Chong Wang

Chong Wang, Xiaofeng Ren, Yanxiang Zhao

A nonlocal diffuse interface model is used to study bubble assemblies in ternary systems. As model parameters vary, a large number of morphological phases appear as stable stationary states. One open question related to the polarity direction of double bubble assemblies is answered numerically. Moreover, the average size of bubbles in a single bubble assembly depends on the sum of the minority constituent areas and the long range interaction coefficients. One identifies the ranges for area fractions and the long range interaction coefficients for double bubble assemblies.

Xiang Gao, Weihao Gao, Wenzhi Xiao et al.

Machine learning has become a promising approach for molecular modeling. Positional quantities, such as interatomic distances and bond angles, play a crucial role in molecule physics. The existing works rely on careful manual design of their representation. To model the complex nonlinearity in predicting molecular properties in an more end-to-end approach, we propose to encode the positional quantities with a learnable embedding that is continuous and differentiable. A regularization technique is employed to encourage embedding smoothness along the physical dimension. We experiment with a variety of molecular property and force field prediction tasks. Improved performance is observed for three different model architectures after plugging in the proposed positional encoding method. In addition, the learned positional encoding allows easier physics-based interpretation. We observe that tasks of similar physics have the similar learned positional encoding.

Willie Neiswanger, Chong Wang, Eric Xing

Communication costs, resulting from synchronization requirements during learning, can greatly slow down many parallel machine learning algorithms. In this paper, we present a parallel Markov chain Monte Carlo (MCMC) algorithm in which subsets of data are processed independently, with very little communication. First, we arbitrarily partition data onto multiple machines. Then, on each machine, any classical MCMC method (e.g., Gibbs sampling) may be used to draw samples from a posterior distribution given the data subset. Finally, the samples from each machine are combined to form samples from the full posterior. This embarrassingly parallel algorithm allows each machine to act independently on a subset of the data (without communication) until the final combination stage. We prove that our algorithm generates asymptotically exact samples and empirically demonstrate its ability to parallelize burn-in and sampling in several models.