The accurate prediction of phase diagrams is of central importance for both the fundamental understanding of materials as well as for technological applications in material sciences. However, the computational prediction of the relative stability between phases based on their free energy is a daunting task, as traditional free energy estimators require a large amount of simulation data to obtain uncorrelated equilibrium samples over a grid of thermodynamic states. In this work, we develop deep generative machine learning models for entire phase diagrams, employing normalizing flows conditioned on the thermodynamic states, e.g., temperature and pressure, that they map to. By training a single normalizing flow to transform the equilibrium distribution sampled at only one reference thermodynamic state to a wide range of target temperatures and pressures, we can efficiently generate equilibrium samples across the entire phase diagram. Using a permutation-equivariant architecture allows us, thereby, to treat solid and liquid phases on the same footing. We demonstrate our approach by predicting the solid-liquid coexistence line for a Lennard-Jones system in excellent agreement with state-of-the-art free energy methods while significantly reducing the number of energy evaluations needed.

While neural networks have been successfully applied to the full-spectrum k-distribution (FSCK) method at a large range of thermodynamics with k-values predicted by a trained multilayer perceptron (MLP) model, the required a-values still need to be calculated on-the-fly, which theoretically degrades the FSCK method and may lead to errors. On the other hand, too complicated structure of the current MLP model inevitably slows down the calculation efficiency. Therefore, to compensate among accuracy, efficiency and storage, the simple MLP designed based on the nature of FSCK method are developed, i.e., the simple FSCK MLP (SFM) model, from which those correlated k-values and corresponding ka-values can be efficiently obtained. Several test cases have been carried out to compare the developed SFM model and other FSCK tools including look-up tables and traditional FSCK MLP (TFM) model. Results show that the SFM model can achieve excellent accuracy that is even better than look-up tables at a tiny computational cost that is far less than that of TFM model. Considering accuracy, efficiency and portability, the SFM model is not only an excellent tool for the prediction of spectral properties, but also provides a method to reduce the errors due to nonlinear effects.

Targeted free energy perturbation uses an invertible mapping to promote configuration space overlap and the convergence of free energy estimates. However, developing suitable mappings can be challenging. Wirnsberger et al. (2020) demonstrated the use of machine learning to train deep neural networks that map between Boltzmann distributions for different thermodynamic states. Here, we adapt their approach to free energy differences of a flexible bonded molecule, deca-alanine, with harmonic biases with different spring centers. When the neural network is trained until ``early stopping'' - when the loss value of the test set increases - we calculate accurate free energy differences between thermodynamic states with spring centers separated by 1 \r{A} and sometimes 2 \r{A}. For more distant thermodynamic states, the mapping does not produce structures representative of the target state and the method does not reproduce reference calculations.

What is consciousness, and how does it emerge from inanimate matter? After all, the atoms that constitute the brain -- the birthplace of consciousness -- are the same as the atoms that make up the chair you are currently sitting on. Why are we sentient and self-aware even though a multitude of inanimate objects around us are not? At what point do physical entities -- neurons, in this case -- give rise to something as abstract as consciousness? These are the questions that have, for the better part of the last two decades, occupied some of the greatest minds in physics, cognitive science and neuroscience. A team of scientists in France and Canada has now come up with an intriguing solution to the problem of consciousness.