This workshop aims to bring together a diverse, multi-disciplinary cross-section of pioneering researchers to foster a community, share ideas, and work together to build a lasting mathematical and social foundation. The key themes of this workshop include i) neural network design and approximability; ii) modeling, inference, prediction, and data assimilation; and iii) high-performance algorithms and scalability. The participants of this workshop possess complementary expertise in numerical analysis, approximation theory, functional analysis, probability theory, nonlinear programming, high-performance computing, computer science, statistics, engineering, and industrial applications. Putting all this knowledge together will create a synergy of effects that will profoundly impact the rigorous development of new and lasting machine learning methods for scientific computing applications.