Financial Forecasting Equations with Scientific Machine Learning

Abstract

Financial markets are inherently nonlinear, dynamic, and noisy, posing significant challenges for traditional time series forecasting methods. This document explores a novel approach to financial forecasting by integrating Scientific Machine Learning (SciML) techniques, specifically the Sparse Identification of Nonlinear Dynamics (SINDy) algorithm, with domain knowledge from financial time series analysis and advanced feature engineering. We aim to discover interpretable differential equations that govern market behavior.

Financial concepts such as returns and volatility are incorporated as features, guided by methodologies. The resulting hybrid framework enables both data-driven discovery of governing equations and quantitative forecasting, with an emphasis on sparse, explainable models. Our experiments on cryptocurrency and equity datasets demonstrate the potential of SINDy-based models to extract meaningful dynamics and offer competitive forecasting performance, especially when enhanced with carefully engineered financial features. This work contributes to the growing field of explainable SciML applications in finance, bridging theoretical dynamics and real-world market signals.