https://www.chenk.top/en/tags/neural-odes/Recent content in Neural ODEs on Chen Kai BlogHugoenMon, 15 Apr 2024 09:00:00 +0000https://www.chenk.top/en/ode/18-advanced-topics-summary/Mon, 15 Apr 2024 09:00:00 +0000https://www.chenk.top/en/ode/18-advanced-topics-summary/<p><strong>The journey ends here.</strong> Eighteen chapters ago we picked up a falling apple. Today we&rsquo;re going to finish in the same vein in which we began — by treating ODEs as the <em>universal language of change</em> — but standing on a much taller mountain.</p> <p>This chapter does three things. First, it surveys four active research frontiers that are reshaping how we <em>model</em> dynamical systems: Neural ODEs, delay equations, stochastic differential equations, and fractional calculus. Second, it reviews the entire series with a problem-solving flowchart and a chapter-by-chapter map. Third, it draws explicit connections from the classical theory you have just mastered to modern machine learning — the place where ODEs are most alive in 2025.</p>