238 papers
This paper demonstrates that while unconstrained and symmetry-preserving data-driven neural networks both outperform classical large-eddy simulation closures in accuracy, enforcing physical symmetries is crucial for generating more physically consistent velocity-gradient statistics and improving the overall quality of the learned closure.
This paper proposes a novel reformulation of the structured distance to singularity problem as a nonlinear system of equations in two vector unknowns, enabling a faster multivariate Newton-based algorithm that maintains accuracy while ensuring monotonic convergence and avoiding singularities.
This paper presents a robust and unconditionally stable space-time Galerkin time-domain boundary element method for predicting acoustic scattering and shielding by complex geometries, which is validated through analytical cases and successfully applied to a practical trailing edge-mounted propeller scenario with good agreement to experimental data.
This paper establishes theoretical uniform-in-time error bounds for the deterministic ensemble transform Kalman filter applied to infinite-dimensional nonlinear dynamical systems, demonstrating that appropriate multiplicative covariance inflation ensures bounded estimation errors and justifying its practical effectiveness.
This paper presents a scalable monolithic Newton-Krylov-multigrid solver that extends efficient spatial multigrid methods to a space-time waveform relaxation framework for the all-at-once solution of discretized Navier-Stokes equations.
This paper investigates the sensitivity of the Reynolds lubrication equation to large surface gradients and compares its predictions with Stokes flow solutions in various corner geometries, demonstrating that while pressure drop errors increase with steeper gradients, the recirculation zones observed in Stokes flows do not significantly disrupt bulk flow characteristics.
This paper proposes and analyzes a new filtered two-step variational integrator for charged-particle dynamics in moderate to strong magnetic fields, establishing its second-order accuracy, uniform convergence properties, and long-time near-conservation of energy and momentum through backward error analysis and modulated Fourier expansions.
This paper proposes neural network methods, specifically PINNs and RVPINNs, to approximate solutions for Neumann series problems of non-expansive Perron-Frobenius operators, providing theoretical error estimates and demonstrating their effectiveness through numerical examples in 1D, 2D, and a two-cavity system.
This paper proposes and theoretically validates two stochastic gradient descent-based variational inference methods for infinite-dimensional inverse problems, utilizing constant-rate iterations with randomization to efficiently sample from posterior distributions and demonstrating their effectiveness through preconditioning and numerical applications to linear and non-linear problems.
This paper establishes optimal -th order temporal convergence for POD-based reduced order models of semilinear reaction-diffusion equations by employing BDF-q schemes ($1\le q\le 5$) and utilizing first-order difference quotients of snapshots to derive pointwise-in-time error bounds.
This paper develops and analyzes two numerical algorithms based on inverse eigenvalue problems and linear algebra techniques to compute recurrence coefficients for multiple orthogonal polynomials on the step-line, demonstrating their accuracy and stability through experiments on both ill-conditioned and well-conditioned examples.
This paper presents a novel Lightning Method-based approach for solving the planar heat equation that combines Laplace transformation, Talbot inversion, and collocation to achieve spectral accuracy and robust performance across diverse geometric domains and time intervals.
This paper establishes uniform-in-time error bounds for the perturbed observation variant of the ensemble Kalman filter applied to the partially observed Lorenz 96 model by utilizing additive covariance inflation to overcome analytical challenges posed by non-symmetric matrices, with and without projecting the background covariance onto the observation space.
This paper proposes an accurate and memory-efficient sum-of-Gaussians tensor neural network (SOG-TNN) algorithm that overcomes the curse of dimensionality and handles Coulomb singularities in high-dimensional Schrödinger equations through a low-rank tensor representation and a novel range-splitting scheme for electron-electron interactions.
This paper presents improved algorithms for various kernel matrix linear algebra tasks, such as matrix-vector products and spectral norm computation, by leveraging kernel density estimation to achieve faster runtimes with reduced dependencies on the number of data points and error tolerance compared to existing methods.
This paper presents a new formulation of extended lubrication theory and demonstrates through comparison with existing models and numerical Stokes solutions that its accuracy depends significantly on surface variation magnitude and length scale ratio, making it suitable for a wide range of fluid domain geometries.
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.