Related papers: Modeling Cosmic-Ray Transport: A CRPropa based sto…
Handling big data has largely been a major bottleneck in traditional statistical models. Consequently, when accurate point prediction is the primary target, machine learning models are often preferred over their statistical counterparts for…
We identify effective stochastic differential equations (SDE) for coarse observables of fine-grained particle- or agent-based simulations; these SDE then provide useful coarse surrogate models of the fine scale dynamics. We approximate the…
We show the necessity for a new approach towards comprehensive and consistent simulations of the propagation of galactic cosmic rays. Our developments are optimised for addressing the spatially 3-dimensional inhomogeneous diffusion problem…
In recent years we have witnessed a growth in mathematics for deep learning, which has been used to solve inverse problems of partial differential equations (PDEs). However, most deep learning-based inversion methods either require paired…
Cosmic rays (CRs) are an important source of feedback in a variety of astrophysical contexts. Magneto-hydrodynamical (MHD) simulations treating CRs as a fluid have shown that how their feedback operates is strongly dependent on their…
This paper introduces a statistical treatment of inverse problems constrained by models with stochastic terms. The solution of the forward problem is given by a distribution represented numerically by an ensemble of simulations. The goal is…
We study diffusion of Cosmic Rays (CRs) in turbulent magnetic fields using test particle simulations. Electromagnetic fields are produced in direct numerical MHD simulations of turbulence and used as an input for particle tracing, particle…
We present a numerical algorithm for the incorporation of the active cosmic ray transport, into the ZEUS-3D magnetohydrodynamical code. The cosmic ray transport is described by the diffusion-advection equation. The applied form of the…
Modern HPC architectures consist of heterogeneous multi-core, many-node systems with deep memory hierarchies. Modern applications employ ever more advanced discretisation methods to study multi-physics problems. Developing such applications…
Energetic electrons are of interest in many types of plasmas, however previous modeling of their properties has been restricted to the use of linear Fokker-Planck collision operators or non-relativistic formulations. Here, we describe a…
Score-based diffusion models have emerged as a powerful class of generative methods, achieving state-of-the-art performance across diverse domains. Despite their empirical success, the mathematical foundations of those models remain only…
Continuous Time Random Walk models (CTRW) of anomalous diffusion are studied, where the anomalous exponent $\beta(x) \in (0,1)$ varies in space. This type of situation occurs e.g. in biophysics, where the density of the intracellular matrix…
We study fully nonlinear second-order (forward) stochastic partial differential equations (SPDEs). They can also be viewed as forward path-dependent PDEs (PPDEs) and will be treated as rough PDEs (RPDEs) under a unified framework. We…
The interpretation of experimental data of ultra-high energy cosmic rays (UHECRs) above 10^17 eV is still under controversial debate. The development and improvement of numerical tools to propagate UHECRs in galactic and extragalactic space…
This article introduces a framework for measuring the uncertain behaviour of a changing system in terms of the solution of a class of fractional stochastic differential equations (fsDEs). This is accomplished via operational matrices based…
Anisotropic diffusion is imperative in understanding cosmic ray diffusion across the Galaxy, the heliosphere, and the interplay of cosmic rays with the Galactic magnetic field. This diffusion term contributes to the highly stiff nature of…
Sequential propagation of chaos (SPoC) is a recently developed tool to solve mean-field stochastic differential equations and their related nonlinear Fokker-Planck equations. Based on the theory of SPoC, we present a new method (deepSPoC)…
Understanding the transport of energetic cosmic rays belongs to the most challenging topics in astrophysics. Diffusion due to scattering by electromagnetic fluctuations is a key process in cosmic-ray transport. The transition from a…
In this paper we exactly solve the diffusion-advection equation for cosmic-ray transport. With this purpose we use the Theory of Ultradistributions of J. Sebastiao e Silva, to give a general solution for this equation. From this solution,…
We consider stochastic differential equations (SDEs) driven by a fractional Brownian motion with a drift coefficient that is allowed to be arbitrarily close to criticality in a scaling sense. We develop a comprehensive solution theory that…