3 papers
stat.ML2026
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…
math.ST2025
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…
math.DS2024
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…