1517 papers
This paper demonstrates that the Modified Method of Characteristics (MMOC) offers a computationally efficient and accurate alternative to Lax-Friedrichs and Lax-Wendroff schemes for the inverse design of the Doswell frontogenesis equation, despite not preserving identity conservation.
This paper proposes a general framework for efficient experimental design that uses randomized matrix sketching and gradient-free ensemble sampling to down-sample data while preserving the sensitivity information of the Fisher Information Matrix, thereby ensuring robust parameter reconstruction in inverse problems.
This paper demonstrates that adding sparse random Gaussian perturbations to a non-normal matrix regularizes its eigenvalue stability and eigenvector conditioning, achieving results comparable to dense perturbations while modifying only a small fraction of the matrix entries.
This paper proposes a fully online, batch-free covariance matrix estimator constructed solely from Newton iterates for sketched Newton methods, enabling consistent online statistical inference for model parameters in streaming data scenarios without requiring matrix factorization.
This paper proposes a novel continuous mathematical framework that rigorously interprets the Transformer architecture as a discretization of a structured integro-differential equation, thereby characterizing self-attention as a non-local integral operator and layer normalization as a time-dependent projection to provide a unified, operator-theoretic foundation for understanding and designing these models.
This paper presents and analyzes a two-scale mathematical model for colloidal deposition in porous media with evolving microstructures, establishing weak solvability for the non-clogging regime and demonstrating through numerical simulations how local clogging impacts effective transport and storage properties.
This paper establishes a global uniqueness theorem for simultaneously reconstructing obstacle geometry and impedance boundary conditions from multi-frequency near-field backscattering data using high-frequency asymptotic expansions, and proposes a novel three-stage numerical framework that achieves robust and efficient reconstruction without solving the direct scattering problem.
This paper introduces ProxiCBO, a provably convergent interacting-particle method that combines consensus-based optimization with proximal gradient techniques to effectively solve non-convex composite optimization problems in signal processing, outperforming existing methods in accuracy and particle efficiency.
This paper establishes a last-iterate convergence rate for SGD with greedy step size over smooth quadratics in the interpolation regime, improving upon the previous bound by introducing stochastic contraction processes and analyzing them through a discrete-to-continuous reduction.
This paper establishes a quantitative stability estimate for the moment measure problem and leverages this result to develop and numerically validate a semi-discrete approximation approach solved via a Newton method.
This paper presents and rigorously analyzes a novel, explicit, and symmetric second-order splitting scheme for charged-particle dynamics in strong magnetic fields under maximal ordering, which achieves improved uniform error bounds for position and parallel velocity while ensuring long-term energy near-conservation.
This paper resolves the ill-posed nature of policy iteration for stationary discounted Hamilton–Jacobi–Bellman equations by introducing a monotone semi-discrete scheme with artificial viscosity, which ensures geometric convergence to a unique discrete solution and provides sharp error estimates that decouple iteration and discretization errors.
This paper demonstrates that Oblivious Subspace Injection (OSI), while sufficient for constant-factor guarantees in randomized low-rank approximation and least-squares regression, is theoretically insufficient to ensure relative error bounds without additional control over the optimal residual or tail component.
This paper investigates log-weighted quadrature domains (LQDs) defined by a singular weight, establishing a generalized Schwarz function characterization, proving that simply connected LQDs correspond to Riemann maps whose outer factors are exponentials of rational functions, and providing explicit formulae linking quadrature functions to Riemann maps via the Faber transform.
This paper presents and analyzes a stable $hp$-finite element/boundary element coupling method on non-matching unstructured meshes using Nitsche's method, which avoids the Babuška-Brezzi condition by providing explicit stabilization thresholds and a priori error estimates for both bounded and unbounded domain configurations.
This paper introduces and analyzes a novel high-order conformal finite element method using Lagrange elements and the BDF2 time scheme to efficiently solve multidimensional nonlinear collisional breakage equations while preserving key physical quantities and achieving optimal convergence rates.
This paper establishes the local well-posedness of a diffusion-enhanced modified Navier-Stokes-Cahn-Hilliard-Oldroyd system motivated by thrombus modeling and validates the model through Physics-Informed Neural Network (PINN) simulations that utilize Metropolis-Hastings sampling based on energy decay.
This paper presents and analyzes a Discontinuous Petrov-Galerkin (DPG) method with optimal test functions for an elastic circular arch model, demonstrating through theoretical analysis and numerical experiments that the approach achieves optimal convergence rates and can be further improved by employing a suitably scaled test space norm.
This paper investigates the benefits of combining anisotropic and lengthscale-informed sparse grid constructions for kernel interpolation with separable Matérn kernels, demonstrating through theory and experiments that adapting to dimension-dependent regularity and lengthscale parameters improves both asymptotic and pre-asymptotic convergence rates.