Mechanistic Neural Networks for Scientific Machine Learning

Abstract

This paper presents *Mechanistic Neural Networks*, a neural network design for machine learning applications in the sciences. It incorporates a new *Mechanistic Block* in standard architectures to explicitly learn governing differential equations as representations, revealing the underlying dynamics of data and enhancing interpretability and efficiency in data modeling. Central to our approach is a novel fast, parallel and scalable *Relaxed Linear Programming Solver* (NeuRLP) using a differentiable optimization approach for ODE learning and solving. Mechanistic Neural Networks demonstrate their versatility for scientific machine learning applications on tasks from equation discovery to dynamic systems modeling.