Related papers: The Ensemble Schr{\"o}dinger Bridge filter for Non…

A new integrable system of two symmetrically coupled derivative nonlinear Schroedinger equations is detected by means of the singularity analysis. A nonlinear transformation is proposed which uncouples the equations of the new system.

Ensemble models refer to methods that combine a typically large number of classifiers into a compound prediction. The output of an ensemble method is the result of fitting a base-learning algorithm to a given data set, and obtaining diverse…

Regression trees and their ensemble methods are popular methods for nonparametric regression: they combine strong predictive performance with interpretable estimators. To improve their utility for locally smooth response surfaces, we study…

We investigate the ability to discover data assimilation (DA) schemes meant for chaotic dynamics with deep learning. The focus is on learning the analysis step of sequential DA, from state trajectories and their observations, using a simple…

We study Bayesian inverse problems with mixed noise, modeled as a combination of additive and multiplicative Gaussian components. While traditional inference methods often assume fixed or known noise characteristics, real-world…

Particle and ensemble filters are increasingly utilized for inference, optimization, and forecast; however, both filtering methods use discrete distributions to simulate continuous state space, a drawback that can lead to degraded…

Data assimilation is a technique for increasing the accuracy of simulations of solutions to partial differential equations by incorporating observable data into the solution as time evolves. Recently, a promising new algorithm for data…

We propose the Entropic-regularized Robust Optimal Transport (E-ROBOT) framework, a novel method that combines the robustness of ROBOT with the computational and statistical benefits of entropic regularization. We show that, rooted in the…

A new type of ensemble Kalman filter is developed, which is based on replacing the sample covariance in the analysis step by its diagonal in a spectral basis. It is proved that this technique improves the aproximation of the covariance when…

Particle filters contain the promise of fully nonlinear data assimilation. They have been applied in numerous science areas, but their application to the geosciences has been limited due to their inefficiency in high-dimensional systems in…

In this paper, we introduce a new adaptive data analysis method to study trend and instantaneous frequency of nonlinear and non-stationary data. This method is inspired by the Empirical Mode Decomposition method (EMD) and the recently…

This paper contains the latest installment of the authors' project on developing ensemble based data assimilation methodology for high dimensional fluid dynamics models. The algorithm presented here is a particle filter that combines model…

Ensemble forecast post-processing is a necessary step in producing accurate probabilistic forecasts. Conventional post-processing methods operate by estimating the parameters of a parametric distribution, frequently on a per-location or…

Numerous fields of nonlinear physics, very different in nature, produce signals and images, that share the common feature of being essentially constituted of piecewise homogeneous phases. Analyzing signals and images from corresponding…

We introduce a flexible, scalable Bayesian inference framework for nonlinear dynamical systems characterised by distinct and hierarchical variability at the individual, group, and population levels. Our model class is a generalisation of…

Alternative machine learning approaches that are computationally light with low latency and can work with only a small training dataset are needed for applications where the insatiable demand of deep learning methods for computing power and…

Recent progress in effective nonlinearity, achieved by exploiting multiple scatterings within the linear optical regime, has been demonstrated to be a promising approach to enable nonlinear optical processing without relying on actual…

For a fixed flow-based generative model under a small inference budget, sample quality can depend strongly on where the sampler spends its few function evaluations. Flow matching and Schr\"odinger bridges define probability paths, yet their…

Data assimilation (DA) is a key component of many forecasting models in science and engineering. DA allows one to estimate better initial conditions using an imperfect dynamical model of the system and noisy/sparse observations available…

We look at a stochastic time-varying optimization problem and we formulate online algorithms to find and track its optimizers in expectation. The algorithms are derived from the intuition that standard prediction and correction steps can be…