Learning the structure of a 2D colloidal suspension through deep learning from bright-field images

Abstract Colloidal suspensions may be stable or unstable due to aggregation, which would alter the properties of the suspension and is related to many-body interactions and the delicate balance between repulsive and attractive forces, which also defines the internal structure and its macroscopic properties. Experimental studies about many-body interactions demand a lot of resources and time due to the accumulation of statistics necessary to obtain reliable results. A way to study the colloidal suspension structure is to process a great amount of bright-field images. Taking advantage of the emerging deep generative networks, we propose a method to complement this study to reduce both experimental and computational costs. The method consists of designing and tuning an architecture based on Generative Adversarial Networks (GANs) that learns the static structure of a colloidal suspension from experimental images depending on concentration and generates images to concentrations outside of the experimental data. This allows the exploration of the fully accessible phase space and carry out a visual recognition of regions of interest. The best-performed network was Wasserstein Generative Adversarial Network with Gradient Penalty (WCGAN-GP), trained from bright-field images of a confined colloidal suspension formed by spherical polystyrene particles in water at different area fractions. Experimental results showed that the algorithm generates new images with a high accuracy rate (85%–98%) on the expected particle number at different concentrations; also, it was able to reproduce the static structure of the colloidal suspension, i.e., the pair correlation function ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>g</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>r</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:math> ) lies within the experimental variation, not only for the trained data set but also for any other intermediate concentration. The correlation coefficient between experimental and generated ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>g</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>r</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:math> ) was very strong (0.86–0.99) for concentrations of 0.1 and higher. The proposed GAN could be used to construct phase diagrams, identifying stable and unstable zones of colloidal systems with different interaction potentials.