Phase change materials (PCMs) have been widely investigated to function as a thermal buffer, particularly for components experiencing transient power loads. PCMs absorb some of the heat generated during periods of high-power dissipation and can enable longer periods of use before throttling of the processor or shut-off is required to prevent damage. Many studies with PCMs have focused on the functionality of PCM-laden heat sinks and, although these studies demonstrated extensions in high power operating times before the system overheated, the thermal pathway between the PCM-laden heat sink and heat source prevents their effective use as the heat generation rates increase. This study explores the concept of integrating PCMs at or near the silicon chip level near the heat source. Machine learning algorithms generate optimized patterns for balancing high heat storage zones and high thermal conductivity pathways within the embedded cooling layer on the backside of the silicon die. Reductions in both the hotspot temperatures and fluctuations in the transient temperature response highlights the effectiveness of embedded cooling and the machine learning algorithms provide a robust, efficient method for optimizing performance.