Leveraging physics-informed neural computing for transport simulations of nuclear fusion plasmas
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For decades, plasma transport simulations in tokamaks have used the finite difference method (FDM), a relatively simple scheme to solve the transport equations, a coupled set of time-dependent partial differential equations. In this FDM approach, typically over 𝑂(105) time steps are needed for a single discharge, to mitigate numerical instabilities induced by stiff transport coefficients. It requires significant computing time as costly transport models are repeatedly called in a serial manner, proportional to the number of time steps. Additionally, the unidirectional calculations of FDM make it difficult to predict regions prior to the initial condition or apply additional temporal constraints. In this study, we discuss using a new scheme to solve plasma transport based on physics-informed neural networks (PINNs). PINN iteratively updates a function that maps spatiotemporal coordinates to plasma states, gradually reducing errors in transport equations. The required number of updates in PINNs is several orders of magnitude less than the chronological iterations in FDM. Furthermore, it is free from numerical instabilities arising from finite grids and enables more versatile semi-predictive simulations with arbitrary spatiotemporal constraints. In this paper, we discuss the features and potentials of the tokamak transport solver using PINNs through comparisons with FDM, and also its drawbacks and challenges.
Abstract
For decades, plasma transport simulations in tokamaks have used the finite difference method (FDM), a relatively simple scheme to solve the transport equations, a coupled set of time-dependent partial differential equations. In this FDM approach, typically over 𝑂(105) time steps are needed for a single discharge, to mitigate numerical instabilities induced by stiff transport coefficients. It requires significant computing time as costly transport models are repeatedly called in a serial manner, proportional to the number of time steps. Additionally, the unidirectional calculations of FDM make it difficult to predict regions prior to the initial condition or apply additional temporal constraints. In this study, we discuss using a new scheme to solve plasma transport based on physics-informed neural networks (PINNs). PINN iteratively updates a function that maps spatiotemporal coordinates to plasma states, gradually reducing errors in transport equations. The required number of updates in PINNs is several orders of magnitude less than the chronological iterations in FDM. Furthermore, it is free from numerical instabilities arising from finite grids and enables more versatile semi-predictive simulations with arbitrary spatiotemporal constraints. In this paper, we discuss the features and potentials of the tokamak transport solver using PINNs through comparisons with FDM, and also its drawbacks and challenges.
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