Phase behavior of continuous-space systems: A supervised machine learning approach

Importance of feature construction in machine learning for phase transitions

Machine learning is an important tool in the study of the phase behavior from molecular simulations. In this work we use un-supervised machine learning methods to study the phase behavior of two off-lattice models, a binary Lennard-Jones (LJ) mixture and the Widom-Rowlinson (WR) mixture. We find that the choice of the feature vector is crucial to the ability of the algorithm to predict a phase transition. We consider two feature vectors, one where the elements are distances of the particles of a given species from a probe (distance-based feature) and one where the elements are +1 if there is an excess of particles of the same species within a cut-off distance and -1 otherwise (affinity-based feature). We use principal component analysis (PCA) and t-distributed stochastic neighbor embedding (t-SNE) methods to investigate the phase behavior at a critical composition. We find that the choice of the feature vector is key to the success of unsupervised machine learning algorithm in predicting the phase behavior, and the sophistication of the machine learning algorithm is of secondary importance. In the case of the LJ mixture both feature vectors are adequate to accurately predict the critical point, but in the case of the WR mixture the affinity-based feature vector provides accurate estimates of the critical point, but the distance-based feature vector does not provide a clear signature of the phase transition. The study suggests that physical insight in choice of input features is an important aspect of implementing machine learning methods.

Phase Behavior of Poly(ethylene oxide) in Room Temperature Ionic Liquids: A Molecular Simulation and Deep Neural Network Study

The phase behavior of polymers in room temperature ionic liquids is a topic of considerable interest. In this work we study the phase diagram of poly(ethylene oxide) in four imidazolium ionic liquids (ILs) using molecular simulation. We develop united atom models for 1-butyl-2,3-dimethylimidazolium ([BMMIM]), 1-ethyl-2,3-dimethylimidazolium ([EMMIM]), and 1-ethyl-3-methylimidazolium ([EMIM]) in an analogous fashion to previously developed models for 1-butyl-3-methylimidazolium ([BMIM]) and tetrafluoroborate ([BF₄]) using symmetry-adapted perturbation theory. At high temperatures we obtain the coexistence concentrations using an interface method where the polymer and IL are simulated in a large elongated box, and an interface between coexisting phases is formed. At lower temperatures we use a deep neural network (DNN) method. The input descriptors for the DNN are the cohesive energy of mixing, the volume change of mixing, and the coordination numbers between cation and polymer, all of which are obtained from simulations of mixed systems at a series of temperatures. The DNN is trained by using the phase-separated systems at high temperatures and a mixed phase at low temperatures. The method predicts a lower critical solution temperature which decreases as the alkyl chain length on the cation is decreased, consistent with experiment. The simulations show that methylation of the cation has little effect on the phase diagram. This is in contrast to what is seen in experiments but could be because the polymer chains in the simulations are too short. At low temperatures the chains display two conformational motifs, namely a crown ether conformation and a ring conformation, each of which can wrap the chain around a single cation. This provides the entropic penalty for mixing and a reason for demixing as the temperature is raised. Such conformations might not be possible for longer chains. The combination of data-driven techniques and molecular simulation shows promise in the study of the phase behavior and physical properties of complex fluids.