224 papers
This paper proves a consistency result for the Domain of Dependence (DoD) cut cell stabilization method with arbitrary polynomial degrees and sufficiently regular exact solutions, thereby enabling a rigorous error analysis for high-order applications.
This paper proposes a novel sampling method for unnormalized Boltzmann densities that leverages a sequence of Langevin samplers to efficiently simulate a probability flow ODE derived from linear stochastic interpolants by generating intermediate samples and robustly estimating the velocity field, while providing theoretical convergence guarantees and demonstrating effectiveness on challenging multimodal distributions and Bayesian inference tasks.
This paper proposes a memory-efficient, quasi matrix-free solver that leverages the self-similarity of lattice structures through a reduced-order modeling strategy within a domain-decomposition framework to enable fast, full fine-scale nonlinear simulations of complex hyperelastic metamaterials on standard hardware.
This paper presents a Lanczos tau method for approximating and optimizing the -norm of delay differential algebraic systems, proving its convergence and stability under specific conditions while deriving efficient gradient formulas for robust controller synthesis and demonstrating accelerated convergence through spline-based extensions.
This paper evaluates and compares different auxiliary problem designs for homotopy continuation methods, demonstrating that a new approach based on the entropy solution offers a robust and systematic strategy for solving the nonlinear coupling challenges in multiphase flow within porous media.
This paper demonstrates that a natively spiking neuromorphic algorithm for solving partial differential equations possesses intrinsic fault tolerance, maintaining accuracy even when up to 32% of neurons and 90% of spikes are dropped, with this robustness being tunable via structural hyperparameters.
This paper addresses the continuous inverse problem of reconstructing a geometric -rough path driving a rough differential equation to match an observed trajectory by establishing a rigorous framework for approximating the solution through convergent discrete inverse problems and developing a numerical algorithm based on path signatures that iteratively updates local gradients.
This paper proposes a fast, deterministic tensor completion method that leverages standard linear algebra to recover tensors from fiberwise observations along a single mode, offering efficient recovery guarantees without relying on random sampling assumptions.
This paper presents a deterministic, realizability-preserving finite element framework for proton therapy dose calculation that solves the energy-dependent moment model backward in energy using a monolithic convex limiting strategy and Strang-type operator splitting to ensure physically admissible, accurate dose distributions.
This paper presents a theoretical analysis establishing quantitative error bounds for Bayesian inverse problems using generative priors, demonstrating that the posterior error inherits the convergence rate of the prior in Wasserstein distance, and validates these findings through numerical experiments on benchmarks and an elliptic PDE inverse problem.
This paper develops a discrete solvability analysis for perturbed saddle-point problems in Banach spaces with non-regular loads in , using a projector based on the adjoint of a weighted Clément quasi-interpolation to derive a priori estimates, supercloseness results, and convergence analysis for a modified Stenberg postprocessing scheme, with applications illustrated through the linearized Poisson–Boltzmann equation and numerical experiments.
This paper presents a method for obtaining precise and inexpensive upper bounds on the condition number of Chebyshev filtered vectors, which is then used to implement an adaptive QR-factorization selection mechanism in the ChASE library that enhances performance without compromising accuracy.
This paper introduces the tubal tensor train (TTT) decomposition, a novel tensor network model that integrates t-product algebra with the tensor train structure to achieve linear storage scaling for high-order tensors, and validates its effectiveness through efficient algorithms and applications in image/video compression, tensor completion, and hyperspectral imaging.
This paper proposes a fast graph neural network-based method for estimating the condition numbers of sparse matrices with linear complexity relative to the number of non-zero elements, demonstrating significant speedups over traditional Hager-Higham and Lanczos methods.
This paper proposes a trust-region interior-point stochastic sequential quadratic programming (TR-IP-SSQP) method that utilizes adaptive stochastic oracles to solve optimization problems with stochastic objectives and deterministic nonlinear constraints, proving its global almost-sure convergence to first-order stationary points and demonstrating practical performance on benchmark and logistic regression problems.
This paper presents a novel QR decomposition-based compression scheme combined with a tailored preconditioner and volume integral equations to enable fast and accurate iterative solutions for electromagnetic scattering from large-scale metasurfaces composed of thousands of sub-wavelength scatterers.
The paper introduces Geo-ADAPT-VQE, a geometry-aware adaptive variational quantum eigensolver that utilizes natural gradients for operator selection to achieve faster, more stable convergence and significantly shorter ansatz circuits compared to existing gradient-based methods.
This paper introduces a geometrically explicit Cosserat rod formulation that unifies Lie-group configuration coordinates with piecewise-linear strain parameterization to create a robust, locking-free simulation framework capable of efficiently modeling complex rod networks and closed-loop structures on SE(3).
This paper presents a novel, fully geometric, and conservative 3D Volume-of-Fluid method that combines a modified advection scheme for mixed cells with a height-function-based contact angle imposition to accurately simulate moving contact lines with hysteresis on complex embedded boundaries while overcoming severe time-step limitations.
This paper introduces a novel class of single- and multi-level Fourier-RQMC algorithms that leverage frequency-domain integration and randomized quasi-Monte Carlo sampling to achieve superior accuracy and computational efficiency in estimating multivariate shortfall risk and optimal capital allocations compared to traditional Monte Carlo methods.