Convolution Operator Network for Forward and Inverse Problems (FI-Conv): Application to Plasma Turbulence Simulations

TL;DR

FI-Conv is a novel neural network framework combining U-Net and ConvNeXt V2 blocks, capable of predicting complex plasma turbulence evolution and estimating PDE parameters efficiently, outperforming existing methods in accuracy and computational cost.

Contribution

We introduce FI-Conv, a new convolutional operator network that effectively predicts forward and inverse problems in complex spatio-temporal systems like plasma turbulence.

Findings

Accurately predicts plasma state evolution over short times.

Captures statistical properties of plasma quantities over longer times.

Infers PDE parameters from data without retraining the model.

Abstract

We propose the Convolutional Operator Network for Forward and Inverse Problems (FI-Conv), a framework capable of predicting system evolution and estimating parameters in complex spatio-temporal dynamics, such as turbulence. FI-Conv is built on a U-Net architecture, in which most convolutional layers are replaced by ConvNeXt V2 blocks. This design preserves U-Net performance on inputs with high-frequency variations while maintaining low computational complexity. FI-Conv uses an initial state, PDE parameters, and evolution time as input to predict the system future state. As a representative example of a system exhibiting complex dynamics, we evaluate the performance of FI-Conv on the task of predicting turbulent plasma fields governed by the Hasegawa-Wakatani (HW) equations. The HW system models two-dimensional electrostatic drift-wave turbulence and exhibits strongly nonlinear behavior, making accurate approximation and long-term prediction particularly challenging. Using an autoregressive forecasting procedure, FI-Conv achieves accurate forward prediction of the plasma state evolution over short times (t ~ 3) and captures the statistic properties of derived physical quantities of interest over longer times (t ~ 100). Moreover, we develop a gradient-descent-based inverse estimation method that accurately infers PDE parameters from plasma state evolution data, without modifying the trained model weights. Collectively, our results demonstrate that FI-Conv can be an effective alternative to existing physics-informed machine learning methods for systems with complex spatio-temporal dynamics.