Abstract
The inference of physical parameters from measured distributions constitutes a core task in physics data analyses. Among recent deep learning methods, so-called conditional invertible neural networks provide an elegant approach owing to their probability-preserving bijective mapping properties. They enable training the parameter-observation correspondence in one mapping direction and evaluating the parameter posterior distributions in the reverse direction. Here, we study the inference of cosmic-ray source properties from cosmic-ray observations on Earth using extensive astrophysical simulations. We compare the performance of conditional invertible neural networks (cINNs) with the frequently used Markov Chain Monte Carlo (MCMC) method. While cINNs are trained to directly predict the parameters’ posterior distributions, the MCMC method extracts the posterior distributions through a likelihood function that matches simulations with observations. Overall, we find good agreement between the physics parameters derived by the two different methods. As a result of its computational efficiency, the cINN method allows for a swift assessment of inference quality.
Highlights
Among recent deep learning methods, so-called conditional invertible neural networks provide an elegant approach owing to their probability-preserving bijective mapping properties
We compare the performance of conditional invertible neural networks with the frequently used Markov Chain Monte Carlo (MCMC) method
While conditional invertible neural networks (cINNs) are trained to directly predict the parameters’ posterior distributions, the MCMC method extracts the posterior distributions through a likelihood function that matches simulations with observations
Summary
Information about our universe is obtained from four different messengers: electromagnetic waves, cosmic rays, neutrinos, and gravitational waves. To obtain dedicated information about properties of the universe, e.g., the source of the messenger, the influences of the other contributions (propagation, detector effects) have to be reversed by mathematical methods This process is usually referred to as inference. Instead of the complete true energy distribution at the source, we aim to determine a set of characteristic quantities at the source, describing the set of different atomic nuclei (composition), the power of the energy spectrum (spectral index), and the maximum accelerator energy This astrophysical scenario is kept very simple, but already shows the sensitivity of the measurements to source properties of cosmic rays [3]. We present a normalizing flow network for the determination of cosmic-ray source parameters from measured distributions The quality of this so-called conditional invertible neural network (cINN) is investigated in a comparative study with the traditional MCMC method.
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