Publikationen
J. Martin, J. Lübke, T. Li, M. Buzzicotti, R. Grauer, L. BiferaleGeneration of cosmic ray trajectories by a Diffusion Model trained on test particles in 3D magnetohydrodynamic turbulenceModels for the transport of high-energy charged particles through strong magnetic turbulence play a key role in space and astrophysical studies, such as describing the propagation of solar energetic particles and high-energy cosmic rays. Inspired by the recent advances in high-performance machine learning techniques, we investigate the application of generative diffusion models to synthesizing test particle trajectories obtained from a turbulent magnetohydrodynamics simulation. We consider velocity increment, spatial transport, and curvature statistics, and find excellent agreement with the baseline trajectories for fixed particle energies. Additionally, we consider two synthetic turbulence models for comparison. Finally, challenges toward an application-ready transport model based on our approach are discussed. ApJS 277 (2025) 48  
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Jeremiah Lübke, Frederic Effenberger, Mike Wilbert, Horst Fichtner, Rainer GrauerTowards Synthetic Magnetic Turbulence with Coherent StructuresSynthetic turbulence is a relevant tool to study complex astrophysical and space plasma environments inaccessible by direct simulation. However, conventional models lack intermittent coherent structures, which are essential in realistic turbulence. We present a novel method, featuring coherent structures, conditional structure function scaling and fieldline curvature statistics comparable to magnetohydrodynamic turbulence. Enhanced transport of charged particles is investigated as well. This method presents significant progress towards physically faithful synthetic turbulence. EPL 145 (2024) 43001
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Jeremiah Lübke, Jan Friedrich, Rainer GrauerStochastic interpolation of sparsely sampled time series by a superstatistical random process and its synthesis in Fourier and wavelet spaceWe present a novel method for stochastic interpolation of sparsely sampled time signals based on a superstatistical random process generated from a multivariate Gaussian scale mixture. In com- parison to other stochastic interpolation methods such as Gaussian process regression, our method possesses strong multifractal properties and is thus applicable to a broad range of real-world time series, e.g. from solar wind or atmospheric turbulence. Furthermore, we provide a sampling algo- rithm in terms of a mixing procedure that consists of generating a 1 + 1-dimensional field u(t, ξ), where each Gaussian component uξ(t) is synthesized with identical underlying noise but differ- ent covariance function Cξ(t,s) parameterized by a log-normally distributed parameter ξ. Due to the Gaussianity of each component uξ(t), we can exploit standard sampling alogrithms such as Fourier or wavelet methods and, most importantly, methods to constrain the process on the sparse measurement points. The scale mixture u(t) is then initialized by assigning each point in time t a ξ(t) and therefore a specific value from u(t, ξ), where the time-dependent parameter ξ(t) follows a log-normal process with a large correlation time scale compared to the correlation time of u(t, ξ). We juxtapose Fourier and wavelet methods and show that a multiwavelet-based hierarchical ap- proximation of the interpolating paths, which produce a sparse covariance structure, provide an adequate method to locally interpolate large and sparse datasets. Journal of Physics: Complexity 4 (2023) 15005
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