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
Energy-conserving scheme for a shallow-water model with capillary effects
We consider numerical approximations of shallow-water and thin-film flow models with capillary effects.Asymptotic-Preserving Tensor Neural Networks for 3D High-Field Kinetic Equations with Applications to Uncertainty Quantification
Kinetic equations in the high-field regime describe particle transport dominated by electric-field acceleration and collisional relaxation.Continuous Space-Time Finite Element Simulations for Biomedical Flows with Large Boundary Motion and Time-Periodicity
We present an axisymmetric continuous simplex space-time finite element method for incompressible fluid flow.Data-driven discovery of intrinsic Lie point symmetries of differential equation systems
Discovering continuous symmetries directly from differential-equation data can reveal geometric structure for model reduction and scientific machine learning without symbolic determining equations…Magnetic Bloch eigenvalue problems in nonuniform periodic magnetic fields: a Fourier-finite difference approach
We study magnetic Bloch eigenvalue problems for two-dimensional magnetic Schrödinger operators with nonuniform periodic magnetic fields and periodic scalar potentials, and develop a hybrid…A Tensor-Network Chebyshev-Galerkin Method for Boundary-Value Problems in Computational Mechanics
Quantum-inspired numerical methods for partial differential equations represent discretized fields and operators as quantics tensor trains (QTT), so that their cost depends on how compressible the…Eddies that ride the flow: a model of turbulence with Richardson dispersion and anomalous dissipation
We construct a divergence-free velocity field $\mathbf{u}(\mathbf{x},t)$ on $\mathbb{T}^{n}$ that is a genuine function of position and carries both defining properties of turbulent transport…Improving the accuracy of the momentum-exchange method in lattice Boltzmann methods
In the lattice Boltzmann method (LBM), the momentum-exchange method (MEM) is widely used to evaluate hydrodynamic forces at fluid-solid interfaces due to its computational efficiency and geometric…Physics-informed traditional and generative Mori-Zwanzig-reduced models for multiscale systems
Model reduction via the Mori-Zwanzig (MZ) formalism is well understood for coarse-grained representations constructed from standard basis functions such as Fourier functions.De Rham cohomological architectures for PINNs and PDEs with topological holes
We attempt to alleviate failure modes of classical physics-informed neural networks (PINNs) in scenarios of topological pathologies corresponding to punctures, holes, poles, and voids by introducing…Remap for ALE Hydrodynamics via Direct Interpolation and Constraint Optimization
This work presents an optimization-based remap approach for arbitrary Lagrangian-Eulerian (ALE) hydrodynamics that preserves sharp features and physical bounds while conserving global quantities…Embedding a de Rham Complex Structure into Eig-PIELM for Maxwell Eigenvalue Problems
The perfect electric conductor (PEC) boundary condition alone does not eliminate the gradient nullspace of the Maxwell curl-curl operator.POD-CNF: reduced order modeling of parametrized stochastic PDEs via normalizing flows and proper orthogonal decomposition
Reduced-order models (ROMs) learned from trusted numerical simulations enable the real-time simulation of complex physical systems, making computationally prohibitive tasks-such as uncertainty…Computational performance versus numerical accuracy in the acoustic terms of weakly-compressible SPH
Accurate computation of the acoustic terms in weakly-compressible SPH, including the equation of state, its inverse, and the evaluation of the local speed of sound, is essential to ensure energy…Unrolled gradients in disguise: bridging interpolation-based and Jacobian regularization for stable neural dynamics
Hybrid models and neural differential equations (NDEs) are becoming increasingly important for modelling physical systems; however, they often encounter stability and accuracy issues during…Symbol-based residual certification of reduced and neural surrogates for tempered-fractional CGMY pricing
We certify reduced and neural approximations of European-put price trajectories under the Carr--Geman--Madan--Yor model by residual bounds for the spline Galerkin discretisation of the…Factorized approximate inverse preconditioners in the tensor train format
We present a preconditioning pipeline that accelerates Tensor Train (TT) linear solvers for symmetric positive-definite problems.Variational learning of energy-stable macroscopic flow equations from microscopic laws
We present a generalized variational approach for constructing energy-stable macroscopic partial differential equations (PDEs) directly from microscopic physical laws.Tensor Contraction with ZX Calculus, a Graph-Theoretic Approach
Tensors are higher dimensional generalisations of vectors and matrices.Black Hole Love Numbers with Physics-Informed Neural Networks
We develop and validate a physics-informed neural network (PINN) framework for computing the tidal Love numbers of black holes directly from their perturbation equations.