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Artificial Intelligence (AI) and Machine Learning (ML) has gained significant traction in the biological and biomedical research fields, in part due to a culture of open data sharing and reuse. AI/ML methodology is well-suited to recognize and predict biological patterns from high-dimensional next-generation sequencing data (e.g. whole genome sequencing, transcriptomic sequencing), as well as from biological or medical imaging data (e.g. microscopy, computed tomography, ultrasound, magnetic resonance imaging, radiography). These methodologies hold particular promise for space biosciences research and automated space health monitoring systems. However, there are key considerations for properly training, validating, and testing a machine learning model in biological research or clinical application. Inexperienced researchers can produce models that perform poorly outside of the training dataset. Open Science principles such as data sharing and open-source code must go hand-in-hand with publicly available, high-quality training curricula in best practices, with modules centered on real-life scientific use cases and data so future AI/ML practitioners gain experience on real problems. Here we present the development of open-source training materials for AI/ML and space biosciences, as part of the NASA Transform to Open Science Training (TOPST) initiative. We develop 4 independent training programs, focused on the following topics: 1) Fundamentals of Machine Learning and Space Biosciences Domain, 2) Open Science, Artificial Intelligence, and Ethical Best Practices for Data Sharing and Analysis, 3) Using AI/ML Classification to Identify Gene Networks Affected By Space Exposure in Mouse Liver, and 4) Using Neural Networks to Find DNA Damage Patterns in Immune Cells after Radiation. All programs leverage cloud-based NASA biological datasets. The curriculum we present will enable worldwide access to training in AI/ML and scientific analysis.