object detection (SOD) methods are prone to losing details, blurring edges, and insufficient fusion of single-modal information in complex scenes, this paper proposes a dynamic uncertainty…
We consider adaptive finite element methods (AFEMs) with inexact algebraic solvers for second-order symmetric linear elliptic diffusion problems. Optimal complexity of AFEM, i.e., optimal convergence rates with respect to the overall…
The accessibility of spatially distributed data, enabled by affordable sensors, field, and numerical experiments, has facilitated the development of data-driven solutions for scientific problems, including climate change, weather…
Spherical deep learning has been widely applied to a broad range of real-world problems. Existing approaches often face challenges in balancing strong spherical geometric inductive biases with the need to model real-world heterogeneity. To…
We introduce the Neural Preconditioning Operator (NPO), a novel approach designed to accelerate Krylov solvers in solving large, sparse linear systems derived from partial differential equations (PDEs). Unlike classical preconditioners that…
We present scalable iterative solvers and preconditioning strategies for Hybridizable Discontinuous Galerkin (HDG) discretizations of partial differential equations (PDEs) on graphics processing units (GPUs). The HDG method is implemented…
Artificial intelligence and deep learning are currently reshaping numerical simulation frameworks by introducing new modeling capabilities. These frameworks are extensively investigated in the context of model correction and…
The numerical simulation of the physical systems has become in recent years a fundamental tool to perform analyses and predictions in several application fields, spanning from industry to the academy. As far as large scale simulations are…
As deep learning continues to advance and is applied to increasingly complex scenarios, the demand for concurrent deployment of multiple neural network models has arisen. This demand, commonly referred to as multi-tenant computing, is…
Many important real-world applications, such as System Identification with Gaussian Processes, involve solving linear systems with symmetric positive-definite matrices. The iterative CG method and direct solvers based on the Cholesky…
Homogenization is a fundamental tool for studying multiscale physical phenomena. Traditional numerical homogenization methods, heavily reliant on finite element analysis, demand significant computational resources, especially for complex…
Numerous Neural Combinatorial Optimization (NCO) solvers have been proposed to address Vehicle Routing Problems (VRPs). However, most of these solvers focus exclusively on single-vehicle VRP variants, overlooking the more realistic min-max…
Automatic segmentation of an image to identify all meaningful parts is one of the most challenging as well as useful tasks in a number of application areas. This is widely studied. Selective segmentation, less studied, aims to use limited…
An encoder-decoder neural network has been used to examine the possibility for acceleration of a partial integro-differential equation, the Fokker-Planck-Landau collision operator. This is part of the governing equation in the massively…
We consider the preconditioned conjugate gradient method (PCG) with optimal preconditioner in the frame of the boundary element method (BEM) for elliptic first-kind integral equations. Our adaptive algorithm steers the termination of PCG as…
The recent rise of deep learning has led to numerous applications, including solving partial differential equations using Physics-Informed Neural Networks. This approach has proven highly effective in several academic cases. However, their…