Related papers: Learning to Assimilate in Chaotic Dynamical System…

Data assimilation algorithms estimate the state of a dynamical system from partial observations, where the successful performance of these algorithms hinges on costly parameter tuning and on employing an accurate model for the dynamics.…

Variational data assimilation optimizes for an initial state of a dynamical system such that its evolution fits observational data. The physical model can subsequently be evolved into the future to make predictions. This principle is a…

Data assimilation is a central problem in many geophysical applications, such as weather forecasting. It aims to estimate the state of a potentially large system, such as the atmosphere, from sparse observations, supplemented by prior…

Data assimilation refers to the process of obtaining an estimate of a system's state using a model for the system's time evolution and a time series of measurements that are possibly noisy and incomplete. However, for practical reasons, the…

Data assimilation, consisting in the combination of a dynamical model with a set of noisy and incomplete observations in order to infer the state of a system over time, involves uncertainty in most settings. Building upon an existing…

Data-driven prediction and physics-agnostic machine-learning methods have attracted increased interest in recent years achieving forecast horizons going well beyond those to be expected for chaotic dynamical systems. In a separate strand of…

Data assimilation is an iterative approach to the problem of estimating the state of a dynamical system using both current and past observations of the system together with a model for the system's time evolution. Rather than solving the…

We consider the problem of data-assisted forecasting of chaotic dynamical systems when the available data is in the form of noisy partial measurements of the past and present state of the dynamical system. Recently there have been several…

The reconstruction from observations of high-dimensional chaotic dynamics such as geophysical flows is hampered by (i) the partial and noisy observations that can realistically be obtained, (ii) the need to learn from long time series of…

In this computational paper, we perform sensitivity analysis of long-time (or ensemble) averages in the chaotic regime using the shadowing algorithm. We introduce automatic differentiation to eliminate the tangent/adjoint equation solvers…

Many dynamical systems are difficult or impossible to model using high fidelity physics based models. Consequently, researchers are relying more on data driven models to make predictions and forecasts. Based on limited training data,…

Chaos is ubiquitous in physical systems. The associated sensitivity to initial conditions is a significant obstacle in forecasting the weather and other geophysical fluid flows. Data assimilation is the process whereby the uncertainty in…

In this article we develop algorithms for data assimilation based upon a computational time dependent stable/unstable splitting. Our particular method is based upon shadowing refinement and synchronization techniques and is motivated by…

This paper is a contribution in the context of variational data assimilation combined with statistical learning. The framework of data assimilation traditionally uses data collected at sensor locations in order to bring corrections to a…

Extensive numerical evidence shows that the assimilation of observations has a stabilizing effect on unstable dynamics, in numerical weather prediction and elsewhere. In this paper, we apply mathematically rigorous methods to showing why…

A deterministic multiscale toy model is studied in which a chaotic fast subsystem triggers rare transitions between slow regimes, akin to weather or climate regimes. Using homogenization techniques, a reduced stochastic parametrization…

We study prediction-assimilation systems, which have become routine in meteorology and oceanography and are rapidly spreading to other areas of the geosciences and of continuum physics. The long-term, nonlinear stability of such a system…

We present a supervised learning method to learn the propagator map of a dynamical system from partial and noisy observations. In our computationally cheap and easy-to-implement framework a neural network consisting of random feature maps…

Data Assimilation is the process in which we improve the representation of the state of a physical system by combining information coming from a numerical model, real-world observations, and some prior modelling. It is widely used to model…

The literature is rich with studies, analyses, and examples on parameter estimation for describing the evolution of chaotic dynamical systems based on measurements, even when only partial information is available through observations.…