226 papers
This paper introduces ALFCG, the first adaptive, projection-free framework for stochastic composite nonconvex optimization that eliminates the need for global smoothness constants or line search by using self-normalized accumulators to estimate local smoothness, achieving optimal iteration complexity up to logarithmic factors while outperforming state-of-the-art baselines.
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.
This paper presents a framework for the certified and accurate computation of deep neural network function space norms (including , , and ) by combining interval arithmetic, adaptive refinement, and quadrature to derive guaranteed global bounds from local certificates, thereby enabling reliable error control for PDE applications like PINNs.
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 presents an integrated machine learning framework that combines a Klinkenberg-enhanced constitutive relation with a Hopf-Cole-transformed linear system and a Deep Least-Squares solver to accurately model nonlinear gas flow in porous media and efficiently estimate pressure-dependent permeability and slippage parameters.
This paper introduces a Runge-Kutta stage-aligned computation method that reduces the computational complexity of explicit Lagrangian metapopulation models from quadratic to linear scaling with respect to the number of spatial patches, enabling efficient and exact numerical simulations of epidemic spread without relying on heuristic approximations.
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 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 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 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 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 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 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 the probabilistic superiority of stochastic symplectic methods over non-symplectic ones by proving that the former asymptotically preserve the large deviations principles governing the exponential decay of hitting probabilities for the mean position and velocity of stochastic Hamiltonian systems, a result demonstrated via the Gärtner–Ellis theorem on the linear stochastic oscillator.
This paper establishes that symplectic discretizations, including spectral Galerkin spatial semi-discretization and temporal full discretization, weakly asymptotically preserve the large deviations principle of the stochastic linear Schrödinger equation, thereby providing an effective numerical approach for approximating the LDP rate function in infinite-dimensional spaces.
This paper presents a convergence analysis for minimum action methods coupled with finite difference schemes, establishing that the convergence orders of the discrete Freidlin-Wentzell action functional are $1/21\theta$-method for small-noise stochastic differential equations in the context of large deviations.
This paper establishes the convergence of the probability density for a fully discrete finite difference method solving the stochastic Cahn--Hilliard equation with multiplicative space-time white noise by introducing a novel localization argument to overcome the non-Lipschitz drift and partially resolving an open problem regarding the numerical computation of the solution's density.
This paper establishes the Freidlin--Wentzell large deviations principle for the stochastic Cahn--Hilliard equation with small noise and proves the convergence of the one-point large deviations rate function for its spatial finite difference method by utilizing -convergence of objective functions and overcoming non-Lipschitz drift challenges through discrete interpolation inequalities.