245 papers
This paper introduces a multilevel training framework for Kolmogorov-Arnold Networks (KANs) that leverages their structural equivalence to multichannel MLPs and the properties of spline basis functions to create a properly nested hierarchy of models, resulting in orders-of-magnitude improvements in training accuracy and speed, particularly for physics-informed neural networks.
This paper establishes the regularizing properties of quantum relative entropy for solving the inverse problem of quantum state tomography in high or infinite dimensions, providing the necessary theoretical foundations and computational tools to apply iterative convex optimization algorithms to practical examples like PINEM and optical homodyne tomography.
This paper proves the -convergence of the time-splitting scheme to the unique global strong solution of the nonlinear Dirac equation in 1+1 dimensions by establishing pointwise estimates, constructing a modified Glimm-type functional for stability, and demonstrating the precompactness of the approximate solutions.
This paper presents a general framework for deriving Nitsche Finite Element Methods to enforce equality and inequality constraints in solid mechanics by reformulating stabilized saddle point problems into a minimization form suitable for nonlinear applications and automatic differentiation, while validating the approach through numerical convergence studies.
This paper establishes quantitative error estimates linking microscopic fluctuations in interacting particle systems and regularized stochastic PDEs to their macroscopic mobilities, while also characterizing the asymptotic behavior of fluctuation structures in irregular Dean-Kawasaki type equations through renormalized kinetic solutions.
This paper proposes an efficient, spectrally accurate, and memory-economic numerical method combining a preconditioned conjugate gradient algorithm with an anisotropic truncated kernel method to compute the complex ground states of three-dimensional rotating dipolar Bose-Einstein condensates under strongly anisotropic traps, successfully addressing challenges like kernel singularities and fast rotation to reveal novel patterns such as bent vortices.
This paper proves that a median lattice algorithm, which aggregates multiple rank-1 lattice sampling rules via componentwise median, achieves high-probability, nearly optimal worst-case -approximation rates for multivariate periodic functions in weighted Korobov spaces, with dimension-independent constants for under specific weight summability conditions.
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.