Analysis & PDE · Mathematics & Statistics
Analysis of PDEs
The newest papers in Analysis of PDEs that ReadSearch has read, newest first. Each links to its own page, with its authors, date, where it was published and the original.
37 papers, from 10 September 2026 to 5 November 2026: 37 arXiv preprints.
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Newest papers
Rigorously Certified Neural-Network Computation of Nonlinear Water Waves at Near-Machine Precision
We present a computational framework that combines machine-learning-based discovery with rigorous computer-assisted numerical certification and formal verification for strongly nonlinear partial…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…Deep Neural Operator Learning for stochastic heat equations and applications
In this paper, we establish a universal approximation theorem for solution operators of semilinear stochastic heat equations in spatial dimension \(d\ge2\), extending deep neural operator…Solving the Nonlinear Westervelt Equation in Ultrasound Propagation Using Physics-Informed Neural Networks
Modeling the nonlinear acoustic wave propagation in biological tissues needs accuracy, especially in ultrasound imaging and therapeutic applications.Certified folding-free deformable image registration: A whole-cell Jacobian certificate and a sequential variational solver
Registration maps propagate labels, measure local volume change, and map results back through their inverses; requiring invertibility.On a Class of Non-Local Elliptic-Transport Systems in Score-Guided Probability Flow on $SE(3)$: Score-Singularity Resolution, Space-Time ADN Shift, and Markov Mean-Field Games
We establish mathematical foundations for optimal spatiotemporal vector fields governing continuous score-guided probability flows over bounded submanifolds $M \subset SE(3)$ on the Special…Immersed Boundary Electrodiffusion in the Wasserstein Gradient Flow Formalism: Global Well-Posedness, Non-Equilibrium Thermodynamics, and Singular Asymptotics
We introduce a unified optimal transport framework for the Immersed Boundary (IB) electrodiffusion active pump model.Differentiability and Convexity of the Solution Maps for Fully Non-linear Parabolic HJB Equations
We study the dependence on the terminal condition of solutions to a fully nonlinear parabolic Hamilton--Jacobi--Bellman (HJB) equation, when the terminal condition varies along a finite-dimensional…A Dynamic Inventory Rationing Model for Last-Mile Delivery of Medication in Liberia's Community Health Program
We study the dynamic allocation of scarce medications in Liberia's community health program.SympFormer: Inertial Attention Blocks from Damped Hamiltonian Dynamics on Spaces of Probability Measures
The attention mechanism underpins modern large language models, yet their dynamics remain only partially understood.A Jump-Modified Wasserstein Gradient Flow for Maximum Mean Discrepancy with Energy Kernels
We study a jump-modified Wasserstein gradient flow of the squared maximum mean discrepancy generated by the energy kernels $K(z)=-|z|^q$, $0<q<2$, in every dimension $d\ge2$ as well as the…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…Average lower bound on magnetic double-well tunneling with asymptotically large well separation
We study tunneling between two identical, smooth, compactly supported potential wells in a constant perpendicular magnetic field, with the coupling and magnetic field fixed and the well separation…Low Residuals, Wrong Value: Learning the Viscosity Solution of Hamilton-Jacobi-Isaacs Equations with PINNs
Physics-informed neural networks (PINNs) and other residual-trained solvers judge a candidate solution by the size of its sampled PDE residual.LowNet: Looped Wavelet Neural Networks with 24 Learnable Parameters for Solving Poisson Equations
Poisson equations frequently appear in various fields, such as mathematics, physics and informatics.On the tradeoff between robustness and geometric accuracy in adversarial training
For non-parametric binary classification in the presence of an adversary, we prove an optimal quantitative estimate for adversarial classifiers controlling geometric accuracy, as measured by the…Interior smoothness and zero-variance geometry for finite-maturity Heston American puts
We study finite-maturity American puts in the Heston model without the Feller condition.Dynamical BEC formation and vanishing entropy for trapped bosons in non-relativistic QED via nonlinear resonance cascades
The dynamical formation of a complete Bose-Einstein condensate and the asymptotic purification of trapped bosons coupled to a quantized radiation field are rigorously established.An optimization problem for $δ'$ leaky stars
We consider singular Schrödinger operators with an attractive $δ'$ interaction of strength $β$ supported by a star graph and prove that the ground-state eigenvalue is uniquely maximized by stars of…Localized Generative Design of Ship Hulls with Diffusion Models and High-Fidelity Assessment
Practical ship design requires localized refinement and performance evaluation.