DiffFind: Discovering Differential Equations from Time Series

Lalithsai Posam, Shubhranshu Shekhar, Meng-Chieh Lee, Christos Faloutsos

Abstract: Given one or more time sequences, how can we extract their governing equations? Single and co-evolving time sequences appear in numerous settings, including medicine (neuroscience - EEG signals, cardiology - EKG), epidemiology (covid/flu spreading over time), physics (astrophysics, material science), marketing (sales and competition modeling; market penetration), and numerous more. Linear differential equations will fail, since the underlying equations are often non-linear (SIR model for virus/product spread; Lotka-Volterra for product/species competition, Van der Pol for heartbeat modeling).