This report provides an overview of recent work that harnesses the Big Data Revolution and Large Scale Computing to address grand computational challenges in Multi-Messenger Astrophysics, with a particular emphasis on real-time discovery campaigns. Acknowledging the transdisciplinary nature of Multi-Messenger Astrophysics, this document has been prepared by members of the physics, astronomy, computer science, data science, software and cyberinfrastructure communities who attended the NSF-, DOE- and NVIDIA-funded "Deep Learning for Multi-Messenger Astrophysics: Real-time Discovery at Scale" workshop, hosted at the National Center for Supercomputing Applications, October 17-19, 2018. Highlights of this report include unanimous agreement that it is critical to accelerate the development and deployment of novel, signal-processing algorithms that use the synergy between artificial intelligence (AI) and high performance computing to maximize the potential for scientific discovery with Multi-Messenger Astrophysics. We discuss key aspects to realize this endeavor, namely (i) the design and exploitation of scalable and computationally efficient AI algorithms for Multi-Messenger Astrophysics; (ii) cyberinfrastructure requirements to numerically simulate astrophysical sources, and to process and interpret Multi-Messenger Astrophysics data; (iii) management of gravitational wave detections and triggers to enable electromagnetic and astro-particle follow-ups; (iv) a vision to harness future developments of machine and deep learning and cyberinfrastructure resources to cope with the scale of discovery in the Big Data Era; (v) and the need to build a community that brings domain experts together with data scientists on equal footing to maximize and accelerate discovery in the nascent field of Multi-Messenger Astrophysics.

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