This project aims to revolutionize how scientists discover new materials, which are essential for advancing technologies like solar cells, batteries, medicine, and catalysts. Materials discovery is often driven by complex and expensive simulation methods, typically accurate but time-intensive. The emerging machine and deep learning (MDL) models, trained on the massive simulated data collected over the past decades, offer a faster alternative. Unfortunately, these mdoels often fail to predict critical material properties, such as material stability, that the current project shall focus on. This project addresses these shortcomings of MDL models by integrating fundamental physical principles into the training of MDL models. By doing so, the models will better capture the intricate relationships between materials, leading to more reliable predictions. The project will benefit science and our society in a multitude of ways. Faster and more accurate materials discovery will accelerate innovation in clean energy, electronics, healthcare, national security, and more. The project also contributes to the advancement of artificial intelligence by introducing new techniques for constrained learning, which will impact fields beyond materials science. Additionally, the project emphasizes education and engagement by providing interdisciplinary training for graduate students, equipping them with skills at the intersection of computer science, materials science, and engineering. The goal