Predicting company growth using scaling theory informed machine learning

Predicting company growth is a critical yet challenging task because observed dynamics blend an underlying structural growth with volatile fluctuations. Here, we propose a Scaling-Theory-Informed Machine Learning framework (STIML) that integrates a scaling-based model that predicts the mechanism-driven average growth, together with a data-driven forecasting model to learn the residual fluctuations. Using Compustat data of 31,553 North American companies, we extend the growth model to multiple financial indicators, and evaluate STIML against growth model-only and purely data-driven baselines. Across 16 target variables, we show that company growth can be decomposed into trend-driven and fluctuation-driven predictability, whose relative importance varies strongly with company size, while the trend component remains robust across different levels of volatility. Interpretability analyses further show that STIML captures multivariate dependencies beyond autocorrelation, and that macroeconomic variables contribute significantly less to predictive performance on average. Moreover, we find the scaling-based growth model overlooks asymmetric deviations, which instead contain the structured and learnable signals, suggesting a path to refine mechanistic growth models.