Advances in random differential equations: COMPUTATIONAL METHODS AND MULTIDISCIPLINARY APPLICATIONS

• Autores: Vicente José Bevia Escrig
• Directores de la Tesis: Juan Carlos Cortés López (dir. tes.)
• Lectura: En la Universitat Politècnica de València ( España ) en 2024
• Idioma: inglés
• Tribunal Calificador de la Tesis: José Carlos Valverde Fajardo (presid.) , Cristina Santamaría Navarro (secret.) , Francisco Rodríguez Mateo (voc.)
• Enlaces
  • Tesis en acceso abierto en: RiuNet
• Resumen

  • Uncertainty quantification involves various methods and computational techniques to address inherent gaps in the mathematical modeling of real-world phenomena. These methods are particularly valuable for modeling biological, physical, and social processes that contain elements that cannot be precisely determined. For example, the transmission rate of an infectious disease or the growth rate of a tumor are influenced by genetic, environmental, or behavioral factors that are not fully understood, introducing uncertainties that impact outcomes.

    This PhD thesis aims to develop and extend analytical and computational techniques for quantifying uncertainty in random differential equation systems using a system's probability density function. By employing the random variable transformation theorem and the Liouville (continuity) equation, we tackle both forward and inverse uncertainty quantification problems in random systems with real-world data. We also design a computational method to efficiently estimate a system's probability density by solving the Liouville equation with GPU acceleration. Finally, we examine uncertainty evolution in a class of impulse-forced systems, providing new insights into the dynamics of their probability density functions.