Improved MCMC Methods for Molecular Simulation

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We aim at answering questions such as what is the probability that a drug molecule binds a target protein? The molecule equilibrium probability is given by the well-known Boltzmann distribution. Existing methods based on molecular dynamics struggle to generate accurate and independent samples from Boltzmann distributions, especially in high dimensions. We will address these limitations by using advances in deep learning, probabilistic modelling and approximate inference. We will use an initial flexible proposal distribution given by a normalising flow. Samples from the flow will then be used to initialise a fixed-length Markov chain whose output will be improved samples with less bias. This will result in independent samples. To eliminate any bias in the sampling procedure, we will use importance sampling to weight the samples using the flow density. To reduce variance in the weights we will use 1) Hamiltonian Annealed Importance Sampling (HAIS) and 2) alpha divergence methods, which minimise weight variance when alpha = 2. We will produce new deep learning based methods for molecule simulation. Such methods will contribute to pushing the state of the outcomes art in the modelling and simulation of molecular processes, with applications to drug design.