ABSTRACT
This chapter introduces the fundamentals of artificial intelligence (AI) and delineates its possibilities for model discovery, focusing primarily on dynamical systems. The presentation deals mostly with deep learning and autoencoders and other related more specialized architectures. The narrative is tailored to researchers seeking to unravel physical models distilled from big data in very diverse material scales, from subatomic to molecular to cosmological. With the leveraging of AI, dynamical systems have found fertile ground for development, as argued in this chapter. Machine learning identifies parsimonious models providing physical underpinnings of time series data. However, such heavily parametrized models hardly yield physical laws, especially as we turn to multi-scale biological or cosmological complexities. This chapter addresses these imperatives as it takes the problem of AI-based model discovery to the next level, introducing topological methods that enable metamodel discovery and suitable computational tools to decode the metamodel as a dynamical system. The methods advance model discovery, enabling reverse engineering of dynamical systems arising in a range of cosmological and astrophysical contexts. The topological methods for AI-based metamodel discovery are introduced at a fairly elementary level. The approach is mainly directed at building metamodels of complex hierarchical dynamics and can be decoded to full detail after learning to propagate the coarse-grained dynamics.
As an illustration of a cosmological application, this chapter deals with the problem of quantum gravity as an emergent property in the physics of machine learning. To that effect, the chapter explores the possibility of constructing a quantum holographic autoencoder as a physical system consisting of a neural network with emergent quantum behavior arising from nonlocal equilibrated hidden variables. This system leads to the development of a relativistic gravitational scheme involving hidden variables. Thus, the network with equilibrated nontrainable variables becomes in effect a quantum gravity autoencoder for the network exhibiting emergent gravity in the non-equilibrium regime prior to the equilibration of the nontrainable variables. In this way, a quantum metamodel for gravity is built that fulfills at least in part a major imperative for physicists seeking a unified field theory.
