Causally interpretable multi-step time series forecasting: A new machine learning approach using simulated differential equations

By: William Schoenberg (University of Bergen, Norway) Abstract This work re presents a new approach which generates then analyzes a highly non - linear complex system of differential equations to do interpretable time series forecasting at a high level of accuracy. This approach provides insight and understanding into the mechanisms responsible for gener ating past and future behavior. Core to this method is the construction of a highly non - linear complex system of differential equations that is then analyzed to determine the origins of behavior. This paper demonstrates the technique on Mass and Senge's two state Inventory Workforce model ( 1975) and then explores its application to the real world problem of organogenesis in mice . The organogenesis application consists of a fourteen - state system where the generated set of equations reproduces observed behavior with a high level of accuracy ( 0.88 0 Introduction: Accurate time series forecasting is very important to a variety of scientific fields, engineering disciplines, and socially constructed systems including businesses, and governments (Palit & Popovic, 2006) . Past effort s on this problem have focused on developing more accurate methods or models useful for predicting time series data, starting with linear statistical models and evolving into non - linear models and ultimately machine learning techniques (Bontempi, et, al, 2012) .