GyroGaussian: A Linear Representation of Fusion Plasma Turbulence with Exact and Differentiable Physics

Gyrokinetic simulations model the plasma turbulence governing heat transport in magnetically confined fusion devices. These 5D simulations are computationally expensive and produce massive data volumes, with a single snapshot requiring tens of gigabytes of storage. This makes directly storing intermediate timesteps impractical and motivates the use of (lossy) compression. Recent neural compression approaches achieve favorable rate–distortion trade-offs by augmenting conventional $L_2$ reconstruction objectives with physics-informed losses that preserve derived quantities such as the electrostatic potential and heat flux. However, neural network based representations can be difficult to optimize and refine when additional constraints are imposed. We introduce GyroGaussian, a compression method for gyrokinetic fields inspired by Gaussian splatting. GyroGaussian represents each plasma field as a weighted sum of independent Gaussian–Gabor atoms, yielding a representation that is linear in its coefficients. This linearity enables a staged optimization strategy in which atoms are first fitted to minimize reconstruction error, then refined against the potential, and subsequently new atoms are added to correct the transport. Moreover, relevant derived quantities admit closed-form expressions in terms of the atom coefficients, enabling efficient refinement via a Gauss–Newton procedure. Experiments on gyrokinetic simulation data show that GyroGaussian achieves improved trade-offs at matched storage over established compression baselines on derived physical quantities while remaining competitive on field reconstruction, and improving over state-of-the-art physics-informed compressors. These results demonstrate Gaussian splatting as an effective and flexible approach to high-fidelity compression of scientific simulation data.