Solving Maxwell's equations using deep learning

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Radio waves, light and micro waves are all examples of electromagnetic waves and they are essential to a myriad of technologies that we interact with on a daily basis. Much effort has been devoted to methods for simulating how electromagnetic waves interact with matter. For example, understanding how radio waves propagate through the atmosphere has been important to the development of satellite communications. Simulations have also been important to develop understanding of how the radiation emitted by mobile phones interacts with the human body, for example. There are in fact many examples of where the propagation of electromagnetic waves through heterogeneous media is important.These simulation technique have recently been employed in biomedical optical imaging to aid in the interpretation of optical coherence tomography (OCT) images. OCT is a three-dimensional imaging technique which is now routinely available at high street opticians. It is highly effective for detecting a range of retinal diseases at an early stage. Performing OCT imaging as part of a routine optician examination is excellent for improving early detection of disease, however, there are simply not enough ophthalmologists to analyse these images. One excellent approach to solving this problem uses artificial intelligence, trained using historical OCT images which have already been analysed by ophthalmologists, to analyse new images. We propose to enrich this approach by using computers to simulate OCT images of the retina to improve the capabilities of the artificial intelligence system. The advantage of this approach is that, unlike real OCT images, the underlying condition of the retina is known precisely for simulated images.There is currently a problem which prevents us from simulating realistic OCT images of the retina, which is that these simulations take far too long to compute. These simulations take so long because of the time it takes to simulate how light travels in the retina. We plan to significantly speed up this calculation using artificial intelligence, in particular, deep neural networks. Developing a deep neural network approach to simulate light propagation will enable us to calculate simulated OCT of the retina for retinal structures which are of clinical importance. This will help to improve the analysis of OCT images. This fast method of simulating light propagation will be applicable to an immense range of applications where the propagation of electromagnetic waves is important.