Numerical analysis & scientific computing
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- From Inverse Problems to Adjoint Gradients: A Discrete, Implementation-Oriented Tutorial on PDE-Constrained Optimization
- Instability of Gaussian elimination is exponentially rare (proof of partial result)
- On randomized batch-sampling coordinate descent methods for solving linear least-squares problems
- The Numerical Linear Algebra of Large Language Models
- Quasi-Optimal Randomized Recovery of ℋ2 Matrices
- Pressure Monotonicity for a Rotation-Based Biot Discretization with Circumcentric Mass Lumping
- A Locally Conservative Enriched Linearized Neural Network Approximation to Elliptic PDEs
- CEENs: Causality-enforced evolutional networks for solving time-dependent partial differential equations
- Arbitrarily High-Order Structure-Preserving Parametric Finite Element Methods for Geometric PDEs via Local Pullback Flow Maps
- Conditioning and Singular Value Distribution of Jacobi Weighted Histopolation Matrices
- Checkable NTK Positivity and Finite-Width Gradient Descent for Scalar- and Vector-Valued PINNs with Strong-Form, Weak-Form, and Nonlocal Linear Constraints
- Operator splitting methods for non-autonomous evolution equations comprising three parts, with application to the Bloch-Torrey equation of MRI
- Inference of Hamiltonian and Lie-Poisson structures from vector field samples
- On the involution preserving properties of semi-discrete Active Flux methods on simplex
- Into the danger zone: stable extrapolation in high-dimensional function and operator learning
- Annular liquid jets: exact constraint absorption and finite-time loss of global admissibility
- Geometric Ergodicity of Affine Invariant Ensemble Langevin and its Discrete Time Variants
- A High-Accuracy Numerical Homogenization Method for Quasiperiodic Hamilton--Jacobi Equations
- Contour-integral and Fourier transform based multivariable quantum eigenvalue transformation for commuting matrices
- Fast Evaluation of the Azimuthal Fourier Modes of the 3D Helmholtz Green's Function and Their Derivatives
- On architectural choices for interpretability and thermodynamic consistency in Physically Recurrent Neural Networks in the low-data regime
- Latent Score-Based Bayesian Cramér-Rao Bound Estimation for High-Dimensional Imaging Systems
- Bayesian Operator Learning: Posterior Existence and Convergence of Point Estimates for Gaussian Priors
- Learning the Willmore flow with a lightweight neural operator
- Energetic Variational Deep Learning for Solving High-Dimensional Stationary Fokker-Planck Equations