The use of artificial neural networks (NNs) as models of chaotic dynamics has been rapidly expanding. Still, a theoretical understanding of how NNs learn chaos is lacking. Here, we employ a geometric perspective to show that NNs can efficiently model chaotic dynamics by becoming structurally chaotic themselves. We first confirm NN's efficiency in emulating chaos by showing that a parsimonious NN trained only on few data points can reconstruct strange attractors, extrapolate outside training data boundaries, and accurately predict local divergence rates. We then posit that the trained network's map comprises sequential geometric stretching, rotation, and compression operations. These geometric operations indicate topological mixing and chaos, explaining why NNs are naturally suitable to emulate chaotic dynamics.

Geosciences is a field of great societal relevance that requires solutions to several urgent problems facing our humanity and the planet. As geosciences enters the era of big data, machine learning (ML)-that has been widely successful in commercial domains-offers immense potential to contribute to problems in geosciences. However, geoscience applications introduce novel challenges for ML due to combinations of geoscience properties encountered in every problem, requiring novel research in machine learning. This article introduces researchers in the machine learning (ML) community to these challenges offered by geoscience problems and the opportunities that exist for advancing both machine learning and geosciences. We first highlight typical sources of geoscience data and describe their common properties. We then describe some of the common categories of geoscience problems where machine learning can play a role, discussing the challenges faced by existing ML methods and opportunities for novel ML research. We conclude by discussing some of the cross-cutting research themes in machine learning that are applicable across several geoscience problems, and the importance of a deep collaboration between machine learning and geosciences for synergistic advancements in both disciplines.

In geophysical spatial inference, imperfect model predictions are combined with noisy, sparse measurements to estimate spatial fields better than either source alone. In addition to changing brightness appearance, fields with coherent structures are readily perceived as deforming patterns. Often ignored, the failure to assimilate pattern information leads to poor spatial estimates. Here, a Bayesian inference problem in appearance and geometry is formulated for coherent fluids and a practical application of deformable models is synthesized. The proposed estimation approach uses a Gabor basis and stochastic optimization incorporating fluid dynamical balance to produce parsimonious non-local deformation solutions in deterministic or ensemble settings. Using this approach, the supervised spatial field estimation and the unsupervised mean field estimation problems are solved, with application to meteorological Data Assimilation, Ensemble Analysis and Nowcasting.

We present a new approach to deformation invariant image matching. Our matcher (a) aligns templates to targets over a broad range of nonlinear deformations, (b) factors the total deformation into spectral categories, where low wavenumber deformations are smooth and global and high wavenumbers are turbulent and local, and (c) weighs the reduction in template-target misfit within each category to differentiate between relevant and irrelevant deformations. It accomplishes this by aligning images in a scale-cascaded fashion, with more complex, local deformations following simpler, more global ones. Each step of the cascade involves finding an iterative solution to a nonlinear optimization problem using a Gabor deformation basis. Cascaded alignment makes deformation invariant matching feasible and efficient. Our approach is applied to recognize the flexible bodies of salamanders from a large database; results indicate that the method is very promising.

We present a model-based system for tracking rotating fluids, and apply it to a laboratory study of atmospheric circulation. Tracking is accomplished by filtering uncertain and high-dimensional states of a nonlinear general circulation model with optical measurements of the physical fluidpsilas velocity. Realtime performance is achieved by using a nonuniform discretization of the modelpsilas spatial resolution, and by using time-snapshots of model-state to construct spatially-localized reduced-rank square-root representations of forecast uncertainty. Realtime performance, economical and repeatable experimentation, and a direct connection to planetary flows implies that the proposed physical-numerical coupling can be useful for addressing many perceptual geophysical fluid dynamics problems. To the best of our knowledge, such a system has not hitherto been reported.

Predictive environmental sensor networks provide complex engineering and systems challenges. These systems must withstand the event of interest, remain functional over long time periods when no events occur, cover large geographical regions of interest to the event, and support the variety of sensor types needed to detect the phenomenon. Prediction of the phenomenon on the network complicates the system further, requiring additional computation on themicrocontrollers and utilizing prediction models that are not typically designed for sensor networks. This paper describes a system architecture and deployment to meet the design requirements and to allow model-driven control, thereby optimizing the prediction capability of the system. We explore the application of river flood prediction using this architecture, describing our work on a centralized form of the prediction model, network implementation, component testing and infrastructure development in Honduras, deployment on a river in Massachusetts, and results of the field experiments. Our system uses only a small number of nodes to cover basins of 1000-10000 square km2 using an unique heterogeneous communication structure to provide real-time sensed data, incorporating self-monitoring for failure, and adapting measurement schedules to capture events of interest.