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

2026-02-04

AI Summary

This work addresses the challenge of balancing accuracy and efficiency in forward prediction and parameter inversion for highly nonlinear, rapidly varying spatiotemporal dynamical systems—such as plasma turbulence—by proposing FI-Conv, a convolutional operator network based on the U-Net architecture. FI-Conv uniquely integrates ConvNeXt V2 blocks into the operator learning framework, substantially reducing computational complexity while preserving the ability to model high-frequency features. The method enables efficient autoregressive forward prediction and facilitates gradient-based parameter inversion without retraining. Evaluated on the Hasegawa–Wakatani turbulence model, FI-Conv achieves high-accuracy short-term state prediction (at t≈3), maintains statistical fidelity over long-term evolution (up to t≈100), and accurately recovers underlying PDE parameters from observational trajectory data.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Search and Optimization: Non-convex Optimization

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• User Modeling, Personalization and Recommendation: Federated recommendation systems and personalization
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

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.

Problem

• forward prediction
• inverse problems
• plasma turbulence
• spatio-temporal dynamics
• parameter estimation

Innovation

• ConvNeXt V2
• U-Net
• forward-inverse problems
• plasma turbulence
• physics-informed machine learning