Automated Tuning of Fuzzy Systems to Solve Ordinary Differential Equations

Physics-Informed Neural Networks (PINNs) have recently emerged as a powerful method for solving differential equations by leveraging machine learning techniques. However, while neural networks benefit from universal approximation properties, they often lack interpretability, making their inner workings difficult to understand. In contrast, fuzzy systems, which also exhibit universal approximation capabilities, offer a more transparent alternative due to their rule-based structure. In this paper, we introduce Physics-Informed Fuzzy Systems (PIFS) as a novel approach to solving Ordinary Differential Equations (ODEs). Using the recently developed FuzzyLogic.jl framework, we demonstrate how fuzzy systems can be optimized to approximate ODE solutions effectively. Our study compares the accuracy and interpretability of fuzzy systems against PINNs, and shows that PIFS can achieve faster convergence and lower model complexity, highlighting their potential for physics-informed machine learning.