Related papers: Bayesian inference for geophysical fluid dynamics …

Machine learning has become a central technique for modeling in science and engineering, either complementing or as surrogates to physics-based models. Significant efforts have recently been devoted to models capable of predicting field…

Biological systems commonly exhibit complex spatiotemporal patterns whose underlying generative mechanisms pose a significant analytical challenge. Traditional approaches to spatiodynamic inference rely on dimensionality reduction through…

We propose a new sampling-based approach for approximate inference in filtering problems. Instead of approximating conditional distributions with a finite set of states, as done in particle filters, our approach approximates the…

A recent study in turbulent flow simulation demonstrated the potential of generative diffusion models for fast 3D surrogate modeling. This approach eliminates the need for specifying initial states or performing lengthy simulations,…

The recent surge in machine learning (ML) methods for geophysical modeling has raised the question of how these methods might be applied to data assimilation (DA). We focus on diffusion modeling (a form of generative artificial…

Deep learning has emerged as a promising tool for precipitation downscaling. However, current models rely on likelihood-based loss functions to properly model the precipitation distribution, leading to spatially inconsistent projections…

A generative diffusion model is used to produce probabilistic ensembles of precipitation intensity maps at the 1-hour 5-km resolution. The generation is conditioned on infrared and microwave radiometric measurements from the GOES and DMSP…

We introduce generative models for accelerating simulations of complex systems through learning and evolving their effective dynamics. In the proposed Generative Learning of Effective Dynamics (G-LED), instances of high dimensional data are…

Denoising diffusion models have proven to be a flexible and effective paradigm for generative modelling. Their recent extension to infinite dimensional Euclidean spaces has allowed for the modelling of stochastic processes. However, many…

The calibration of a reservoir model with observed transient data of fluid pressures and rates is a key task in obtaining a predictive model of the flow and transport behaviour of the earth's subsurface. The model calibration task, commonly…

One of the pivotal tasks in scientific machine learning is to represent underlying dynamical systems from time series data. Many methods for such dynamics learning explicitly require the derivatives of state data, which are not directly…

Diffusion-based generative models employ stochastic differential equations (SDEs) and their equivalent probability flow ordinary differential equations (ODEs) to establish a smooth transformation between complex high-dimensional data…

Gaussian mixtures are a common density representation in nonlinear, non-Gaussian Bayesian state estimation. Selecting an appropriate number of Gaussian components, however, is difficult as one has to trade of computational complexity…

This paper introduces an approach to endow generative diffusion processes the ability to satisfy and certify compliance with constraints and physical principles. The proposed method recast the traditional sampling process of generative…

Diffusion models generate high-quality synthetic data. They operate by defining a continuous-time forward process which gradually adds Gaussian noise to data until fully corrupted. The corresponding reverse process progressively "denoises"…

Variable selection for high-dimensional, highly correlated data has long been a challenging problem, often yielding unstable and unreliable models. We propose a resample-aggregate framework that exploits diffusion models' ability to…

This tutorial provides a broad introduction to Bayesian data assimilation that will be useful to practitioners, in interpreting algorithms and results, and for theoretical studies developing novel schemes with an understanding of the rich…

Recent developments in generative modeling have utilized score-based methods coupled with stochastic differential equations to sample from complex probability distributions. However, these and other performant sampling methods generally…

We present a generative AI algorithm for addressing the pressing task of fast, accurate, and robust statistical computation of three-dimensional turbulent fluid flows. Our algorithm, termed as GenCFD, is based on an end-to-end conditional…

Bayesian models based on Gaussian processes (GPs) offer a flexible framework to predict spatially distributed variables with uncertainty. But the use of nonstationary priors, often necessary for capturing complex spatial patterns, makes…