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Recently, we have shown that deep neural networks can be used to solve the Schrödinger Equation (https://journals.aps.org/pra/abstract/10.1103/PhysRevA.96.042113), classical spin models (https://doi.org/10.1103/PhysRevE.97.032119), and 2d-materials such as graphene and boron-nitride (https://doi.org/10.1016/j.commatsci.2018.03.005).

I will argue that these "deep models" can be used to simulate and understand matter in a way which was not previously possible. Specifically, I will show how our recently reported extensive deep neural networks (https://arxiv.org/abs/1708.06686) can be used to infer the properties of meso-scale materials based on training data generated from much smaller structural motifs (evaluated using electronic structure methods such as density functional theory). Extensive deep neural networks scale as O(N) and can be efficiently evaluated in parallel using petascale computational platforms.

Landauer's famous dictum that 'information is physical' has been enthusiastically taken on by a range of communities, with researchers in areas from quantum and unconventional computing to biology, psychology, and economics adopting the language of information processing. However, this rush to make all science about computing runs the risk of collapsing into triviality: if every physical process is computing, then to say that something performs computation gives no meaningful information about it, leaving computational language devoid of content. In this talk I will give an introduction to Abstraction/Representation Theory, a framework for representing both computing and physical science that allows us to draw a meaningful distinction between them. The use of AR theory - with its commuting-diagrammatic framework and associated algebra of representation - allows us to take significant steps towards giving a formal language and framework for the processes of science. I will show how AR theory represents this process (including the potential for automation), and the insights it gives into the usage and limits of computation as a formal process language for, and description of, physical sciences.