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 4
Multiplicative vs. Additive State Coupling in Learned Optimizer Schedules
We learn schedules for a continuous penalty relaxation of MAX-CUT by backpropagating through an unrolled classical solver.A Gaussian Process State Space Formulation for Materials Constitutive Modeling: Application to Quasi-brittle Materials
Constitutive models for history-dependent, path-dependent materials typically encode this dependence in prescribed functional forms through internal variables such as damage or plastic strain that…Deep ReLU Networks Can Fail the Best Approximation Property for Continuous Target Functions
We construct a continuous function on $[-1,1]^2$ for which the infimum of the $L^2$-approximation error over the class of ReLU networks with two hidden layers and architecture $(2,2,1,1)$ is not…Convex Equilibrium Potentials for Monge--Ampère: Curvature Bounds and A Posteriori Evaluation
Equilibrium neural networks define their hidden state as the fixed point of a contraction, so their effective depth is set at evaluation time rather than by the architecture.Structure-preserving reduced-order models of thin panels in supersonic and hypersonic flow
We build structure-preserving reduced-order models for both challenge problems of the AePW-4 High-Speed Working Group.Phase Transition from Random Features to Fully Trainable Networks
Constructing accurate and computationally tractable approximation spaces is a fundamental task in scientific computing.On exact solutions to three-dimensional Yukawa lattice model and BCC to FCC phase transitions
We determine the global minimizers of the three-dimensional Yukawa lattice energy at every fixed density.Density-Level Backward Error for Low-NFE Generative Flows
Low-NFE generative ODE sampling is constrained not only by solver order, but also by how a fixed budget of network evaluations is distributed along the flow.Tractable Inference with Kolmogorov-Arnold Networks
Machine-learning surrogates in computational science often require not only accurate predictions but also expectations, variances, conserved integrals, and normalization constants.A Transformer-based Approach for Real-time Multi-agent Path Planning with Varying Initial/Final Conditions
We address the problem of real-time multi-agent path planning under prescribed initial and final configurations, formulated as a high-dimensional optimal control problem subject to inter-agent…BCC optimality for the three-dimensional Coulomb lattice energy
We prove that the body-centered cubic lattice uniquely minimizes the renormalized Coulomb energy among three-dimensional Bravais lattices of fixed covolume, up to orthogonal transformations.Soliton Profiles in 1D: Enhanced Neural-Network Solvers and Constrained Deep Ritz Methods
We develop and compare enhanced neural-network solvers for one-dimensional ground-state profiles, which are solutions of $$ Q^{\prime\prime}=bQ-γQ^{p},\quad Q>0,\quad p>1, \quad b, γ>0, $$ the…Computing excited states of dipolar Bose--Einstein condensates by constrained gentlest ascent dynamics
Dipolar Bose--Einstein condensates (BECs), i.e., BECs with long-range dipole-dipole interactions (DDI), exhibit extraordinarily rich physics and serve as a versatile experimental platform for…Automatic Differentiation with Constraints in Forward and Inverse Problems
Approximate solutions of partial differential equations (PDEs) on unstructured grids can be represented on a graph.Norm-optimal model order reduction in reproducing kernel Hilbert spaces
We consider the problem of model order reduction (MOR) in reproducing kernel Hilbert spaces (RKHSs).DSINC beyond Heston: the 3/2 and other non-affine stochastic-volatility models
This paper extends the damped-sinc (DSINC) method for American options beyond the affine Heston class to general one-factor stochastic-volatility models.Local crystallization in three-dimensional quantization
A long-standing conjecture on the quantization problem due to Gersho, which remains open in dimensions higher than two, posits that optimal quantizers crystallize into a lattice structure; in…A counterexample to Gale's conjecture in $\mathbb{R}^3$
It is known that for every partition of the sphere $S^2$ of unit diameter into four parts, the largest diameter of a part is at least $\sqrt{(3+\sqrt{3})/6} = 0.88807\dots$, and this bound is…Residual-Based Adaptive Refinement in Hybrid Variational-Collocation PINNs for Singular Elliptic PDEs with Mixed Dirichlet-Neumann Boundary Conditions
Solutions of second-order elliptic PDE problems on nonconvex or cracked domains with mixed Dirichlet-Neumann conditions typically lie outside $H^2(Ω)$.Polar Switch: Fast Muon Orthogonalization with Polynomial Circuits
Muon, a 2024-born optimizer for language models, differs from the 2015-born spectral gradient descent mainly in its fast, GPU-friendly Newton--Schulz polynomial for orthogonalizing the gradient…