The Challenge of Machine Learning in Space Weather Nowcasting and Forecasting

The numerous recent breakthroughs in machine learning (ML) make imperative to carefully ponder how the scientific community can benefit from a technology that, although not necessarily new, is today living its golden age. This Grand Challenge review paper is focused on the present and future role of machine learning in space weather. The purpose is twofold. On one hand, we will discuss previous works that use ML for space weather forecasting, focusing in particular on the few areas that have seen most activity: the forecasting of geomagnetic indices, of relativistic electrons at geosynchronous orbits, of solar flares occurrence, of coronal mass ejection propagation time, and of solar wind speed. On the other hand, this paper serves as a gentle introduction to the field of machine learning tailored to the space weather community and as a pointer to a number of open challenges that we believe the community should undertake in the next decade. The recurring themes throughout the review are the need to shift our forecasting paradigm to a probabilistic approach focused on the reliable assessment of uncertainties, and the combination of physics-based and machine learning approaches, known as gray-box.Comment: under revie

Short-term power demand forecasting using the differential polynomial neural network

Power demand forecasting is important for economically efficient operation and effective control of power systems and enables to plan the load of generating unit. The purpose of the short-term electricity demand forecasting is to forecast in advance the system load, represented by the sum of all consumers load at the same time. A precise load forecasting is required to avoid high generation cost and the spinning reserve capacity. Under-prediction of the demands leads to an insufficient reserve capacity preparation and can threaten the system stability, on the other hand, over-prediction leads to an unnecessarily large reserve that leads to a high cost preparations. Differential polynomial neural network is a new neural network type, which forms and resolves an unknown general partial differential equation of an approximation of a searched function, described by data observations. It generates convergent sum series of relative polynomial derivative terms which can substitute for the ordinary differential equation, describing 1-parametric function time-series. A new method of the short-term power demand forecasting, based on similarity relations of several subsequent day progress cycles at the same time points is presented and tested on 2 datasets. Comparisons were done with the artificial neural network using the same prediction method.Web of Science8230629

A Tractable Fault Detection and Isolation Approach for Nonlinear Systems with Probabilistic Performance

This article presents a novel perspective along with a scalable methodology to design a fault detection and isolation (FDI) filter for high dimensional nonlinear systems. Previous approaches on FDI problems are either confined to linear systems or they are only applicable to low dimensional dynamics with specific structures. In contrast, shifting attention from the system dynamics to the disturbance inputs, we propose a relaxed design perspective to train a linear residual generator given some statistical information about the disturbance patterns. That is, we propose an optimization-based approach to robustify the filter with respect to finitely many signatures of the nonlinearity. We then invoke recent results in randomized optimization to provide theoretical guarantees for the performance of the proposed filer. Finally, motivated by a cyber-physical attack emanating from the vulnerabilities introduced by the interaction between IT infrastructure and power system, we deploy the developed theoretical results to detect such an intrusion before the functionality of the power system is disrupted

Data Driven Regional Weather Forecasting: Example using the Shallow Water Equations

Using data alone, without knowledge of underlying physical models, nonlinear discrete time regional forecasting dynamical rules are constructed employing well tested methods from applied mathematics and nonlinear dynamics. Observations of environmental variables such as wind velocity, temperature, pressure, etc allow the development of forecasting rules that predict the future of these variables only. A regional set of observations with appropriate sensors allows one to forgo standard considerations of spatial resolution and uncertainties in the properties of detailed physical models. Present global or regional models require specification of details of physical processes globally or regionally, and the ensuing, often heavy, computational requirements provide information of the time variation of many quantities not of interest locally. In this paper we formulate the construction of data driven forecasting (DDF) models of geophysical processes and demonstrate how this works within the familiar example of a 'global' model of shallow water flow on a mid-latitude beta plane. A sub-region, where observations are made, of the global flow is selected. A discrete time dynamical forecasting system is constructed from these observations. DDF forecasting accurately predicts the future of observed variables.Comment: 46 pages, 10 figure

Physics Informed Neural Networks in Temporal Graphs

Lo scopo della tesi è quello di sviluppare nuove tecniche di interpretable physics informed machine learning per trovare modelli epidemiologici, e comparare queste tecniche ad altre già esistenti. I modelli imparati dovrebbero aiutare a capire la malattia e a prevederla.The goal of this thesis is to develop new interpretable physics informed machine learning techniques for finding epidemiological models, and compare these techniques to existing ones. These learned models should help understanding the disease and forecasting it

Non-Intrusive Reduced Models based on Operator Inference for Chaotic Systems

This work explores the physics-driven machine learning technique Operator Inference (OpInf) for predicting the state of chaotic dynamical systems. OpInf provides a non-intrusive approach to infer approximations of polynomial operators in reduced space without having access to the full order operators appearing in discretized models. Datasets for the physics systems are generated using conventional numerical solvers and then projected to a low-dimensional space via Principal Component Analysis (PCA). In latent space, a least-squares problem is set to fit a quadratic polynomial operator, which is subsequently employed in a time-integration scheme in order to produce extrapolations in the same space. Once solved, the inverse PCA operation is applied to reconstruct the extrapolations in the original space. The quality of the OpInf predictions is assessed via the Normalized Root Mean Squared Error (NRMSE) metric from which the Valid Prediction Time (VPT) is computed. Numerical experiments considering the chaotic systems Lorenz 96 and the Kuramoto-Sivashinsky equation show promising forecasting capabilities of the OpInf reduced order models with VPT ranges that outperform state-of-the-art machine learning methods such as backpropagation and reservoir computing recurrent neural networks [1], as well as Markov neural operators [2].Comment: 16 pages, 37 figures, accepted for publication in the IEEE-TAI-PIM