218 papers
This paper introduces a novel, locally conservative spatial discretization for the compressible Euler equations of thermally perfect gases that guarantees discrete entropy conservation while preserving linear invariants and kinetic energy, offering improved accuracy and robustness over existing methods.
This paper proves and numerically validates that tensor-product -finite element approximations for the Dirichlet integral fractional Laplacian on a 3D cuboid with analytic forcing achieve root exponential convergence in the energy norm, specifically bounded by , by leveraging analytic regularity in weighted Sobolev spaces and geometrically refined meshes.
This paper presents an accelerated direct solver based on boundary integral equations and low-rank proxy approximations that efficiently handles scalar wave scattering by multiple 2D transmissive inclusions, achieving computational complexity and demonstrating superior performance with the PMCHWT formulation over the Burton-Miller approach.
This paper proposes a novel direct sampling method that utilizes multi-frequency far-field measurements to simultaneously reconstruct both the temporal radiating time and the spatial support of time-dependent electromagnetic sources governed by Maxwell's equations.
This paper establishes strong convergence rates for semi-discrete and fully discrete finite element approximations of a fourth-order stochastic pseudo-parabolic equation driven by additive noise, supported by numerical experiments.
This paper introduces a stable, unconditionally robust four-field mixed finite element method for incompressible nonlinear elasticity that utilizes a discontinuous displacement field to eliminate the need for stabilization in both 2D and 3D, while providing theoretical well-posedness, error estimates, and an efficient postprocessing technique to recover accurate continuous solutions.
This paper investigates the use of additive overlapping Schwarz domain decomposition methods as scalable preconditioners for solving the large sparse linear systems arising in pose-graph SLAM optimization, demonstrating through numerical experiments and structural analogies to finite element problems that these techniques ensure the convergence of the preconditioned conjugate gradient method remains independent of problem size.
This paper proposes a novel -adaptive algorithm for the Poisson equation with fixed polynomial degree that guarantees -robust error contraction and optimal algebraic convergence rates under a verifiable a posteriori criterion, supported by numerical experiments.
This paper proposes an efficient, unconditionally stable predictor-corrector algorithm combining orthogonal spline collocation finite elements with variable time stepping to achieve high-order accuracy and suppress numerical oscillations in solving the FitzHugh-Nagumo system.
This paper develops and analyzes a continuous data assimilation framework using a nudging-based approach and a capped finite element splitting scheme to recover trajectories of a coupled Navier-Stokes-Cahn-Hilliard system with an auxiliary field from coarse spatial observations, demonstrating its effectiveness in synchronizing mismatched initial conditions through numerical experiments.
XConv is a drop-in replacement for standard convolutional layers that significantly reduces memory usage during training by storing compressed activations and approximating weight gradients via randomized trace estimation, while maintaining performance comparable to exact gradient methods without imposing architectural constraints or requiring codebase modifications.
This paper proposes a unified, target-gradient-free generative sampling framework that enforces time-reversibility constraints via Maximum Mean Discrepancy minimization between forward and backward Markov trajectories, enabling efficient sampling from complex continuous, discrete, and hybrid distributions using only energy evaluations.
This paper presents a physics-informed neural network (PINN) framework that robustly reconstructs hidden state variables and estimates biophysical parameters in multiscale neuronal models using only partial, noisy voltage observations, effectively overcoming the convergence failures and sensitivity issues common in traditional numerical methods.
This paper introduces a family of mean-normalized matrix operator norms to derive width-independent smoothness bounds for deep neural networks, leading to the development of MOGA, a row/column-normalized optimizer that enables stable hyperparameter transfer across model widths and outperforms Muon in speed while maintaining competitive performance.
This paper introduces OptEMA, a novel adaptive Exponential Moving Average optimizer that achieves nearly optimal convergence rates in both stochastic and zero-noise regimes without requiring prior knowledge of Lipschitz constants or manual hyperparameter tuning.
This paper establishes the optimal trade-off between width and depth for deep ReLU neural networks to memorize separated data points, proving that the product of the squared width and squared depth must scale as .
This paper introduces a unified framework that models quantization and sparsification as additive noise to derive a principled, noise-corrective gradient path, enabling the stable training of neural networks at arbitrary low precisions and sparsity levels without relying on heuristic estimators like the Straight-Through Estimator.
This paper presents a quantum numerical scheme for solving anisotropic diffusion and convection equations that utilizes vector-norm analysis to achieve an exponential reduction in the required number of time-steps compared to previous operator-norm bounds.
This paper proposes unfolding-free majorization-minimization algorithms for nonnegative CP and Tucker tensor decompositions under -divergences, utilizing tensor contractions and joint update strategies to achieve theoretical convergence guarantees and significant computational speedups over traditional unfolding-based methods.
This paper introduces a novel, exactly solvable ordinary differential equation model incorporating an Allee effect to study rate-induced tipping, featuring finite-time extinction, a derived integral inequality for tipping conditions, a superior numerical method, and a practical application to the historical rise and fall of Japanese inland fisheries.