Parametric Learning of Time-Advancement Operators for Unstable Flame Evolution
This work addresses the need for faster and more cost-effective engineering simulations by providing a unified learning approach for parametric PDEs, though it is incremental as it builds on existing operator learning methods.
This study tackled the problem of learning time-advancement operators for parametric PDEs by extending Fourier Neural Operator and Convolutional Neural Network methods to handle additional parameter inputs, achieving accurate short-term predictions and robust long-term statistics for flame evolution data.
This study investigates the application of machine learning, specifically Fourier Neural Operator (FNO) and Convolutional Neural Network (CNN), to learn time-advancement operators for parametric partial differential equations (PDEs). Our focus is on extending existing operator learning methods to handle additional inputs representing PDE parameters. The goal is to create a unified learning approach that accurately predicts short-term solutions and provides robust long-term statistics under diverse parameter conditions, facilitating computational cost savings and accelerating development in engineering simulations. We develop and compare parametric learning methods based on FNO and CNN, evaluating their effectiveness in learning parametric-dependent solution time-advancement operators for one-dimensional PDEs and realistic flame front evolution data obtained from direct numerical simulations of the Navier-Stokes equations.