Related papers: A probabilistic framework for learning non-intrusi…

Aerial operation in turbulent environments is a challenging problem due to the chaotic behavior of the flow. This problem is made even more complex when a team of aerial robots is trying to achieve coordinated motion in turbulent wind…

This work presents, to the best of the authors' knowledge, the first generalizable and fully data-driven adaptive framework designed to stabilize deep learning (DL) autoregressive forecasting models over long time horizons, with the goal of…

The statistics obtained from turbulent flow simulations are generally uncertain due to finite time averaging. The techniques available in the literature to accurately estimate these uncertainties typically only work in an offline mode, that…

Extreme weather events epitomize high cost: to society through their physical impacts, and to computer servers that simulate them to assess risk and advance physical understanding. It costs hundreds of simulation years to sample a few…

We propose the use of physics-informed neural networks for solving the shallow-water equations on the sphere in the meteorological context. Physics-informed neural networks are trained to satisfy the differential equations along with the…

Accurate and computationally-viable representations of clouds and turbulence are a long-standing challenge for climate model development. Traditional parameterizations that crudely but efficiently approximate these processes are a leading…

We propose a hybrid meta-learning framework for forecasting and anomaly detection in nonlinear dynamical systems characterized by nonstationary and stochastic behavior. The approach integrates a physics-inspired simulator that captures…

Atmospheric weather systems are coherent structures consisting of discrete cloud cells forming patterns of rows/streets, mesoscale clusters and spiral bands which maintain their identity for the duration of their appreciable life times in…

Existing procedures for model validation have been deemed inadequate for many engineering systems. The reason of this inadequacy is due to the high degree of complexity of the mechanisms that govern these systems. It is proposed in this…

In applications, an anticipated situation is where the system of interest has never been encountered before and sparse observations can be made only once. Can the dynamics be faithfully reconstructed from the limited observations without…

Atmospheric flows exhibit long-range spatiotemporal correlations manifested as the fractal geometry to the global cloud cover pattern concomitant with inverse power law form for power spectra of temporal fluctuations on all space-time…

We propose a Machine Learning (ML) non-Markovian closure modeling framework for accurate predictions of statistical responses of turbulent dynamical systems subjected to external forcings. One of the difficulties in this statistical closure…

Chaotic systems make long-horizon forecasts difficult because small perturbations in initial conditions cause trajectories to diverge at an exponential rate. In this setting, neural operators trained to minimize squared error losses, while…

Reservoir computing is a powerful tool for forecasting turbulence because its simple architecture has the computational efficiency to handle large systems. Its implementation, however, often requires full state-vector measurements and…

Chaos arises in many complex dynamical systems, from weather to power grids, but is difficult to accurately model using data-driven emulators, including neural operator architectures. For chaotic systems, the inherent sensitivity to initial…

The use of artificial neural networks as models of chaotic dynamics has been rapidly expanding. Still, a theoretical understanding of how neural networks learn chaos is lacking. Here, we employ a geometric perspective to show that neural…

We explore the hyperparameter space of reservoir computers used for forecasting of the chaotic Lorenz '63 attractor with Bayesian optimization. We use a new measure of reservoir performance, designed to emphasize learning the global climate…

A novel correction algorithm is proposed for multi-class classification problems with corrupted training data. The algorithm is non-intrusive, in the sense that it post-processes a trained classification model by adding a correction…

In recent years, there have been a surge in applications of neural networks (NNs) in physical sciences. Although various algorithmic advances have been proposed, there are, thus far, limited number of studies that assess the…

In this effort we propose a data-driven learning framework for reduced order modeling of fluid dynamics. Designing accurate and efficient reduced order models for nonlinear fluid dynamic problems is challenging for many practical…