Solving partial differential equations analytically is often extremely complicated or even impossible. In practice, numerical approaches such as the finite element method are traditionally used. These approaches rely on generated meshes and predefined basis functions. Therefore, they are often computationally complex and struggle with convergence issues. In recent years, machine learning approaches have been introduced as an alternative approach to solving differential equations. SWIM-PDE is a data-driven machine learning approach to this task, which is based on sampled neural networks. Unlike classical neural network-based models, no expensive training loop based on backpropagation and some sort of gradient descent is needed. We model spaghetti breaking with a finite element method and SWIM- PDE. Our focus is specifically on the post-break dynamics of a dry spaghetti rod that has been bent until it breaks. We use our experiments to compare SWIM-PDE with a finite element method and to conclude the current capabilities and limitations of SWIM-PDE.     «

Solving partial differential equations analytically is often extremely complicated or even impossible. In practice, numerical approaches such as the finite element method are traditionally used. These approaches rely on generated meshes and predefined basis functions. Therefore, they are often computationally complex and struggle with convergence issues. In recent years, machine learning approaches have been introduced as an alternative approach to solving differential equations. SWIM-PDE i...     »