Solving Ordinary Differential Equations Using Custom Loss Convolutional Neural Network Method

Deep learning and machine learning are pivotal in diverse fields, particularly in mathematical problem-solving. This study introduces a novel approach for solving ordinary differential equations (ODEs) using a single-layer convolutional neural network (CNN) with a logistic sigmoid activation function. The methodology employs a control variable approach, allowing exploration of hyperparameters and optimizer choices. The primary objective is to design a CNN capable of accurately resolving ODEs, trained with the Adam optimizer and backpropagation. Extensive experiments involve custom loss functions tailored to ODE characteristics, examining the impact of varying neural network architectures on solutions. Key findings include the successful application of the CNN-based approach, adaptability assessments through control variables, and insights into the influence of network structure on ODE solutions. This research contributes to the intersection of neural networks and mathematical problem-solving, offering a promising avenue for efficiently addressing ODEs. The findings provide a foundation for enhanced mathematical problem-solving, demonstrating the potential of CNNs and custom loss functions. The implications extend to various scientific and engineering domains, opening avenues for improved efficiency and accuracy in solving ODEs in real-world applications.