Solving Maxwell's equations using deep learning

无线电波、光波和微波都是电磁波的例子，它们对我们每天与之互动的无数技术至关重要。人们一直致力于研究模拟电磁波与物质相互作用的方法。例如，了解无线电波如何在大气层中传播对卫星通信的发展至关重要。例如，模拟对于理解移动的电话发出的辐射如何与人体相互作用也很重要。事实上，电磁波在非均匀介质中的传播有很多重要的例子，这些模拟技术最近已被用于生物医学光学成像，以帮助解释光学相干层析成像（OCT）图像。OCT是一种三维成像技术，现在在商业街的眼镜商处常规可用。它对于在早期阶段检测一系列视网膜疾病非常有效。作为常规配镜检查的一部分，进行OCT成像对于改善疾病的早期检测是非常好的，然而，根本没有足够的眼科医生来分析这些图像。解决这个问题的一个很好的方法是使用人工智能，使用已经由眼科医生分析过的历史OCT图像进行训练，以分析新图像。我们建议通过使用计算机来模拟视网膜的OCT图像来丰富这种方法，以提高人工智能系统的能力。这种方法的优点在于，与真实的OCT图像不同，对于模拟图像而言，视网膜的基本状况是精确已知的。这些模拟需要这么长的时间，因为它需要时间来模拟光如何在视网膜中传播。我们计划使用人工智能，特别是深度神经网络来显著加快计算速度。开发一种模拟光传播的深度神经网络方法将使我们能够计算具有临床重要性的视网膜结构的视网膜模拟OCT。这将有助于改善OCT图像的分析。这种模拟光传播的快速方法将适用于电磁波传播很重要的广泛应用。

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.