32 citations · 183 across the 54 of their papers we have counts for
10 papers · 1 filter
Time-uniform accuracy of ensemble Kalman filters with localization
Xiaoou Cheng, Daniel Sanz-Alonso, Nathan Waniorek
This paper establishes time-uniform accuracy guarantees for deterministic square-root ensemble Kalman filters in linear--Gaussian state-space models under perfect-model dynamics. F…
Non-asymptotic Analysis of Matérn Regression: The Roles of Target and Kernel Lengthscales
Daniel Sanz-Alonso
Theoretical guarantees for kernel regression are typically formulated in terms of smoothness, but practical accuracy depends critically on how the design resolution compares with t…
Sharp Frobenius-Norm Concentration for Sample Moment Tensors
Jiaheng Chen, Daniel Sanz-Alonso
This paper establishes sharp dimension-free Frobenius-norm concentration inequalities for sample moment tensors. Our bounds are optimal over the sub-Gaussian class, while for Gauss…
From Spectral Methods to Sample Complexity Bounds for Fourier Neural Operators
Nisha Chandramoorthy, Daniel Sanz-Alonso, Nathan Waniorek
We establish approximation and learning guarantees for Fourier neural operators (FNOs) applied to time- solution operators of dissipative evolution equations. The analysis build…
Optimal Multiscale Learning of Linear Operators
Jiaheng Chen, Daniel Sanz-Alonso
We study the statistical and computational limits of learning bounded linear operators between Sobolev spaces from noisy input-output data. In wavelet coordinates, the problem is r…
Continuous Data Assimilation with Learned Surrogate Dynamics
Wenwen Li, Daniel Sanz-Alonso
Continuous data assimilation seeks to estimate the state of a dynamical system from partial observations. In many applications, however, the state dynamics are unknown or prohibiti…
Functional Multi-Target Detection via Bispectrum Inversion
Anna Little, Daniel Sanz-Alonso, Mikhail Sweeney +1
This paper develops a functional theory for multi-target detection, where a compactly supported signal is recovered from a single noisy observation containing many unknown translat…
Concentration Inequalities for Sample Cross-Covariances
Jiaheng Chen, Daniel Sanz-Alonso
This paper establishes sharp dimension-free concentration and expectation bounds for the deviation of a sample cross-covariance matrix from its mean. For sub-Gaussian random vector…
Auto-differentiable data assimilation: Co-learning of states, dynamics, and filtering algorithms
Melissa Adrian, Daniel Sanz-Alonso, Rebecca Willett
Data assimilation algorithms estimate the state of a dynamical system from partial observations, where the successful performance of these algorithms hinges on costly parameter tun…
Convergence Rates for Learning Pseudo-Differential Operators
Jiaheng Chen, Daniel Sanz-Alonso
This paper establishes convergence rates for learning elliptic pseudo-differential operators, a fundamental operator class in partial differential equations and mathematical physic…