Emulating phase separating mixtures

As I’ve discussed previously, phase separation, or de-mixing, has fascinated me for a long time. It is one of the most ubiquitous examples of material self-assembly, occurring frequently in complex fluids and living systems. Many technologically important metallic alloys derive their strength not from the raw components but how those components are arranged after demising has taken place. Below are three snapshot from a two dimensional model for phase separation of two polymers, with the concentration of each component colour coded in red and blue. Experimentally, we typically observe these structures with length scales ranging from many tens of nanometers to tens of micrometers.

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Polymer blends with structures similar to these have found use in  applications ranging from structural aerospace components for the latest generation of aircraft to flexible solar cells. Despite the technological relevance and the fascinating underpinning physics, the prediction of how microstructure evolves has failed to maintain pace with synthetic and formulation advances. The interplay of non-equilibrium statistical physics, diffusion, rheology and hydrodynamics, causes multiple processes with overlapping time and length scales.

My interest is in whether the data-driven approach of machine learning (ML) provides an alternative empirical paradigm to physics/hypothesis-based modelling, enabling predictions to be made using observations alone, even in the absence of physical knowledge. 

A first step in machine learning is to develop model emulators, also known as surrogate models. This is where we train a machine learning algorithm with data from a computational model, or a simulation, and then use the emulator to explore, more efficiently, what happens as we move around parameter space. 

This is something we are currently working on, and here is an output from an early attempt in one dimension. A small error in the coding can often lead to some surprisingly visually appealing images:

Screenshot 2018-12-13 at 08.24.40

In this case, it was just the graphical representation part of the code that contained the bug. The underlying data shows the match between the full computational solution to the equations I am working with in blue and the emulated data in red. The match, although not entirely obvious from this picture, is surprisingly good, especially as we have a great deal of work to do in order to optimise the hyper-parameters of the Gaussian process.

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