Resumen
Artificial neural networks have changed many fields by giving scientists a strong way to model complex phenomena. They are also becoming increasingly useful for solving various difficult scientific problems. Still, people keep trying to find faster and more accurate ways to simulate dynamic systems. This research explores the transformative capabilities of physics-informed neural networks, a specialized subset of artificial neural networks, in modeling complex dynamical systems with enhanced speed and accuracy. These networks incorporate known physical laws into the learning process, ensuring predictions remain consistent with fundamental principles, which is crucial when dealing with scientific phenomena. This study focuses on optimizing the application of this specialized network for simultaneous system dynamics simulations and learning time-varying parameters, particularly when the number of unknowns in the system matches the number of undetermined parameters. Additionally, we explore scenarios with a mismatch between parameters and equations, optimizing network architecture to enhance convergence speed, computational efficiency, and accuracy in learning the time-varying parameter. Our approach enhances the algorithm?s performance and accuracy, ensuring optimal use of computational resources and yielding more precise results. Extensive experiments are conducted on four different dynamical systems: first-order irreversible chain reactions, biomass transfer, the Brusselsator model, and the Lotka-Volterra model, using synthetically generated data to validate our approach. Additionally, we apply our method to the susceptible-infected-recovered model, utilizing real-world COVID-19 data to learn the time-varying parameters of the pandemic?s spread. A comprehensive comparison between the performance of our approach and fully connected deep neural networks is presented, evaluating both accuracy and computational efficiency in parameter identification and system dynamics capture. The results demonstrate that the physics-informed neural networks outperform fully connected deep neural networks in performance, especially with increased network depth, making them ideal for real-time complex system modeling. This underscores the physics-informed neural network?s effectiveness in scientific modeling in scenarios with balanced unknowns and parameters. Furthermore, it provides a fast, accurate, and efficient alternative for analyzing dynamic systems.