Related papers: Learning to Assimilate in Chaotic Dynamical System…

Data assimilation (DA) aims to estimate the full state of a dynamical system by combining partial and noisy observations with a prior model forecast, commonly referred to as the background. In atmospheric applications, this problem is…

Modeling complex dynamical systems under varying conditions is computationally intensive, often rendering high-fidelity simulations intractable. Although reduced-order models (ROMs) offer a promising solution, current methods often struggle…

Quantifying forecast uncertainty is a key aspect of state-of-the-art numerical weather prediction and data assimilation systems. Ensemble-based data assimilation systems incorporate state-dependent uncertainty quantification based on…

This paper presents a fast algorithm for estimating hidden states of Bayesian state space models. The algorithm is a variation of amortized simulation-based inference algorithms, where a large number of artificial datasets are generated at…

Many tasks in explainable machine learning, such as data valuation and feature attribution, perform expensive computation for each data point and are intractable for large datasets. These methods require efficient approximations, and…

Learning dynamics from dissipative chaotic systems is notoriously difficult due to their inherent instability, as formalized by their positive Lyapunov exponents, which exponentially amplify errors in the learned dynamics. However, many of…

The data-driven recovery of the unknown governing equations of dynamical systems has recently received an increasing interest. However, the identification of governing equations remains challenging when dealing with noisy and partial…

Data assimilation provides a systematic framework for combining dynamical models with partial and noisy observations to infer the evolving state of a system. In this work, we undertake a comparative study of Data Assimilation with Transfer…

Dynamical weather and climate prediction models underpin many studies of the Earth system and hold the promise of being able to make robust projections of future climate change based on physical laws. However, simulations from these models…

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…

The task of modelling and forecasting a dynamical system is one of the oldest problems, and it remains challenging. Broadly, this task has two subtasks - extracting the full dynamical information from a partial observation; and then…

We propose a method for learning dynamical systems from high-dimensional empirical data that combines variational autoencoders and (spatio-)temporal attention within a framework designed to enforce certain scientifically-motivated…

Agent-based models are a powerful tool for studying the behaviour of complex systems that can be described in terms of multiple, interacting ``agents''. However, because of their inherently discrete and often highly non-linear nature, it is…

Data assimilation (DA) addresses the problem of sequentially estimating the state of a dynamical system from noisy and incomplete observations. In this work, we employ a diffusion model as a world model to simulate and predict the system's…

We scrutinize the use of machine learning, based on reservoir computing, to build data-driven effective models of multiscale chaotic systems. We show that, for a wide scale separation, machine learning generates effective models akin to…

Predicting chaotic dynamical systems is critical in many scientific fields, such as weather forecasting, but challenging due to the characteristic sensitive dependence on initial conditions. Traditional modeling approaches require extensive…

Discovering the underlying dynamics of complex systems from data is an important practical topic. Constrained optimization algorithms are widely utilized and lead to many successes. Yet, such purely data-driven methods may bring about…

The striking fractal geometry of strange attractors underscores the generative nature of chaos: like probability distributions, chaotic systems can be repeatedly measured to produce arbitrarily-detailed information about the underlying…

This paper develops a computational framework for optimizing the parameters of data assimilation systems in order to improve their performance. The approach formulates a continuous meta-optimization problem for parameters; the…

The generation of initial conditions via accurate data assimilation is crucial for weather forecasting and climate modeling. We propose DiffDA as a denoising diffusion model capable of assimilating atmospheric variables using predicted…