Introduction

In recent years, the combination of machine learning and scientific computing has led to dramatic changes in scientific computing. In particular, operator learning can be a technique for discovering formulas for solutions of partial differential equations using machine learning, and it is expected to enable real-time predictions for various applications such as weather forecasting. However, the theoretical foundations of operator learning —such as understanding its physical properties and error analysis— have not yet been established. This project will integrate infinite-dimensional data science and physics to develop a trustworthy operator learning theory and methodology.