Dissertation defense
Student: Roberta Duarte Pereira
Program: Astronomia
Title: ''Operator-Learning for Magnetohydrodynamic Turbulence''
Advisor: Prof. Dr. Rodrigo Nemmen - IAG/USPP
Judging comitee:
- Prof. Dr. Rodrigo Nemmen da Silva – Presidente e Orientador - IAG/USP
- Prof. Dr. Reinaldo Santos de Lima - IAG/USP
- Prof. Dr. Laerte Sodré Junior - IAG/USP
- Prof. Dr. Pedro Leite da Silva Dias – Ciências Atmosféricas - IAG/USP
- Dr. Clécio Roque de Bom – CBPF (por videoconferência)
- Profa. Dra. Nina Sumiko Tomita Hirata - IME/USP
Abstract: In this work, we investigate the application of the Fourier Neural Operator (FNO) to
accelerate magnetohydrodynamic (MHD) simulations. MHD systems are governed
by nonlinear partial differential equations that model the dynamics of conducting
fluids in the presence of magnetic fields. Traditional numerical solvers for MHD are
computationally expensive, particularly in turbulent regimes. We explore the
potential of FNOs - a state-of-the-art machine learning architecture operating in
Fourier space - to learn and predict the evolution of MHD fields from simulation
data. We study a well-established test case, Orszag-Tang vortex, simulated in a
128 ×128 periodic grid using FARGO3D code. We evaluate the FNO’s ability to
simulate velocity, magnetic, and density fields. The results show that the FNO
accurately reproduces large- and intermediate-scale dynamics and generalizes well
to out-of-distribution conditions, such as changes in viscosity and diffusivity. The
results show mean absolute errors in the order of 10e−3 and 10e−4. Spectral
analysis confirms strong alignment between the predicted and reference power
spectra at low- and mid-range wavenumber. The FNO captures the energy
dissipation rate profile with high fidelity and achieves a 24.75× speed-up compared
to conventional solvers. Despite limitations in resolving small-scale features and
capturing temporal discontinuities, the FNO demonstrates potential as a model for
complex MHD systems. This study highlights its viability for accelerating plasma
simulations and enabling real-time analysis in turbulent fluid regimes.
Keywords: machine learning, plasmas, astrophysical plasma, operators, artificial intelligence