230 papers
This paper establishes that symplectic discretizations, including spectral Galerkin spatial semi-discretization and temporal full discretization, weakly asymptotically preserve the large deviations principle of the stochastic linear Schrödinger equation, thereby providing an effective numerical approach for approximating the LDP rate function in infinite-dimensional spaces.
This paper presents a convergence analysis for minimum action methods coupled with finite difference schemes, establishing that the convergence orders of the discrete Freidlin-Wentzell action functional are $1/21\theta$-method for small-noise stochastic differential equations in the context of large deviations.
This paper establishes the convergence of the probability density for a fully discrete finite difference method solving the stochastic Cahn--Hilliard equation with multiplicative space-time white noise by introducing a novel localization argument to overcome the non-Lipschitz drift and partially resolving an open problem regarding the numerical computation of the solution's density.
This paper establishes the Freidlin--Wentzell large deviations principle for the stochastic Cahn--Hilliard equation with small noise and proves the convergence of the one-point large deviations rate function for its spatial finite difference method by utilizing -convergence of objective functions and overcoming non-Lipschitz drift challenges through discrete interpolation inequalities.
This paper establishes the central limit theorem for the temporal average of the backward Euler–Maruyama method applied to stochastic ordinary differential equations with super-linearly growing drift coefficients, deriving the result through direct analysis for sub-optimal deviation orders and via a Poisson equation approach for the optimal strong order.
This paper establishes the strong convergence rate of an Euler-Maruyama numerical scheme for one-dimensional stochastic differential equations with distributional drifts in Hölder-Zygmund spaces, supported by theoretical bounds and numerical implementation.
This paper presents a complete solution to the infinite quantum signal processing problem for arbitrary Szegő functions by introducing the Riemann-Hilbert-Weiss algorithm, which provably computes individual phase factors independently and stably using polylogarithmic precision and polynomial computational cost.
This paper proposes a dynamic domain semi-Lagrangian method for stochastic Vlasov equations driven by transport noises that significantly reduces computational costs through volume-preserving characteristics and domain adaptation, while providing a first-order convergence analysis that partially resolves a recent conjecture on numerical convergence.
This paper proposes a method to enable effective stratified sampling in high-dimensional spaces by using neural active manifolds to identify a one-dimensional latent space that captures model variability, allowing for the creation of input partitions that align with model level sets to significantly reduce variance in uncertainty propagation.
This paper presents an error analysis and a new regularization parameter selection strategy for the iterated Golub-Kahan-Tikhonov method applied to discretized ill-posed operator equations, demonstrating its superior accuracy over both standard Golub-Kahan-Tikhonov and iterated Arnoldi-Tikhonov methods, particularly for non-symmetric matrices.
This paper establishes the quasi-optimality of the Crouzeix-Raviart finite element method for nonlinear -Laplace-type problems by proving that its error is bounded by the best-approximation error and a data oscillation term, while also deriving a novel localized a priori error estimate for the conforming lowest-order Lagrange FEM.
This paper introduces a novel computational framework that utilizes Legendre time-dimensional reduction to transform the inverse initial-data problem for compressible anisotropic Navier-Stokes equations into a solvable system of elliptic equations, enabling the robust and accurate reconstruction of initial velocity fields from noisy boundary observations.
This paper establishes the rigorous convergence of hyperbolic approximations to various higher-order PDEs, including the KdV and Kuramoto-Sivashinsky equations, by proving that weak solutions of the approximations converge to smooth solutions of the limiting problems, a result supported by numerical evidence.
This paper presents a quadrature-based model reduction framework for Lagrangian hydrodynamics that utilizes a strongly energy-conservative variant of the empirical quadrature procedure to achieve near machine-precision total energy conservation while maintaining accuracy comparable to standard methods.
This paper demonstrates that the union of randomly digitally shifted Korobov polynomial lattice point sets achieves a star discrepancy with an inverse that depends linearly on the dimension, thereby narrowing the search for explicit constructions from a continuum to a finite set of candidates.
This paper proposes an auto-adaptive sampling method for Physics Informed Neural Networks (PINNs) that utilizes arbitrary problem-specific heuristics to accurately resolve interfacial regions in Allen-Cahn equations without post-hoc resampling, demonstrating superior performance over residual-adaptive frameworks.
This paper presents numerically stable, closed-form algorithms for computing the eigenvalues of real, diagonalizable $3 \times 3$ matrices using four specific invariants, demonstrating that these methods are both more accurate for repeated eigenvalues and approximately ten times faster than the LAPACK library while maintaining comparable precision.
This paper establishes a minimax theory for operator learning in Hilbert spaces, proving that even with higher regularity assumptions, learning generic Lipschitz operators from noisy samples inevitably suffers from a curse of sample complexity where the risk cannot decay at any algebraic rate.
This paper introduces a novel numerical method that combines a functional equation for the Laplace-Stieltjes transform with a moment-matching technique to efficiently and stably compute the density of the Kesten-Stigum limit for supercritical Galton-Watson processes with arbitrary offspring laws.
This paper introduces a novel Geometric Structure-Preserving Interpolation (-SPIN) method that utilizes geodesic elements and a projection-based relaxation of rotation-deformation coupling to achieve stable, locking-free finite-strain Cosserat micropolar elasticity simulations, particularly in the asymptotic couple-stress limit.