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Register a new userTargeted free energy estimation via learned mappings
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Free energy perturbation (FEP) was proposed by Zwanzig more than six decades ago as a method to estimate free energy differences, and has since inspired a huge body of related methods that use it as an integral building block. Being an importance sampling based estimator, however, FEP suffers from a severe limitation: the requirement of sufficient overlap between distributions. One strategy to mitigate this problem, called Targeted Free Energy Perturbation, uses a high-dimensional mapping in configuration space to increase overlap of the underlying distributions. Despite its potential, this method has attracted only limited attention due to the formidable challenge of formulating a tractable mapping. Here, we cast Targeted FEP as a machine learning problem in which the mapping is parameterized as a neural network that is optimized so as to increase overlap. We develop a new model architecture that respects permutational and periodic symmetries often encountered in atomistic simulations and test our method on a fully-periodic solvation system. We demonstrate that our method leads to a substantial variance reduction in free energy estimates when compared against baselines, without requiring any additional data.
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We present an approach that extends the theory of targeted free energy perturbation (TFEP) to calculate free energy differences and free energy surfaces at an accurate quantum mechanical level of theory from a cheaper reference potential. The convergence is accelerated by a mapping function that increases the overlap between the target and the reference distributions. Building on recent work, we show that this map can be learned with a normalizing flow neural network, without requiring simulations with the expensive target potential but only a small number of single-point calculations, and, crucially, avoiding the systematic error that was found previously. We validate the method by numerically evaluating the free energy difference in a system with a double-well potential and by describing the free energy landscape of a simple chemical reaction in the gas phase.
Finding complex reaction and transformation pathways, involving many intermediate states, is in general not possible on the DFT level with existing simulation methods due to the very large number of required energy and force evaluations. This is due to a large extent to the fact that for complex reactions, it is not possible to determine which atom in the educt is mapped onto which atom in the product. Trying out all possible atomic index mappings is not feasible because of the factorial increase in the number of possible mappings. By using a penalty function that is invariant under index permutations, we can bias the potential energy surface in such a way that it obtains the characteristics of a structure seeker whose global minimum is the product. By performing a Minima Hopping based global optimization on this biased potential energy surface we can rapidly find intermediate states that lead into the global minimum. Based on this information we can then extract the full reaction pathway. We first demonstrate for a benchmark system, namely LJ38 that our method allows to preferentially find intermediate states that are relevant for the lowest energy reaction pathway and that we, therefore, need a much smaller number of intermediate states than previous methods to find the lowest energy reaction pathway. Finally, we apply the method to two real systems, C60 and C20H20 and show that the found reaction pathway contains valuable information on how the system can be synthesized.
Machine learning methods have nowadays become easy-to-use tools for constructing high-dimensional interatomic potentials with ab initio accuracy. Although machine learned interatomic potentials are generally orders of magnitude faster than first-principles calculations, they remain much slower than classical force fields, at the price of using more complex structural descriptors. To bridge this efficiency gap, we propose an embedded atom neural network approach with simple piecewise switching function based descriptors, resulting in a favorable linear scaling with the number of neighbor atoms. Numerical examples validate that this piecewise machine learning model can be over an order of magnitude faster than various popular machine learned potentials with comparable accuracy for both metallic and covalent materials, approaching the speed of the fastest embedded atom method (i.e. several {mu}s/atom per CPU core). The extreme efficiency of this approach promises its potential in first-principles atomistic simulations of very large systems and/or in long timescale.
A popular way to accelerate the sampling of rare events in molecular dynamics simulations is to introduce a potential that increases the fluctuations of selected collective variables. For this strategy to be successful, it is critical to choose appropriate variables. Here we review some recent developments in the data-driven design of collective variables, with a focus on the combination of Fishers discriminant analysis and neural networks. This approach allows to compress the fluctuations of metastable states into a low-dimensional representation. We illustrate through several examples the effectiveness of this method in accelerating the sampling, while also identifying the physical descriptors that undergo the most significant changes in the process.
In previous works it was shown that protein 3D-conformations could be encoded into discrete sequences called dominance partition sequences (DPS), that generated a linear partition of molecular conformational space into regions of molecular conformations that have the same DPS. In this work we describe procedures for building in a cubic lattice the set of 3D-conformations that are compatible with a given DPS. Furthermore, this set can be structured as a graph upon which a combinatorial algorithm can be applied for computing the mean energy of the conformations in a cell.
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