No abstract

Knowledge of thermodynamic properties of mixtures is essential in many fields of science and engineering. However, the experimental data is usually scarce, so prediction methods are needed. Matrix completion methods have proven to be very successful in predicting thermodynamic properties of binary mixtures. In this approach, the experimental data is organized in a matrix whose rows and columns correspond to the two components, and whose entries indicate the value of the studied thermodynamic property at fixed conditions. In the present work, we extend the concept to tensor completion methods (TCMs). This allows to account for the variation of the studied property depending on the chosen conditions. The feasibility is demonstrated by applying a TCM to predict activity coefficients at infinite dilution. The third dimension of the tensor is used to describe the influence of the temperature. The TCM is shown to yield better predictions than the well‐established UNIFAC method. Furthermore, the proposed TCM is able to learn and unveil the physical law describing the temperature dependence of activity coefficients from the scarce experimental mixture data only.

We develop new method PROTES for optimization of the multidimensional arrays and discretized multivariable functions, which is based on a probabilistic sampling from a probability density function given in the low-parametric tensor train format. We tested it on complex multidimensional arrays taken, among other, from real-world applications, including unconstrained binary optimization and optimal control problems, for which the possible number of elements is up to 2 100 elements. In numerical experiments, both on analytic model functions and on complex problems, our algorithm outperform existing popular discrete optimization methods (Particle Swarm Optimization, Covariance Matrix Adaptation, Differential Evolution and others). Moreover, we take the same set of hyperparameters of our algorithm for all numerical applications.

No abstract

No abstract