Analyzing Multimodal Probability Measures with Autoencoders.

Finding collective variables to describe some important coarse-grained information on physical systems, in particular metastable states, remains a key issue in molecular dynamics. Recently, machine learning techniques have been intensively used to complement and possibly bypass expert knowledge in order to construct collective variables. Our focus here is on neural network approaches based on autoencoders. We study some relevant mathematical properties of the loss function considered for training autoencoders and provide physical interpretations based on conditional variances and minimum energy paths. We also consider various extensions in order to better describe physical systems, by incorporating more information on transition states at saddle points, and/or allowing for multiple decoders in order to describe several transition paths. Our results are illustrated on toy two-dimensional systems and on alanine dipeptide.

Computing Surface Reaction Rates by Adaptive Multilevel Splitting Combined with Machine Learning and Ab Initio Molecular Dynamics.

Computing accurate rate constants for catalytic events occurring at the surface of a given material represents a challenging task with multiple potential applications in chemistry. To address this question, we propose an approach based on a combination of the rare event sampling method called adaptive multilevel splitting (AMS) and ab initio molecular dynamics. The AMS method requires a one-dimensional reaction coordinate to index the progress of the transition. Identifying a good reaction coordinate is difficult, especially for high dimensional problems such as those encountered in catalysis. We probe various approaches to build reaction coordinates such as support vector machine and path collective variables. The AMS is implemented so as to communicate with a density functional theory-plane wave code. A relevant case study in catalysis, the change of conformation and the dissociation of a water molecule chemisorbed on the (100) γ-alumina surface, is used to evaluate our approach. The calculated rate constants and transition mechanisms are discussed and compared to those obtained by a conventional static approach based on the Eyring-Polanyi equation with harmonic approximation. It is revealed that the AMS method may provide rate constants that are smaller than those provided by the static approach by up to 2 orders of magnitude due to entropic effects involved in the chemisorbed water molecule.