Introducing the Second-Order Features Adjoint Sensitivity Analysis Methodology for Neural Ordinary Differential Equations—I: Mathematical Framework

• Published in: Processes Vol. 12; no. 12; p. 2660
• Main Author: Cacuci, Dan Gabriel
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.12.2024
• Subjects: Analysis; Differential equations; Dynamical systems; Efficiency; Mathematics; Methodology; Methods; Neural networks; Nodes; Ordinary differential equations; Parameter sensitivity; Parameter uncertainty; Sensitivity analysis; System theory; Uncertainty analysis

This work introduces the mathematical framework of the novel “First-Order Features Adjoint Sensitivity Analysis Methodology for Neural Ordinary Differential Equations” (1st-FASAM-NODE). The 1st-FASAM-NODE methodology produces and computes most efficiently the exact expressions of all of the first-or...