Physics-informed Machine Learning (ML) continues to emerge as a leading paradigm that integrates artificial intelligence with engineering dynamic systems. This approach provides new capabilities in real-time sensing, learning, decision-making, and predictions that are ethical, efficient, reliable, safe, and imbued with uncertainty quantification. The foundations of physics-informed ML are rooted in four key disciplines: (i) control theory, (ii) probability and statistics, (iii) optimization, and (iv) dynamical systems (modeling). The integration of all four disciplines is critical for the development of ML algorithms that can be leveraged by engineered systems. Establishing rigorous mathematical connections between these disciplines is a driving inspiration for our efforts in reframing the foundations of ML for the engineering sciences.
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