ALIENs for Continuous Time Economies

Abstract

This paper builds ALIENs (Active Learning Inspired Equilibrium Nets), that extend deep-learning methods for solving continuous-time equilibrium models with high-dimensional states, aggregate shocks, and nonlinear dynamics. The approach combines time-stepping with active learning to turn nonlinear problems into sequences of contraction mappings, improving stability and convergence. By focusing computation on economically important regions of the state space, ALIENs increase accuracy and efficiency. The method is validated across applications ranging from heterogeneous-agent models with free boundaries to high-dimensional asset-pricing models. Additionally, the paper introduces Deep-Macrofin+,a numerical library that facilitates the implementation of these techniques for researchers.