225 papers
This paper extends kinetic-based regularization to accurately estimate spatial derivatives from noisy data through explicit and implicit schemes, demonstrating its effectiveness in enabling stable shock capture for 1D hyperbolic PDEs while preserving conservation laws.
The paper introduces Ptychi-Evolve, an autonomous framework that leverages large language models and evolutionary mechanisms to automatically discover and evolve novel regularization algorithms for ptychography, achieving significant reconstruction quality improvements across diverse imaging datasets.
This paper presents the first direct comparison between gate-based quantum computing (using QAOA) and adiabatic quantum computing (via Ising models) for solving AC power flow problems, demonstrating through numerical experiments on a 4-bus system how these paradigms and quantum-inspired solvers trade off accuracy, scalability, and practical viability for future electricity grid optimization.
This paper demonstrates that replacing first-order time integration with higher-order Runge-Kutta methods and adaptive time stepping in the E3SMv3 rain microphysics model significantly improves computational efficiency and accuracy, achieving over 10x speedup compared to the default scheme while eliminating the need for stability-limiting ad hoc procedures.
This paper introduces a reduced-order model based on periodic capacitance matrices and shape optimization to design metascreens that achieve efficient broadband absorption of low-frequency acoustic waves through superabsorption mechanisms.
This paper introduces Onflow, a model-free, online reinforcement learning algorithm that optimizes portfolio allocation via gradient flows to maximize expected log returns, demonstrating robustness to high transaction costs and superior performance compared to existing dynamic strategies without requiring assumptions about asset return distributions.
This paper investigates whether the recently proposed ensemble eddy viscosity approach, which derives turbulent viscosity parameters directly from ensembles of Navier-Stokes solutions with perturbed data, suffers from the over-diffusion issues commonly found in classical eddy viscosity models when applied to shear flows.
This paper systematically analyzes how numerical ill-conditioning caused by multicollinearity in candidate function libraries undermines the robustness of sparse regression for discovering biological dynamics, demonstrating that while orthogonal polynomial bases can improve model recovery under specific data distributions, they often fail or perform worse than monomial libraries when data sampling deviates from their associated weight functions.
This paper establishes the existence of, develops an algorithm for computing, and demonstrates the application of quadratizations that preserve the dissipativity (stability) properties of polynomial ODE systems, thereby enabling more reliable model analysis and control in fields such as systems theory and synthetic biology.
This paper introduces a new space-time variational formulation for the wave equation that is coercive and continuous in a strong norm, enabling stable and quasi-optimal Galerkin discretizations for impedance and impedance-Dirichlet problems in star-shaped domains.
This paper proposes a novel cascaded accumulator method that efficiently computes time-index powered weighted sums in real-time by reducing multiplicative complexity from to constant multiplications while eliminating the need for storing entire data blocks.
This paper establishes a well-posed first-kind integral equation formulation for acoustic scattering by general compact scatterers, including fractals, and develops a convergent piecewise-constant Galerkin discretization with proven rates for fractal attractors, supported by a fully discrete implementation and numerical examples in Julia.
This paper presents a fully adaptive numerical method for simulating open quantum systems governed by the Lindblad master equation by deriving computable a posteriori error bounds that enable the dynamic adjustment of both time steps and Hilbert space truncation to guarantee accuracy and improve computational efficiency.
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 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 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 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 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 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 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.