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This paper presents a learnable solver tailored to iteratively solve sparse linear systems from discretized partial differential equations (PDEs). Unlike traditional approaches relying on specialized expertise, our solver streamlines the…
Despite the rapid evolution of semantic segmentation for land cover classification in high-resolution remote sensing imagery, integrating multiple data modalities such as Digital Surface Model (DSM), RGB, and Near-infrared (NIR) remains a…
Recent works in learning-integrated optimization have shown promise in settings where the optimization problem is only partially observed or where general-purpose optimizers perform poorly without expert tuning. By learning an optimizer…
This paper presents a homogenization framework for elastomeric metamaterials exhibiting long-range correlated fluctuation fields. Based on full-scale numerical simulations on a class of such materials, an ansatz is proposed that allows to…
Simulation of multiphase poromechanics involves solving a multi-physics problem in which multiphase flow and transport are tightly coupled with the porous medium deformation. To capture this dynamic interplay, fully implicit methods, also…
The widely used density matrix renormalization group (DRMG) method often fails to converge in systems with multiple length scales, such as lattice discretizations of continuum models and dilute or weakly doped lattice models. The local…
We present the Multilevel Bregman Proximal Gradient Descent (ML BPGD) method, a novel multilevel optimization framework tailored to constrained convex problems with relative Lipschitz smoothness. Our approach extends the classical…
Vertex-patch smoothers are essential for the robust convergence of geometric multigrid methods in high-order finite element applications, yet their adoption is traditionally hindered by the prohibitive cost of solving local patch problems.…
This paper proposes Neural-MMGS, a novel neural 3DGS framework for multimodal large-scale scene reconstruction that fuses multiple sensing modalities in a per-gaussian compact, learnable embedding. While recent works focusing on large-scale…
Recent advancements in 3D reconstruction coupled with neural rendering techniques have greatly improved the creation of photo-realistic 3D scenes, influencing both academic research and industry applications. The technique of 3D Gaussian…
We present an efficient numerical method, inspired by transformation optics, for solving the Poisson equation in complex and arbitrarily shaped geometries. The approach operates by mapping the physical domain to a uniform computational…
Homogenisation empowers the efficient macroscale system level prediction of physical scenarios with intricate microscale structures. Here we develop an innovative powerful, rigorous and flexible framework for asymptotic homogenisation of…
Graph similarity learning (GSL), also referred to as graph matching in many scenarios, is a fundamental problem in computer vision, pattern recognition, and graph learning. However, previous GSL methods assume that graphs are homogeneous…
Mapping and localization are crucial problems in robotics and autonomous driving. Recent advances in 3D Gaussian Splatting (3DGS) have enabled precise 3D mapping and scene understanding by rendering photo-realistic images. However, existing…
Heterogeneous materials, crucial in various engineering applications, exhibit complex multiscale behavior, which challenges the effectiveness of traditional computational methods. In this work, we introduce the Micromechanics Transformer…
Geometric matrix completion (GMC) has been proposed for recommendation by integrating the relationship (link) graphs among users/items into matrix completion (MC). Traditional GMC methods typically adopt graph regularization to impose…
Low-altitude Gaussian splatting (LAGS) facilitates 3D scene reconstruction by aggregating aerial images from distributed drones. However, as LAGS prioritizes maximizing reconstruction quality over communication throughput, existing…
Soft, porous mechanical metamaterials exhibit pattern transformations that may have important applications in soft robotics, sound reduction and biomedicine. To design these innovative materials, it is important to be able to simulate them…
A major obstacle to achieving global convergence in distributed and federated learning is the misalignment of gradients across clients, or mini-batches due to heterogeneity and stochasticity of the distributed data. In this work, we show…
Data-driven modeling plays an increasingly important role in different areas of engineering. For most of existing methods, such as genetic programming (GP), the convergence speed might be too slow for large scale problems with a large…