How can we reconstruct the past from the present when evolution obscures the information we need? Machine Learning Evolution Equations connects the analysis of partial differential equations with numerical simulation and machine learning to investigate this question. Through models of diffusion, phase separation, fluid flow, and wave propagation, the book develops methods for learning inverse reconstructions from simulated data. Reconstruction accuracy, physical consistency, and statistical validation provide a framework for assessing what these models can recover. Written for graduate students and researchers, it links rigorous mathematics with reproducible computational experiments.