18 citations · 23 across the 9 of their papers we have counts for
12 papers
Measure Neural Mappings
Ricardo Baptista, Edoardo Calvello, Bohan Chen +2
We introduce and define measure neural mappings (MNMs), which combine measure-dependent neural transport with ensemble consistency for learning operators on probability measures. E…
Attention Kernels for Learning Maps Between Heavy-Tailed Measures
Kailen Hargenrader, Edoardo Calvello, Bohan Chen
Operator learning on probability measures can be accomplished with transformers. For measures with polynomial tails, the exponential weighting in softmax can make the corresponding…
One Operator for Many Densities: Amortized Approximation of Conditioning by Neural Operators
Panos Tsimpos, Edoardo Calvello, Ayoub Belhadji +1
Probabilistic conditioning is concerned with the identification of a distribution of a random variable given a random variable . It is a cornerstone of scientific and engine…
Formulation and Learning Of The Forecasting Problem
Edoardo Calvello, Elizabeth Carlson, Nikola Kovachki +2
Machine learning has opened new frontiers in purely data-driven forecasting of dynamical systems; the resulting methods are showing considerable promise in some application domains…
Demystifying Data-Driven Probabilistic Medium-Range Weather Forecasting
Jean Kossaifi, Nikola Kovachki, Morteza Mardani +15
The recent revolution in data-driven methods for weather forecasting has lead to a fragmented landscape of complex, bespoke architectures and training strategies, obscuring the fun…
Operator Learning at Machine Precision
Aras Bacho, Aleksei G. Sorokin, Xianjin Yang +6
Neural operator learning methods have garnered significant attention in scientific computing for their ability to approximate infinite-dimensional operators. However, increasing th…
Learning Enhanced Ensemble Filters
Eviatar Bach, Ricardo Baptista, Edoardo Calvello +2
The filtering distribution in hidden Markov models evolves according to the law of a mean-field model in state-observation space. The ensemble Kalman filter (EnKF) approximates thi…
Statistical accuracy of the ensemble Kalman filter in the near-linear setting
E. Calvello, J. A. Carrillo, F. Hoffmann +3
Estimating the state of a dynamical system from partial and noisy observations is a ubiquitous problem in a large number of applications, such as probabilistic weather forecasting…
Solving Roughly Forced Nonlinear PDEs via Misspecified Kernel Methods and Neural Networks
Ricardo Baptista, Edoardo Calvello, Matthieu Darcy +3
We consider the use of Gaussian Processes (GPs) or Neural Networks (NNs) to numerically approximate the solutions to nonlinear partial differential equations (PDEs) with rough forc…
Accuracy of the Ensemble Kalman Filter in the Near-Linear Setting
Edoardo Calvello, Pierre Monmarché, Andrew M. Stuart +1
The filtering distribution captures the statistics of the state of a dynamical system from partial and noisy observations. Classical particle filters provably approximate this dist…
Continuum Attention for Neural Operators
Edoardo Calvello, Nikola B. Kovachki, Matthew E. Levine +1
Transformers, and the attention mechanism in particular, have become ubiquitous in machine learning. Their success in modeling nonlocal, long-range correlations has led to their wi…
Ensemble Kalman Methods: A Mean Field Perspective
Edoardo Calvello, Sebastian Reich, Andrew M. Stuart
Ensemble Kalman methods are widely used for state estimation in the geophysical sciences. Their success stems from the fact that they take an underlying (possibly noisy) dynamical…