Abstract: Physics-informed neural networks (PINNs) offer a flexible framework for solving differential equations using physical constraints and data. This study focuses on second-order ...

Abstract: Many problems in science and engineering can be mathematically modeled using partial differential equations (PDEs), which are essential for fields like computational fluid dynamics (CFD), ...

You can use apostrophes to show that you have omitted (left out) some letters when you are joining words together. For example, you can join the words ‘you’ and ‘are’ together. You + are = you're. The ...