Related papers: Score-based Data Assimilation
We propose a novel framework for adaptively learning the time-evolving solutions of stochastic partial differential equations (SPDEs) using score-based diffusion models within a recursive Bayesian inference setting. SPDEs play a central…
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…
Data assimilation is the task of combining mathematical models with observational data. From a mathematical perspective data assimilation leads to Bayesian inference problems which can be formulated in terms of Feynman-Kac formulae. In this…
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…
Four-dimensional variational data assimilation (4D-Var) on a seasonal-to-interdecadal time scale under the existence of unstable modes can be viewed as an optimization problem of synchronized, coupled chaotic systems. The problem is tackled…
Data assimilation techniques are crucial for accurately tracking complex dynamical systems by integrating observational data with numerical forecasts. Recently, score-based data assimilation methods emerged as powerful tools for…
Score-based diffusion models provide a powerful way to model images using the gradient of the data distribution. Leveraging the learned score function as a prior, here we introduce a way to sample data from a conditional distribution given…
Reduced-order models based on level-set methods are widely used tools to qualitatively capture and track the nonlinear dynamics of an interface. The aim of this paper is to develop a physics-informed, data-driven, statistically rigorous…
We present a new continuous data assimilation algorithm based on ideas that have been developed for designing finite-dimensional feedback controls for dissipative dynamical systems, in particular, in the context of the incompressible…
Data assimilation is a method that combines observations (that is, real world data) of a state of a system with model output for that system in order to improve the estimate of the state of the system and thereby the model output. The model…
Generative AI has achieved remarkable empirical success, but from the perspective of statistics it often remains opaque: its predictions may be accurate, yet the underlying mechanism is difficult to interpret, analyze, and trust. This book…
Errors in the representation of clouds in convection-permitting numerical weather prediction models can be introduced by different sources. These can be the forcing and boundary conditions, the representation of orography, the accuracy of…
Sparsity is a common issue in many trajectory datasets, including human mobility data. This issue frequently brings more difficulty to relevant learning tasks, such as trajectory imputation and prediction. Nowadays, little existing work…
Score-based generative models can effectively learn the distribution of data by estimating the gradient of the distribution. Due to the multi-step denoising characteristic, researchers have recently considered combining score-based…
Score-based diffusion models have emerged as effective approaches for both conditional and unconditional generation. Still conditional generation is based on either a specific training of a conditional model or classifier guidance, which…
Score matching is an estimation procedure that has been developed for statistical models whose probability density function is known up to proportionality but whose normalizing constant is intractable, so that maximum likelihood is…
A valuable step in the modeling of multiscale dynamical systems in fields such as computational chemistry, biology, materials science and more, is the representative sampling of the phase space over long timescales of interest; this task is…
Data assimilation (DA) is a fundamental computational technique that integrates numerical simulation models and observation data on the basis of Bayesian statistics. Originally developed for meteorology, especially weather forecasting, DA…
We present a concise derivation for several influential score-based diffusion models that relies on only a few textbook results. Diffusion models have recently emerged as powerful tools for generating realistic, synthetic signals --…
I describe a framework for adaptive scientific exploration based on iterating an Observation--Inference--Design cycle that allows adjustment of hypotheses and observing protocols in response to the results of observation on-the-fly, as data…