Neural Active Manifolds: Nonlinear Dimensionality Reduction for Uncertainty Quantification [0.03%]
神经活性流形：用于不确定性量化非线性降维
Andrea Zanoni,Gianluca Geraci,Matteo Salvador et al.
Andrea Zanoni et al.
We present a new approach for nonlinear dimensionality reduction, specifically designed for computationally expensive mathematical models. We leverage autoencoders to discover a one-dimensional neural active manifold (NeurAM) capturing the ...
Fast Reflected Forward-Backward algorithm: achieving fast convergence rates for convex optimization with linear cone constraints [0.03%]
基于线性锥约束的凸优化快速反射前向反演算法及收敛速率分析
Radu Ioan Boţ,Dang-Khoa Nguyen,Chunxiang Zong
Radu Ioan Boţ
In this paper, we derive a Fast Reflected Forward-Backward (Fast RFB) algorithm to solve the problem of finding a zero of the sum of a maximally monotone operator and a monotone and Lipschitz continuous operator in a real Hilbert space. Our...
Daniel Bach,Andrés Rueda-Ramírez,David A Kopriva et al.
Daniel Bach et al.
Free-stream preservation is an essential property for numerical solvers on curvilinear grids. Key to this property is that the metric terms of the curvilinear mapping satisfy discrete metric identities, i.e., have zero divergence. Divergenc...
Unified Discontinuous Galerkin Analysis of a Thermo/Poro-viscoelasticity Model [0.03%]
含热/渗流的粘弹性模型的一致间断Galerkin分析方法研究
Stefano Bonetti,Mattia Corti
Stefano Bonetti
We present and analyze a discontinuous Galerkin method for the numerical modeling of a Kelvin-Voigt thermo/poro-viscoelastic problem. We present the derivation of the model and we develop a stability analysis in the continuous setting that ...
Automatic Differentiation is Essential in Training Neural Networks for Solving Differential Equations [0.03%]
自动微分在训练神经网络解决微分方程中的作用不可或缺
Chuqi Chen,Yahong Yang,Yang Xiang et al.
Chuqi Chen et al.
Neural network-based approaches have recently shown significant promise in solving partial differential equations (PDEs) in science and engineering, especially in scenarios featuring complex domains or incorporation of empirical data. One a...
Surrogate Modeling of Resonant Behavior in Scattering Problems Through Adaptive Rational Approximation and Sketching [0.03%]
基于自适应有理逼近和素描的散射问题共振特性代理模型化研究
Davide Pradovera,Ralf Hiptmair,Ilaria Perugia
Davide Pradovera
This paper describes novel algorithms for the identification of (almost-)resonant behavior in scattering problems. Our methods, relying on rational approximation, aim at building surrogate models of what we call "field amplification", defin...
Ioannis P A Papadopoulos,Sheehan Olver
Ioannis P A Papadopoulos
We develop a sparse hierarchical hp-finite element method (hp-FEM) for the Helmholtz equation with variable coefficients posed on a two-dimensional disk or annulus. The mesh is an inner disk cell (omitted if on an annulus domain) and concen...
Homotopy Relaxation Training Algorithms for Infinite-Width Two-Layer ReLU Neural Networks [0.03%]
无穷宽两层ReLU神经网络的同伦松弛训练算法
Yahong Yang,Qipin Chen,Wenrui Hao
Yahong Yang
In this paper, we present a novel training approach called the Homotopy Relaxation Training Algorithm (HRTA), aimed at accelerating the training process in contrast to traditional methods. Our algorithm incorporates two key mechanisms: one ...
An Efficient Quasi-Newton Method with Tensor Product Implementation for Solving Quasi-Linear Elliptic Equations and Systems [0.03%]
一种求解拟线性椭圆型方程和方程组的高效拟牛顿法及其张量积实现方法研究
Wenrui Hao,Sun Lee,Xiangxiong Zhang
Wenrui Hao
In this paper, we introduce a quasi-Newton method optimized for efficiently solving quasi-linear elliptic equations and systems, with a specific focus on GPU-based computation. By approximating the Jacobian matrix with a combination of line...
A Posteriori Error Analysis for a Coupled Stokes-Poroelastic System with Multiple Compartments [0.03%]
多重隔室耦合Stokes- poroelastic系统的后验误差分析
Ivan Fumagalli,Nicola Parolini,Marco Verani
Ivan Fumagalli
The computational effort entailed in the discretization of fluid-poromechanics systems is typically highly demanding. This is particularly true for models of multiphysics flows in the brain, due to the geometrical complexity of the cerebral...