Astronomy has always been driven by data. Yet only in recent years has it truly become a big data field. With automatic surveys recording the sky at unprecedented speed, the sheer volume of astronomical data introduces new challenges and opportunities. Modern Astronomy pushes the boundaries of data analysis and artificial intelligence, providing a great domain for machine learning (ML) research. The discipline is entering a phase of maturation, progressing beyond the simplistic utilization of pre-packaged, opaque ML models and evolving towards methodologies where ML plays an essential role within a broader, principled analysis framework. Our current research is focused on three evolving domains where the intersection of ML and astronomy forms symbiosis: (1) Physics-informed learning, (2) Statistical learning with probabilistic frameworks, offering capabilities such as uncertainty quantification and generative models, and (3) Transparent and interpretable ML models for scientific analyses, emphasizing robustness, accuracy, and comprehensibility.