Neural Network Solutions for First-Order Differential Equations: A Physics-Informed Perspective

Abstract

In this study, a Physics-Informed Neural Network (PINN) model was developed and used to solve first-order Or-dinary Differential Equations (ODEs). The proposed model implement the initial conditions and incorporates physical laws through its differential equation into the neural network training process to further improve its ac-curacy and solution. The main interest of this work is to test the accuracy, evaluate and compare the performance of this model with established Artificial Neural Network (ANN) solutions in solving first-order ODEs. We validate the effectiveness and accuracy of these models through the conclusions drawn from the six numerical tests carried out after close evaluation of the results presented by the models which show that the developed PINN model consistently achieves high accuracy with absolute errors in the range of 10-8 and 10-10 compared to the established ANN model. This also illustrates their weakness and lets the researchers make wise decisions in selecting the suitable method of addressing certain ODE problems.

Keywords

• First-Order ODEs
• Physics-Informed Neural Network
• Artificial Neural Network
• Performance
• Accuracy

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