Optimizing Initial Guesses for Nonlinear System Solvers Using Machine Learning: A Comparative Study of Classification Algorithms

This paper focuses on the problem of improving initial guesses provided to solvers of nonlinear systems in terms of enhancing both convergence efficiency and reliability. A novel approach for constructing confidence models of initial guesses is proposed based on a Logistic Regression, Support Vector Machines (SVM), Random Forests, and K-Nearest Neighbors (KNN) classification schemes. Experimental evaluation across diverse nonlinear systems highlights Random Forests as the most effective model with an average accuracy of 81.69%, average precision – of 83.23%, average recall – of 82.16%, average F1 score of 82.69% and the highest AUC score equal to 0.90. Backed up by broad evaluation metrics, the above research inquiries mark the ideal potential of machine learning to revolutionize data processing by increasing solver adaptability, enhancing convergence patterns and economizing computations in scientific and engineering modalities.