Reduced-order Neural Operators for Accelerating Low-Temperature Plasma Chemistry Simulations

In many real-world applications, the simulation of plasma systems for the purposes of design, optimization, or quantification of uncertainty requires a large number of independent computations, which is often limited by computational cost. In this work, we explore the combination of dimensionality reduction techniques and neural operator surrogates to mitigate this expense. Firstly, we test multiple approaches for projecting the plasma dynamics into low-dimensional subspaces. These include both linear techniques (e.g., principal component analysis), which have the advantage of preserving the underlying equations’ form, and non-linear manifold learning approaches (e.g., diffusion maps), which permit a more effective compression of the trajectories at the expense of interpretability. Secondly, we accelerate the simulation of the plasma dynamics in in the reduced order space via emulation through neural operators. These computational objects are machine learning-based surrogates characterized by two main advantages: i) they bypass the numerical integration of the typically stiff underlying equations, and ii) they can predict the dynamical system’s evolution given initial conditions and/or operator parameters unseen during the training phase. We demonstrate these techniques in the context of global chemistry models for low-temperature plasma systems.