[tutorial] Complex Valued Neural Networks for Physics Applications

An implementation in PyTorch

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Artificial neural networks are mainly used for treating data encoded in real values, such as digitized images or sounds. In such systems, using complex-valued tensors would be quite useless. This is however different for physic related topics. When dealing with wave propagation in particular, using complex values is interesting since the physics typically has linear, hence more simple, behavior when considering complex fields. This is sometimes true even when the inputs and the outputs of the system are real values. For instance, consider a complex media that you excite using an amplitude modulator, such as a DMD (Digital Micromirror Device) and you measure the output intensity. You manipulate only real values, but if you want to characterize the system, you have to keep in mind that the phase is a hidden variable as the effect of propagation is represented by the multiplication by a complex matrix on the optical field.

I wrote complexPyTorch a simple implementation of complex-valued functions and modules using the high-level API of PyTorch, allowing to build complex valued artificial neural networks using the guidelines proposed in [C. Trabelsi et al., International Conference on Learning Representations, (2018)].

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