Related papers: A Physics-Informed Data-Driven Algorithm for Ensem…

While deep learning has shown tremendous success in a wide range of domains, it remains a grand challenge to incorporate physical principles in a systematic manner to the design, training, and inference of such models. In this paper, we aim…

Differential equations are important mechanistic models that are integral to many scientific and engineering applications. With the abundance of available data there has been a growing interest in data-driven physics-informed models.…

While diffusion models can successfully generate data and make predictions, they are predominantly designed for static images. We propose an approach for efficiently training diffusion models for probabilistic spatiotemporal forecasting,…

We formulate a reduced-order strategy for efficiently forecasting complex high-dimensional dynamical systems entirely based on data streams. The first step of our method involves reconstructing the dynamics in a reduced-order subspace of…

We propose a methodology that combines generative latent diffusion models with physics-informed machine learning to generate solutions of parametric partial differential equations (PDEs) conditioned on partial observations, which includes,…

Probabilistic time series forecasting is crucial for quantifying future uncertainty, with significant applications in fields such as energy and finance. However, existing methods often rely on computationally expensive sampling or…

In this work, we quantify the time scales and information flow associated with multiscale energy transfer in a weakly turbulent system. This is done through a greedy optimization algorithm which finds the maximum conditional-mutual…

Diffusion models provide expressive priors for forecasting trajectories of dynamical systems, but are typically unreliable in the sparse data regime. Physics-informed machine learning (PIML) improves reliability in such settings; however,…

In this paper, we study the statistical evolution of the large-scale structure (LSS), focusing on the joint probability distribution function (PDF) of the coarse-grained cosmic field and its role in constructing effective dynamics. As the…

The growing complexity of the power grid, driven by increasing share of distributed energy resources and by massive deployment of intelligent internet-connected devices, requires new modelling tools for planning and operation. Physics-based…

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…

Harnessing data to discover the underlying governing laws or equations that describe the behavior of complex physical systems can significantly advance our modeling, simulation and understanding of such systems in various science and…

The growth of computational resources in the past decades has expanded the application of Computational Fluid Dynamics (CFD) from the traditional fields of aerodynamics and hydrodynamics to a number of new areas. Examples range from the…

In this work, we demonstrate how physical principles -- such as symmetries, invariances, and conservation laws -- can be integrated into the dynamic mode decomposition (DMD). DMD is a widely-used data analysis technique that extracts…

The inclusion of convection in stellar evolution models lacks realism, especially near convective-radiative interfaces. Furthermore, the interaction of convection with oscillations prevent us from accurately predicting seismic frequencies,…

Earth System Models (ESMs) are the state of the art for projecting the effects of climate change. However, longstanding uncertainties in their ability to simulate regional and local precipitation extremes and related processes inhibit…

Predicting high-dimensional dynamical systems with irregular time steps presents significant challenges for current data-driven algorithms. These irregularities arise from missing data, sparse observations, or adaptive computational…

Convective available potential energy (CAPE) is an important variable for forecasting severe weather and understanding deep convection and precipitation. The latest versions of the Global Forecast System (GFS) and related Global Ensemble…

This work introduces a novel probabilistic deep learning technique called deep Gaussian mixture ensembles (DGMEs), which enables accurate quantification of both epistemic and aleatoric uncertainty. By assuming the data generating process…

Flash floods in urban areas occur with increasing frequency. Detecting these floods would greatlyhelp alleviate human and economic losses. However, current flood prediction methods are eithertoo slow or too simplified to capture the flood…