2 citations · 3 across the 7 of their papers we have counts for
7 papers
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…
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…
Long-time accuracy of ensemble Kalman filters for chaotic and machine-learned dynamical systems
Daniel Sanz-Alonso, Nathan Waniorek
Filtering is concerned with online estimation of the state of a dynamical system from partial and noisy observations. In applications where the state is high dimensional, ensemble…
Optimal Estimation of Structured Covariance Operators
Omar Al-Ghattas, Jiaheng Chen, Daniel Sanz-Alonso +1
This paper establishes optimal convergence rates for estimation of structured covariance operators of Gaussian processes. We study banded operators with kernels that decay rapidly…
Hierarchical Bayesian Inverse Problems: A High-Dimensional Statistics Viewpoint
Daniel Sanz-Alonso, Nathan Waniorek
This paper analyzes hierarchical Bayesian inverse problems using techniques from high-dimensional statistics. Our analysis leverages a property of hierarchical Bayesian regularizer…
Covariance Operator Estimation: Sparsity, Lengthscale, and Ensemble Kalman Filters
Omar Al-Ghattas, Jiaheng Chen, Daniel Sanz-Alonso +1
This paper investigates covariance operator estimation via thresholding. For Gaussian random fields with approximately sparse covariance operators, we establish non-asymptotic boun…
Analysis of a Computational Framework for Bayesian Inverse Problems: Ensemble Kalman Updates and MAP Estimators Under Mesh Refinement
Daniel Sanz-Alonso, Nathan Waniorek
This paper analyzes a popular computational framework to solve infinite-dimensional Bayesian inverse problems, discretizing the prior and the forward model in a finite-dimensional…