Predicting solar wind streams from the inner-heliosphere to Earth via shifted operator inference

Issan, Opal; Krämer, Boris

doi:10.1016/j.jcp.2022.111689

Cited by 14 publications

(4 citation statements)

References 55 publications

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“…It will be interesting to apply the proposed UQ framework to WSA‐Enlil to make sure the WSA posteriors do not change drastically in time and verify that the WSA‐Enlil model is reliable for real‐time forecasting. Depending on the computational resources and computational complexity of the model at hand, one might need to incorporate surrogate models (computationally efficient approximate models), such as projection‐based reduced‐order models (Benner et al., 2015; Issan & Kramer, 2022) and interpolatory surrogates (Xiu & Karniadakis, 2002), to compute Sobol' sensitivity indices and run MCMC. If the model is computationally efficient (i.e., order of seconds/minutes) we recommend using the MC methods presented in this study as they are unbiased estimators.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Bayesian Inference and Global Sensitivity Analysis for Ambient Solar Wind Prediction

Issan,

Riley,

Camporeale

et al. 2023

Space Weather

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The ambient solar wind plays a significant role in propagating interplanetary coronal mass ejections and is an important driver of space weather geomagnetic storms. A computationally efficient and widely used method to predict the ambient solar wind radial velocity near Earth involves coupling three models: Potential Field Source Surface, Wang‐Sheeley‐Arge (WSA), and Heliospheric Upwind eXtrapolation. However, the model chain has 11 uncertain parameters that are mainly non‐physical due to empirical relations and simplified physics assumptions. We, therefore, propose a comprehensive uncertainty quantification (UQ) framework that is able to successfully quantify and reduce parametric uncertainties in the model chain. The UQ framework utilizes variance‐based global sensitivity analysis followed by Bayesian inference via Markov chain Monte Carlo to learn the posterior densities of the most influential parameters. The sensitivity analysis results indicate that the five most influential parameters are all WSA parameters. Additionally, we show that the posterior densities of such influential parameters vary greatly from one Carrington rotation to the next. The influential parameters are trying to overcompensate for the missing physics in the model chain, highlighting the need to enhance the robustness of the model chain to the choice of WSA parameters. The ensemble predictions generated from the learned posterior densities significantly reduce the uncertainty in solar wind velocity predictions near Earth.

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Section: Conclusion and Discussionmentioning

confidence: 99%

Bayesian Inference and Global Sensitivity Analysis for Ambient Solar Wind Prediction

Issan,

Riley,

Camporeale

et al. 2023

Space Weather

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“…After semi-discretization via the upwind scheme, and an r-dependent linear shift of the longitude to account for advection (see [35] for details), the finite-dimensional nonlinear model is where v(r) = [v(r, φ 1 ), v(r, φ 2 ), . .…”

Section: Model the Heliospheric Upwind Extrapolation (Hux) Modelmentioning

confidence: 99%

Exact and optimal quadratization of nonlinear finite-dimensional non-autonomous dynamical systems

Bychkov¹,

Issan²,

Kramer³

et al. 2023

Preprint

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Quadratization of polynomial and nonpolynomial systems of ordinary differential equations is advantageous in a variety of disciplines, such as systems theory, fluid mechanics, chemical reaction modeling and mathematical analysis. A quadratization reveals new variables and structures of a model, which may be easier to analyze, simulate, control, and provides a convenient parametrization for learning. This paper presents novel theory, algorithms and software capabilities for quadratization of non-autonomous ODEs. We provide existence results, depending on the regularity of the input function, for cases when a quadratic-bilinear system can be obtained through quadratization. We further develop existence results and an algorithm that generalizes the process of quadratization for systems with arbitrary dimension that retain the nonlinear structure when the dimension grows. For such systems, we provide dimension-agnostic quadratization. An example is semi-discretized PDEs, where the nonlinear terms remain symbolically identical when the discretization size increases. As an important aspect for practical adoption of this research, we extended the capabilities of the QBee software towards both non-autonomous systems of ODEs and ODEs with arbitrary dimension. We present several examples of ODEs that were previously reported in the literature, and where our new algorithms find quadratized ODE systems with lower dimension than the previously reported lifting transformations. We further highlight an important area of quadratization: reduced-order model learning. This area can benefit significantly from working in the optimal lifting variables, where quadratic models provide a direct parametrization of the model that also avoids additional hyperreduction for the nonlinear terms. A solar wind example highlights these advantages.

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“…Yang and Shen (2021) introduce a 3D MHD solar wind model driven by boundary conditions that are trained with an artificial neural network from multiple observations. Issan and Kramer (2023) present a datadriven reduced-order model for forecasting heliospheric solar wind speeds. Asensio Ramos et al (2023) provide further information on machine learning in solar physics.…”

Section: Introductionmentioning

confidence: 99%

Prediction of Solar Coronal Structures Using Fourier Neural Operators Based on the Solar Photospheric Magnetic Field Observation

Zhao,

Feng

2024

Space Weather

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This paper constructs the structures of the solar corona (SC) using Fourier neural operators (FNO) based on solar photospheric magnetic field observation. The purpose is to learn the mapping between two infinite‐dimensional function spaces, which takes the photospheric magnetic field as input and the magnetohydrodynamic (MHD) solar wind plasma parameters as output, from a finite collection of input‐output pairs. The FNO‐SC model is established using MHD simulated results of 36 Carrington rotations (CRs) from 2008, 2009, and 2020. The performance of the FNO‐SC model is tested for 6 CRs during various phases of the solar activity such as descending, minimum, and ascending phases to generate the 3D structures of the SC. With the MHD simulations as references, the average structure similarity index measure (SSIM) value for the magnetic field topology from 1 to 3Rs is around 0.88. From 1 to 20Rs, the SSIM values for the number density and radial speed surpass 0.9. Relative to OMNI observations, the mean absolute percentage error for the radial speed generated from the FNO‐SC model does not exceed 0.25. These results indicate that the FNO‐SC model effectively captures the solar coronal structures typical of the periods investigated, by recovering the MHD simulations as well as the observations. The FNO‐SC model is further trained with enriched data from the maximum phase to assess the capability of modeling such a situation. The FNO‐SC model costs 48.7 s for a single CR prediction, and thus facilitates real‐time space weather forecasting.

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Predicting solar wind streams from the inner-heliosphere to Earth via shifted operator inference

Cited by 14 publications

References 55 publications

Bayesian Inference and Global Sensitivity Analysis for Ambient Solar Wind Prediction

Bayesian Inference and Global Sensitivity Analysis for Ambient Solar Wind Prediction

Exact and optimal quadratization of nonlinear finite-dimensional non-autonomous dynamical systems

Prediction of Solar Coronal Structures Using Fourier Neural Operators Based on the Solar Photospheric Magnetic Field Observation

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