Lattice Protein Folding with Variational Annealing

Understanding the principles of protein folding is a cornerstone of computational biology, with implications for drug design, bioengineering, and the understanding of fundamental biological processes. Lattice protein folding models offer a simplified yet powerful framework for studying the complexities of protein folding, enabling the exploration of energetically optimal folds under constrained conditions. However, finding these optimal folds is a computationally challenging combinatorial optimization problem. In this work, we introduce a novel upper-bound training scheme that employs masking to identify the lowest-energy folds in two-dimensional Hydrophobic-Polar (HP) lattice protein folding. By leveraging Dilated Recurrent Neural Networks (RNNs) integrated with an annealing process driven by temperature-like fluctuations, our method accurately predicts optimal folds for benchmark systems of up to 60 beads. Our approach also effectively masks invalid folds from being sampled without compromising the autoregressive sampling properties of RNNs. This scheme is generalizable to three spatial dimensions and can be extended to lattice protein models with larger alphabets. Our findings emphasize the potential of advanced machine learning techniques in tackling complex protein folding problems and a broader class of constrained combinatorial optimization challenges.

Supplementing Recurrent Neural Networks with Annealing to Solve Optimization Problems

Combinatorial optimization problems can be solved by heuristic algorithms such as simulated annealing (SA) which aims to find the global minima solution within a large search space through thermal fluctuations. The algorithm generates new solutions through Markov-chain Monte Carlo techniques. The latter can result in severe limitations, such as slow convergence and a tendency to stay within the same local search space at small temperatures. To overcome these shortcomings, we use the variational classical annealing (VCA) framework that combines autoregressive recurrent neural networks (RNNs) with traditional annealing to sample solutions independent of each other. In this paper, we demonstrate the potential of using VCA as an approach to solving real-world optimization problems. We explore VCA's performance in comparison with SA at solving three popular optimization problems: the maximum cut problem (Max-Cut), the nurse scheduling problem (NSP), and the traveling salesman problem (TSP). For all three problems, we find that VCA outperforms SA on average in the asymptotic limit. Interestingly, we reach large system sizes up to $256$ cities for the TSP. We conclude that in the best-case scenario, VCA can serve as a great alternative when SA fails to find the optimal solution.