Solving Maxwell's equations using deep learning

Lead Research Organisation: University College London
Department Name: Medical Physics and Biomedical Eng


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.


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Macdonald CM (2023) On the inverse problem in optical coherence tomography. in Scientific reports

Description We have demonstrated that it is possible to use machine learning to calculate how light propagates through a medium. It is generally very difficult to calculate how light propagates through a medium, requiring powerful computers and a lot of computation time. We have found that we can achieve this by using machine learning, where a software tool called a neural network is trained to solve this problem.
Exploitation Route Once we publish our initial results it will be used as the starting point for a future application for funding.
Sectors Aerospace, Defence and Marine,Pharmaceuticals and Medical Biotechnology

Description Research Fellows Enhanced Research Expenses 2021
Amount £169,800 (GBP)
Funding ID RF\ERE\210307 
Organisation The Royal Society 
Sector Charity/Non Profit
Country United Kingdom
Start 12/2021 
End 11/2023
Title Time Domain Maxwell Solver (TDMS) 
Description TDMS, the Time Domain Maxwell Solver, is a hybrid C++ and MATLAB tool for solving Maxwell's equations to simulate light propagation through a medium. 
Type Of Material Computer model/algorithm 
Year Produced 2022 
Provided To Others? Yes  
Impact No results have been reported yet