Kolmogorov n-widths for multitask physics-informed machine learning (PIML) methods: Towards robust metrics.

Physics-informed machine learning (PIML) as a means of solving partial differential equations (PDEs) has garnered much attention in the Computational Science and Engineering (CS&E) world. This topic encompasses a broad array of methods and models aimed at solving a single or a collection of PDE problems, called multitask learning. PIML is characterized by the incorporation of physical laws into the training process of machine learning models in lieu of large data when solving PDE problems.