Markku Alho

Ioanna Bouri, Fanni Franssila, Markku Alho et al.

Topological analysis of the magnetic field in simulated plasmas allows the study of various physical phenomena in a wide range of settings. One such application is magnetic reconnection, a phenomenon related to the dynamics of the magnetic field topology, which is difficult to detect and characterize in three dimensions. We propose a scalable pipeline for topological data analysis and spatiotemporal graph representation of three-dimensional magnetic vector fields. We demonstrate our methods on simulations of the Earth's magnetosphere produced by Vlasiator, a supercomputer-scale Vlasov theory-based simulation for near-Earth space. The purpose of this work is to challenge the machine learning community to explore graph-based machine learning approaches to address a largely open scientific problem with wide-ranging potential impact.

Daniel Holmberg, Ivan Zaitsev, Markku Alho et al.

Hybrid-Vlasov simulations resolve ion-kinetic effects in the solar wind-magnetosphere interaction, but even 5D (2D + 3V) configurations are computationally expensive. We show that graph-based machine learning emulators can learn the spatiotemporal evolution of electromagnetic fields and lower order moments of ion velocity distribution in the near-Earth space environment from four 5D Vlasiator runs performed with identical steady solar wind conditions. The initial ion number density is systematically varied, while the grid spacing is held constant, to scan the ratio of the characteristic ion skin depth to the numerical grid size. Using a graph neural network (GNN) operating on the 2D spatial simulation grid comprising 670k cells, we demonstrate that both a deterministic forecasting model (Graph-FM) and a probabilistic ensemble forecasting model (Graph-EFM) based on a latent variable formulation are capable of producing accurate predictions of future plasma states. A divergence penalty is incorporated to encourage divergence-freeness in the magnetic fields. For the probabilistic model, a continuous ranked probability score objective is added to improve the calibration of the ensemble forecasts. The trained emulators achieve over two orders of magnitude speedup per time step on a single GPU compared to 100 CPU Vlasiator simulations. Most forecasted fields have Pearson correlations above 0.95 at 50 seconds lead time. However, we find that fields that exhibit near-zero degenerate distributions in the 5D setting are more challenging for the emulator to maintain high correlations for. Overall, these results demonstrate that GNNs provide a viable framework for rapid ensemble generation in hybrid-Vlasov modeling and highlight promising directions for future work.

Daniel Holmberg, Ivan Zaitsev, Markku Alho et al.

Accurate space weather forecasting is crucial for protecting our increasingly digital infrastructure. Hybrid-Vlasov models, like Vlasiator, offer physical realism beyond that of current operational systems, but are too computationally expensive for real-time use. We introduce a graph-based neural emulator trained on Vlasiator data to autoregressively predict near-Earth space conditions driven by an upstream solar wind. We show how to achieve both fast deterministic forecasts and, by using a generative model, produce ensembles to capture forecast uncertainty. This work demonstrates that machine learning offers a way to add uncertainty quantification capability to existing space weather prediction systems, and make hybrid-Vlasov simulation tractable for operational use.