Applied Math · Mathematics & Statistics
Numerical Analysis
The newest papers in Numerical Analysis that ReadSearch has read, newest first. Each links to its own page, with its authors, date, where it was published and the original.
285 papers, from 31 August 2026 to 5 November 2026: 212 arXiv preprints and 73 OpenAlex records.
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Newest papers, page 3
Meshless Latent Dynamics Models for Model Order Reduction of time-dependent Partial Differential Equations
Latent dynamics learning has emerged as a prominent approach for Model Order Reduction (MOR) of time-dependent, parameterized Partial Differential Equations (PDEs).The information geometry of the Sinkhorn divergence on a Hilbert manifold
The Sinkhorn divergence, the debiased entropic optimal transport cost, determines a metric tensor on probability measures defined along curves, due to Lavenant et al. We construct a real-analytic…In-Context Learning for Multi-Fidelity Multiscale Model Closure and Cross-Operator Out-Of-Distribution Generalization
Multi-fidelity learning uses low-fidelity information (coarse-scale PDE models) together with limited high-fidelity data (fine-scale solutions) to obtain high-accuracy PDE solutions.Scalable Bayesian Quadrature via Operator-Adapted Features
Kernel methods face two recurrent bottlenecks: the cubic cost of inverting an $n\times n$ kernel matrix, as in kernel ridge regression, and the evaluation of kernel integrals, as required in kernel…A Hybrid Physics-informed holomorphic neural networks Method
Physics-informed holomorphic neural networks (PIHNNs) exploit complex-analytic representations to satisfy homogeneous PDEs by construction, but their extension to nonhomogeneous problems is…Dual Area-Volume-of-Fluid (DAVOF): co-advecting volume and face-area fractions for a closed-form, cell-local interface normal and position on unstructured meshes
Geometric Volume-of-Fluid (VOF) on unstructured polyhedral meshes reconstructs the interface orientation from the volume fractions of a stencil of neighbours; on irregular cells and in the presence…Exponential-Nemytskii Neural Operators: Learning Field Evolution Across Step Sizes
In variable-step operator learning, agreement at observed step sizes does not by itself determine predictions at other temporal resolutions.Holomorphic Cauchy Networks for Efficient Stationary Tail Computation in High-Dimensional Reflected Brownian Motions
Stationary tail computation for high-dimensional reflected Brownian motions (RBMs) remains computationally challenging.Quantum circuits of elastic wave equations via Schrödingerisation
We construct explicit quantum circuits for the velocity-stress formulation of elastic wave equations in homogeneous media using Schrödingerisation.AMOR: Adaptive Modal Operator Refinement for Operator Learning on Arbitrary Meshes and Irregular 3D Geometries
Parametric PDEs in science and engineering are often posed on irregular meshes with geometries that may contain holes or complex boundaries, yet popular operator-surrogate architectures such as the…Global $\mathcal{O}\left(k^{-2}\right)$ Convergence of Multilevel Gradient-Regularized Newton Methods
We develop and analyze multilevel gradient-regularized Newton methods for unconstrained convex optimization with Lipschitz-continuous Hessians.Measurement-dependent reduction of open dynamics in the quantum phase estimation algorithm: the visible subspace and the damped Fejér kernel
For the quantum phase estimation (QPE) algorithm we study the minimal space of observables that is sufficient to predict the entire output distribution under open dynamics of the counting register.Model reduction in time: Learning flow maps for reducing stochastic dynamical systems in time
Predictions with dynamical systems can be computationally expensive---even with reduced models---because reaching future prediction times can require many sequential time integration steps.Dynamical Tensor Train Approximation for Wigner--Fokker--Planck Equation with Applications to Open Quantum Systems
We develop a dynamical tensor-train method for the Wigner--Fokker--Planck equation arising in continuous-variable open quantum systems.Balanced Active Subspaces for Optimal Control via Trajectory Optimization
The curse of dimensionality associated with solving the Hamilton-Jacobi-Bellman equation for the value function remains a key obstacle for real-time optimal feedback control of high-dimensional…Greedy Orthogonal Polynomial Manifolds with Lipschitz Control for Dimensionality Reduction and Reduced Modeling
Polynomial manifolds provide nonlinear low-dimensional representations through polynomial decoders.Covariance-Informed Ensemble Score Filtering: Embedding Localized Covariance Geometry into Score-Based Transport
error covariance models are central to atmospheric data assimilation because they spread partial observational information across space, variables, and dynamically coupled scales.Solving and Learning Navier-Stokes Dynamics with the Neural Basis Method
Physics-informed machine learning has become a major direction in predictive modeling of fluid dynamics, combining governing physics with learned representations.CoPiT: A conditional Position-induced Transformer for aerodynamic field prediction on unstructured meshes
High-fidelity Reynolds-averaged Navier--Stokes (RANS) simulations remain a standard tool for aerodynamic analysis, yet each solve on an unstructured mesh is computationally expensive, making…Universal neural network approximation of symmetric polyconvex energies and envelopes
Symmetric polyconvexity provides a sufficient condition for weak lower semicontinuity in small-strain elasticity and a tractable lower bound for the relaxation of non-(quasi)convex energies.