The high performance computing (HPC) and big data (BD) communities traditionally have pursued independent trajectories in the world of computational science. HPC has been synonymous with modeling and simulation, and BD with ingesting and analyzing data from diverse sources, including from simulations. However, both communities are evolving in response to changing user needs and technological landscapes. Researchers are increasingly using machine learning (ML) not only for data analytics but also for modeling and simulation; science-based simulations are increasingly relying on embedded ML models not only to interpret results from massive data outputs but also to steer computations. Science-based models are being combined with data-driven models to represent complex systems and phenomena. There also is an increasing need for real-time data analytics, which requires large-scale computations to be performed closer to the data and data infrastructures, to adapt to HPC-like modes of operation. These new use cases create a vital need for HPC and BD systems to deal with simulations and data analytics in a more unified fashion. To explore this need, the NITRD Big Data and High-End Computing R&D Interagency Working Groups held a workshop, The Convergence of High-Performance Computing, Big Data, and Machine Learning, on October 29-30, 2018, in Bethesda, Maryland. The purposes of the workshop were to bring together representatives from the public, private, and academic sectors to share their knowledge and insights on integrating HPC, BD, and ML systems and approaches and to identify key research challenges and opportunities. The 58 workshop participants represented a balanced cross-section of stakeholders involved in or impacted by this area of research. Additional workshop information, including a webcast, is available at https://www.nitrd.gov/nitrdgroups/index.php?title=HPC-BD-Convergence.