Combining thermodynamics with tensor completion techniques to enable multicomponent microstructure prediction

Yuri Amorim Coutinho, Nico Vervliet, Lieven De Lathauwer, Nele Moelans


Multicomponent alloys show intricate microstructure evolution, providing materials engineers with a nearly inexhaustible variety of solutions to enhance material properties. Multicomponent microstructure evolution simulations are indispensable to exploit these opportunities. These simulations, however, require the handling of high-dimensional and prohibitively large data sets of thermodynamic quantities, of which the size grows exponentially with the number of elements in the alloy, making it virtually impossible to handle the effects of four or more elements. In this paper, we introduce the use of tensor completion for high-dimensional data sets in materials science as a general and elegant solution to this problem. We show that we can obtain an accurate representation of the composition dependence of high-dimensional thermodynamic quantities, and that the decomposed tensor representation can be evaluated very efficiently in microstructure simulations. This realization enables true multicomponent thermodynamic and microstructure modeling for alloy design.

Code description

The goal of this demo is to show how a canonical polyadic decomposition with linearly constrained factor matrices (a TTM) can be used to model thermodynamic tensor data. In particular, the Gibbs free energy, its diffusion potentials andthe second-order derivatives are modeled for an Ag-Cu-Ni-Sn alloy in the liquid phase. Using the linear constraints, a polynomial—and therefore continuous—model is learned.


Y. Coutinho, N. Vervliet, L. De Lathauwer, N. Moelans, "Combining thermodynamics with tensor completion techniques to enable multicomponent microstructure prediction," npj Computational Materials, vol. 6, No. 2, 11 pages, Jan. 2020.

Download code

This repository can be cited as:
S. Hendrikx, M. Boussé, N. Vervliet, M. Vandecappelle, R. Kenis, and L. De Lathauwer, Tensorlab⁺, Available online, Version of Dec 2022 downloaded from