In a nematic liquid crystal, three elastic constants related to three deformation modes of the orientational order (splay, twist and bend) govern the orientational configuration in the equilibrium, as well as the leading relaxational dynamics. In this MSc thesis, a new method for determining elastic constants of nematic liquid crystals is developed based on the combination of mesoscopic continuum modelling and neural networks. First, the relaxation from a random initial state of the nematic liquid crystal to the minimum free energy state is numerically simulated 10⁵ times, using Frank-Oseen free energy minimisation for random values of elastic constants. Simultaneously, the transmittance of the nematic sample for monochromatic polarized light is calculated using the Jones matrix formalism. The obtained time-dependent light transmittances and the corresponding elastic constants form a training data set, based on which a neural network is trained, aiming to approximate a nontrivial function that predicts the unknown elastic constants from the time dependence of the intensity of the transmitted light. This allows us to show which elastic constants can be determined in different types of liquid crystal cells and nematic geometries. In addition, we demonstrate that the neural network, which is originally trained on numerically obtained data, can also be used to determine elastic constants from experimentally measured data. Overall, this work contributes towards the development of machine learning methods in the field of general soft matter, as the new strong methodological tools, allowing us to combine theoretical modelling and experimental approaches.
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