Partial Differential Equations (PDEs) play a fundamental role in modeling complex systems in physics, biology, and engineering, such as in the context of monitoring systems. Traditional numerical methods for solving PDEs, such as finite difference and finite element methods, often suffer from high computational costs, especially in high-dimensional problems and complex domains. In recent years, Neural Networks (NNs) have emerged as a powerful tool for approximating PDE solutions. In this paper, we propose the use of Neural Networks to solve PDEs applied in monitoring systems. To illustrate this concept, we apply it to the Fisher Kolmogorov-Petrovsky-Piskunov Equation.
Solving PDEs in Monitoring Systems Using Neural Networks
Scuro, Carmelo
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2025-01-01
Abstract
Partial Differential Equations (PDEs) play a fundamental role in modeling complex systems in physics, biology, and engineering, such as in the context of monitoring systems. Traditional numerical methods for solving PDEs, such as finite difference and finite element methods, often suffer from high computational costs, especially in high-dimensional problems and complex domains. In recent years, Neural Networks (NNs) have emerged as a powerful tool for approximating PDE solutions. In this paper, we propose the use of Neural Networks to solve PDEs applied in monitoring systems. To illustrate this concept, we apply it to the Fisher Kolmogorov-Petrovsky-Piskunov Equation.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
