Related papers: Multilevel radial basis function surrogates for no…
The rarefied flow and multi-scale flow are crucial for the aerodynamic design of spacecraft, ultra-low orbital vehicles and plumes. By introducing a discrete velocity space, the Boltzmann method, such as the discrete velocity method and…
Neural operators (NOs) struggle with high-contrast multiscale partial differential equations (PDEs), where fine-scale heterogeneities cause large errors. To address this, we use the Generalized Multiscale Finite Element Method (GMsFEM) that…
In this paper, we propose a method for the construction of locally conservative flux fields through a variation of the Generalized Multiscale Finite Element Method (GMsFEM). The flux values are obtained through the use of a Ritz formulation…
In this paper, we propose a randomized generalized multiscale finite element method (Randomized GMsFEM) for flow problems with parameterized inputs and high-contrast heterogeneous media. The method employs a data-driven predictor to…
Quasi-periodic solutions with multiple base frequencies exhibit the feature of $2\pi$-periodicity with respect to each of the hyper-time variables. However, it remains a challenge work, due to the lack of effective solution methods, to…
Porous media are ubiquitous in energy storage and conversion, catalysis, biomechanics, hydrogeology, as well as many other fields. These materials possess high surface-to-volume ratios and their complex channels can restrict and guide the…
The safety of training task policies and their subsequent application using reinforcement learning (RL) methods has become a focal point in the field of safe RL. A central challenge in this area remains the establishment of theoretical…
Approximation of scattered data is often a task in many engineering problems. The Radial Basis Function (RBF) approximation is appropriate for big scattered datasets in $n-$dimensional space. It is a non-separable approximation, as it is…
Simulating complex gas flows from turbulent to rarefied regimes is a long-standing challenge, since turbulence and rarefied flow represent contrasting extremes of computational aerodynamics. We propose a multiscale method to bridge this…
A ubiquitous challenge in design space exploration or uncertainty quantification of complex engineering problems is the minimization of computational cost. A useful tool to ease the burden of solving such systems is model reduction. This…
We present a non-nested multilevel algorithm for solving the Poisson equation discretized at scattered points using polyharmonic radial basis function (PHS-RBF) interpolations. We append polynomials to the radial basis functions to achieve…
Referring remote sensing image segmentation (RRSIS) is a novel visual task in remote sensing images segmentation, which aims to segment objects based on a given text description, with great significance in practical application. Previous…
Approximation of scattered geometric data is often a task in many engineering problems. The Radial Basis Function (RBF) approximation is appropriate for large scattered (unordered) datasets in d-dimensional space. This method is useful for…
Robust beamforming design under imperfect channel state information (CSI) is a fundamental challenge in multiuser multiple-input multiple-output (MU-MIMO) systems, particularly when the channel estimation error statistics are unknown.…
We study personalized federated learning for multivariate responses where client models are heterogeneous yet share variable-level structure. Existing entry-wise penalties ignore cross-response dependence, while matrix-wise fusion…
For multiscale gas flows, kinetic-continuum hybrid method is usually used to balance the computational accuracy and efficiency. However, the kinetic-continuum coupling is not straightforward since the coupled methods are based on different…
Reduced-basis methods (RB methods or RBMs) form one of the most promising techniques to deliver numerical solutions of parametrized PDEs in real-time performance with reasonable accuracy. For incompressible flow problems, RBMs based on LBB…
In this paper, practical utilization of multiple distributed reconfigurable intelligent surfaces (RISs), which are able to conduct group-specific operations, for multi-group multicasting systems is investigated. To tackle the inter-group…
Remote sensing image interpretation plays a critical role in environmental monitoring, urban planning, and disaster assessment. However, acquiring high-quality labeled data is often costly and time-consuming. To address this challenge, we…
The method of fundamental solutions (MFS) is known to be effective for solving 3D Laplace and Stokes Dirichlet boundary value problems in the exterior of a large collection of simple smooth objects. Here we present new scalable MFS…