This paper reviews some of the challenges posed by the huge growth of experimental data generated by the new generation of large-scale experiments at UK national facilities at the Rutherford Appleton Laboratory site at Harwell near Oxford. Such 'Big Scientific Data' comes from the Diamond Light Source and Electron Microscopy Facilities, the ISIS Neutron and Muon Facility, and the UK's Central Laser Facility. Increasingly, scientists are now needing to use advanced machine learning and other AI technologies both to automate parts of the data pipeline and also to help find new scientific discoveries in the analysis of their data. For commercially important applications, such as object recognition, natural language processing and automatic translation, deep learning has made dramatic breakthroughs. Google's DeepMind has now also used deep learning technology to develop their AlphaFold tool to make predictions for protein folding. Remarkably, they have been able to achieve some spectacular results for this specific scientific problem. Can deep learning be similarly transformative for other scientific problems?After a brief review of some initial applications of machine learning at the Rutherford Appleton Laboratory, we focus on challenges and opportunities for AI in advancing materials science.Finally, we discuss the importance of developing some realistic machine learning benchmarks using Big Scientific Data coming from a number of different scientific domains. We conclude with some initial examples of our 'SciML' benchmark suite and of the research challenges these benchmarks will enable. Rosetta protein folding program at the University of Washington in Seattle [8], commented that 'DeepMind's scientists built on two algorithm strategies pioneered by others. First, by comparing vast troves of genomic data on other proteins, AlphaFold was able to better decipher which pairs of amino acids were most likely to wind up close to one another in folded proteins. Second, related comparisons also helped them gauge the most probable distance between neighboring pairs of amino acids and the angles at which they bound to their neighbors. Both approaches do better with the more data they evaluate, which makes them more apt to benefit from machine learning computer algorithms, such as AlphaFold, that solve problems by crunching large data sets' [9]. The predictions of the AlphaFold system were remarkably good and better on average than the other 97 competitors. However, there is still hope for scientists. After the competition David Baker remarked that 'Deep Mind made much better fold level predictions than everybody, including us, using DL on co-evolution data. For problems where there are not many homologous sequences, and for protein structure refinement, I would expect their approach to work less well, as it doesn't have any physical chemistry (they used Rosetta to build their final models from predicted distances)' [10].In this paper, we make some initial explorations into the application of such Deep Learning approaches ap...