A DYNAMICAL SYSTEMS APPROACH TO PSYCHOLOGY: FUSING DIFFERENTIAL EQUATIONS AND RECURRENT NEURAL NETWORKS FOR PROCESS MODELING

Abstract

Traditional psychological models often rely on static, cross-sectional data and latent variable constructs, struggling to capture the temporal, non-linear, and idiosyncratic nature of mental processes. This paper proposes a novel methodological synthesis for psychological science: the integration of theory-driven differential equations (DEs) with data-driven recurrent neural networks (RNNs). We argue that this fusion creates a powerful framework for process modeling, where the core principles of dynamical systems theory such as attractors, bifurcations, and phase transitions provide the theoretical scaffold, while RNNs offer the computational machinery to learn these dynamics directly from intensive longitudinal data. Differential equations allow for the formalization of a priori psychological theories into precise models of change (e.g., models of emotion regulation or cognitive decision-making). Conversely, RNNs, with their inherent memory and feedback loops, are natural black-box identifiers of temporal dependencies and can discover complex dynamics from data when theory is insufficient. We demonstrate how this hybrid approach can be applied to model critical phenomena in psychology, including emotional inertia in depression, critical transitions in psychotherapy, and real-time decision dynamics. This paradigm shift from a variable-centered to a process-centered science promises not only enhanced predictive accuracy but also a deeper, more mechanistic understanding of the causal forces that govern human thought, emotion, and behavior over time.