32 citations · 183 across the 54 of their papers we have counts for
12 papers · 1 filter
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…
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…
Bayesian Optimization on Networks
Wenwen Li, Daniel Sanz-Alonso, Ruiyi Yang
This paper studies optimization on networks modeled as metric graphs. Motivated by applications where the objective function is expensive to evaluate or only available as a black b…
Machine Learning for Inverse Problems and Data Assimilation
Eviatar Bach, Ricardo Baptista, Daniel Sanz-Alonso +1
The aim of this book is to demonstrate the potential for ideas in machine learning to impact on the fields of inverse problems and data assimilation. The perspective is one that is…
Reduced-Order Autodifferentiable Ensemble Kalman Filters
Yuming Chen, Daniel Sanz-Alonso, Rebecca Willett
This paper introduces a computational framework to reconstruct and forecast a partially observed state that evolves according to an unknown or expensive-to-simulate dynamical syste…
Optimization on Manifolds via Graph Gaussian Processes
Hwanwoo Kim, Daniel Sanz-Alonso, Ruiyi Yang
This paper integrates manifold learning techniques within a \emph{Gaussian process upper confidence bound} algorithm to optimize an objective function on a manifold. Our approach i…
Non-Asymptotic Analysis of Ensemble Kalman Updates: Effective Dimension and Localization
Omar Al Ghattas, Daniel Sanz-Alonso
Many modern algorithms for inverse problems and data assimilation rely on ensemble Kalman updates to blend prior predictions with observed data. Ensemble Kalman methods often perfo…
Mathematical Foundations of Graph-Based Bayesian Semi-Supervised Learning
Nicolas García Trillos, Daniel Sanz-Alonso, Ruiyi Yang
In recent decades, science and engineering have been revolutionized by a momentous growth in the amount of available data. However, despite the unprecedented ease with which data a…
Auto-differentiable Ensemble Kalman Filters
Yuming Chen, Daniel Sanz-Alonso, Rebecca Willett
Data assimilation is concerned with sequentially estimating a temporally-evolving state. This task, which arises in a wide range of scientific and engineering applications, is part…
Local Regularization of Noisy Point Clouds: Improved Global Geometric Estimates and Data Analysis
Nicolas Garcia Trillos, Daniel Sanz-Alonso, Ruiyi Yang
Several data analysis techniques employ similarity relationships between data points to uncover the intrinsic dimension and geometric structure of the underlying data-generating me…
Variational Characterizations of Local Entropy and Heat Regularization in Deep Learning
Nicolas Garcia Trillos, Zach Kaplan, Daniel Sanz-Alonso
The aim of this paper is to provide new theoretical and computational understanding on two loss regularizations employed in deep learning, known as local entropy and heat regulariz…
On the Consistency of Graph-based Bayesian Learning and the Scalability of Sampling Algorithms
Nicolas Garcia Trillos, Zachary Kaplan, Thabo Samakhoana +1
A popular approach to semi-supervised learning proceeds by endowing the input data with a graph structure in order to extract geometric information and incorporate it into a Bayesi…