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 9
GAC-PINN: Geometry-Adaptive and Constraint-Enhanced Physics-Informed Neural Networks
For systems with steep gradients, sharp interfaces, or severe spatio-temporal coupling, Physics-informed neural networks (PINNs) suffer from spectral bias, geometric inflexibility, and boundary…Quasi Linear Kernel Attention with Infinite Capacity
The evaluation cost of transformers with softmax attention scales quadratically with sequence length.Universal Approximation of Measure-to-Measure Operators by Pushforwards
Many learning tasks map an input distribution to an output distribution.Neural Harmonic Measure Operator
We introduce Neural Harmonic Measure Operator (NHMO), a neural solver for elliptic PDE problems on variable-shape domains.Tensor-Train Compressed Separable PINNs: A Curvature-Aware Optimization Framework for Parametric PDEs in High Dimensions
In this work, we develop a second-order optimization framework for physics-informed neural networks (PINNs) applied to high-dimensional parametric partial differential equations (PDEs).Preconditioned Physics-Informed Neural Operator Training
Neural operators are typically trained in a supervised fashion, which requires a dataset to be generated with a classical solver.Large-Scale Autonomous Discovery of Kissing Number Constructions
The kissing-number problem is a classical problem in discrete geometry whose exact solution is known in only a few dimensions.Toward Pólya and Szegő's conjecture for logarithmic vs Newtonian capacity
Pólya and Szegő conjectured in 1945 that the disk achieves the largest electrostatic capacity among all planar sets with given logarithmic capacity.A minimizing cone from Cartan polynomials in the Alt-Caffarelli problem
In this paper we study a class of 1-homogeneous solutions of the one-phase problem coming from the Cartan isoparametric cubic polynomials, which exist only in dimensions $d=5,8,14,26$.Optimal Transport Dropout for Structured Predictive Uncertainty
Deterministic neural networks and neural operators provide point predictions with no intrinsic measure of reliability.Calibrated Derivative-Process Sensitivity for Gaussian-Process Variable Selection
Automatic relevance determination (ARD), the default tool for variable selection in Gaussian-process (GP) regression, ranks inputs by inverse lengthscales -- which measure how fast a function…Adapting neural operators for mechanics decisions under changing operating conditions
Neural operators can accelerate repeated nonlinear mechanics calculations, but their accuracy can deteriorate as operating conditions move beyond the training range.Structure-Adaptive Tree Field Integrators
We present a new class of near-linear algorithms for efficiently integrating general tensor fields defined on trees with distance dependent kernels, the Structure-Adaptive Tree Field Integrators…A Lean Formalization of the Hamilton--Perelman Proof of the Three-Dimensional Poincaré Conjecture
We formalize the smooth three-dimensional Poincaré conjecture, together with the Moise smoothing theorem, yielding the topological three-dimensional Poincaré conjecture.Why Directly Learning Periodic Trajectories Can Fail
Operator learning of periodic solutions requires deciding how simulation data should be recorded and represented.Contour-integral and Fourier transform based multivariable quantum eigenvalue transformation for commuting matrices
We study the problem of implementing multivariable matrix-valued functions on a quantum computer and propose two quantum algorithms for multivariable matrix eigenvalue transformations acting on…AECSF: Adaptive Ensemble Conditional Score Filtering for High-Dimensional Nonlinear Data Assimilation
Bayesian state estimation for high-dimensional nonlinear dynamical systems entails a fundamental tension between statistical fidelity and computational tractability, as particle weights can…Fast Differentiable SVD on GPU via Polar Decomposition
We present a fully GPU-oriented SVD pipeline based on polar decomposition, motivated by iterative methods that rely solely on matrix multiplications, such as the Newton-Schulz iteration.Neural Network-Assisted Refinement of Traditional Schemes for One-Dimensional Scalar Conservation Laws
A clear link is established between conventional numerical methods and neural network approximations for solving one-dimensional scalar conservation laws.Deep-Learning Solvers and Surrogates for Infinity and p-Laplace Problems
We investigate the use of neural network solvers for infinity and $p$-Laplace problems, which are fundamental in nonlinear analysis and have practical applications.