Related papers: Neural Differential Equations for the Solar Dynamo
Predictions from science and engineering models depend on the values of the model's input parameters. As the number of parameters increases, algorithmic parameter studies like optimization or uncertainty quantification require many more…
Theoretical models for the solar dynamo range from simple low-dimensional ``toy models'' to complex 3D-MHD simulations. Here we mainly discuss appproaches that are motivated and guided by solar (and stellar) observations. We give a brief…
Sunspot fine structure has been modeled in the past by a combination of idealized magneto-convection simulations and simplified models that prescribe the magnetic field and flow structure to a large degree. Advancement in numerical methods…
Recent data from the Kepler mission has revealed the occurrence of superflares in sun-like stars which exceed by far any observed solar flares in release of energy. A natural idea is that the dynamo mechanism in superflaring stars differs…
Mean-field dynamo theory, describing the evolution of large-scale magnetic fields, has been the mainstay of theoretical interpretation of magnetism in astrophysical objects such as the Sun for several decades. More recently,…
Computational heliophysics has shed light on the fundamental physical processes inside the Sun, such as the differential rotation, meridional circulation, and dynamo-generation of magnetic fields. However, despite the substantial advances,…
Neural network modules conditioned by known priors can be effectively trained and combined to represent systems with nonlinear dynamics. This work explores a novel formulation for data-efficient learning of deep control-oriented nonlinear…
Magnetic fields generated in the Sun's interior by the solar dynamo mechanism drive solar activity over a range of time-scales. While space-based observations of the Sun's corona exist only for few decades, direct sunspot observations exist…
We show that if the turbulent magnetic diffusivity used in solar dynamos is assumed to be 'quenched' by increasing toroidal fields, much larger amplitude and more concentrated toroidal fields can be induced by differential rotation from an…
We present the assessment of a diffusion-dominated mean field axisymmetric dynamo model in reproducing historical solar activity and forecast for solar cycle 25. Previous studies point to the Sun's polar magnetic field as an important proxy…
Predictions of solar cycle 24 obtained from advection-dominated and diffusion-dominated kinematic dynamo models are different if the Babcock-Leighton mechanism is the only source of the poloidal field. Yeates et al. (2008) argue that the…
We consider a dynamo wave in the solar convective shell for the kinematic $\alpha\omega$-dynamo model. The spectrum and eigenfunctions of the corresponding equations are derived analytically with the aid of the WKB method. Our main aim here…
Numerical MHD simulations play increasingly important role for understanding mechanisms of stellar magnetism. We present simulations of convection and dynamos in density-stratified rotating spherical fluid shells. We employ a new 3D…
The ordered magnetic field observed via polarized synchrotron emission in nearby disc galaxies can be explained by a mean-field dynamo operating in the diffuse interstellar medium (ISM). Additionally, vertical-flux initial conditions are…
To understand solar and stellar dynamos combining local and global numerical modelling with long-term observations is a challenging task: even with state of the art computational methods and resources, the stellar parameter regime remains…
We provide a theory of dynamo ($\alpha$ effect) and momentum transport in three-dimensional magnetohydrodynamics. For the first time, we show that the $\alpha$ effect is severely reduced by the shear even in the absence of magnetic field.…
In this work we introduce a new way of binning sunspot group data with the purpose of better understanding the impact of the solar cycle on sunspot properties and how this defined the characteristics of the extended minimum of cycle 23. Our…
The sunspot cycle is the magnetic cycle of the Sun produced by the dynamo process. A central idea of the solar dynamo is that the toroidal and the poloidal magnetic fields of the Sun sustain each other. We discuss the relevant observational…
We discuss recent advances made in modelling the complex magnetohydrodynamics of the Sun using our anelastic spherical harmonics (ASH) code. We have conducted extensive 3--D simulations of compressible convection in rotating spherical…
Neural ordinary differential equations are an attractive option for modelling temporal dynamics. However, a fundamental issue is that the solution to an ordinary differential equation is determined by its initial condition, and there is no…