242 papers
This paper presents a multiscale optimization framework for Lipschitz continuous functions that accelerates convergence and reduces computational costs by solving coarse-grid problems to warm-start fine-grid iterations, achieving provably tighter error bounds and significant speedups in applications like probability density estimation.
This paper establishes a unified theoretical framework for CUR matrix approximation and the Nyström method by deriving determinant-based error bounds that connect local projection errors to global quality and quantify the benefits of oversampling through volume sampling.
This paper presents fast, linear-time solvers for the Reynolds equation on piecewise linear geometries using Schur complement inversion, which achieve second-order accuracy for non-linear heights and are validated by comparing their solutions against the Stokes equation to assess the limits of lubrication theory.
This paper extends the CNF framework to solve coupled and non-linear Partial Differential Equations for forward, inverse, and discovery tasks, while providing a comprehensive survey, implementation, and evaluation of various neural PDE solvers to address challenges like the curse of dimensionality and high computational costs.
FastLSQ is a high-performance framework that solves linear and nonlinear partial differential equations (PDEs) and inverse problems with exceptional speed and accuracy by leveraging sinusoidal random Fourier features to enable exact, closed-form analytical derivatives, thereby eliminating the need for automatic differentiation and iterative training.
This paper proposes and evaluates the IS-AS-preintegration method, a three-step approach combining importance sampling, active subspaces, and preintegration within the quasi-Monte Carlo framework, which significantly enhances variance reduction and option pricing efficiency, particularly for out-of-the-money options.
This study comprehensively compares the computational efficiency and numerical accuracy of Python, MATLAB, and R in solving SI and SIR epidemiological models using Euler, Runge-Kutta, and Predictor-Corrector methods to guide researchers in selecting optimal tools for epidemic modeling.
This paper presents a rigorous framework that extends neural operators to robustly handle out-of-distribution input functions by leveraging kernel approximations and Reproducing Kernel Hilbert Space theory to ensure accurate prediction of both function values and derivatives, validated through solutions of elliptic partial differential equations on manifolds.
This paper establishes the strong convergence with order $1/2$ for a geometric Euler-Maruyama scheme applied to stochastic differential equations on Riemannian manifolds and derives a corresponding Wasserstein bound for sampling via Riemannian Langevin dynamics.
This paper proposes an unsupervised, surrogate-assisted framework that automatically generates and optimizes free-form planar antenna topologies for IoT applications by combining a classifier for topology selection with a bi-stage gradient-based tuning process, as validated through numerical experiments on bandwidth-enhanced patch antennas.
This paper presents a bi-stage optimization framework that automates the design of pixel-based planar antennas by first globally optimizing pixel interconnections to determine topology and then refining the structure with a surrogate-assisted local search to meet performance specifications.
This paper bridges the gap between theoretical estimates and numerical evidence for the local discontinuous Galerkin method applied to convection-diffusion equations by establishing new approximation results for Gauss-Radau projections, thereby proving optimal convergence rates even for solutions with limited spatial regularity.
This paper proposes an implicit-explicit trust region method that leverages the specific Hessian structure of Landau-type free energy functionals to efficiently compute second-order stationary points, enabling the identification of physically stable phases like the FDDD structure in the Landau-Brazovskii model with provable convergence guarantees.
This paper proposes a novel multivariate, data-dependent partition of unity method based on Moving Least Squares and Weighted Essentially Non-Oscillatory techniques to achieve high-order accuracy in smooth regions while effectively suppressing spurious oscillations near discontinuities.
This paper proposes a novel semi-implicit numerical scheme based on a stochastic scalar auxiliary variable (SSAV) reformulation for the stochastic Cahn--Hilliard equation with multiplicative noise, which incorporates Itô correction terms to achieve optimal strong convergence of order one-half while preserving the energy evolution law.
This paper presents a statistically robust framework for reconstructing metal–semiconductor contact regions by combining topological gradients with shape optimization, establishing a central limit theorem for convergence and utilizing a key parameter to refine interface sensitivity and distinguish true structural features from noise.
This paper presents a comparative numerical study of six graph-based splitting algorithms specialized for linear subspaces, identifying optimal relaxation parameters and analyzing iteration counts to reveal performance patterns that may inform future theoretical analysis.
This paper presents a non-intrusive, multi-fidelity reduced-order modeling framework that utilizes Optimal Transport-based displacement interpolation to efficiently correct low-fidelity models and construct accurate parametric surrogates for complex, nonlinear two-phase flow simulations.
This paper validates the legitimacy and effectiveness of a newly proposed high-frequency fast direct solver for electromagnetic integral equations on non-canonical geometries by leveraging semiclassical microlocal results to analyze its asymptotic spectral properties.
This paper introduces Exp-ParaDiag, a novel time-parallel framework that integrates exponential integrators to solve parabolic PDEs and nonlinear problems with rigorous convergence guarantees and temporal accuracy ranging from first to sixth order.