Where will waves go? A scattering network can tell you

To efficiently compute where waves of light, sound, or earthquakes will go when scattered by irregular obstacles is useful in various fields but difficult and expensive to do, even using recent machine learning techniques. To improve the scalability and practicality of such computations, Laurynas Valantinas and Tom Vettenburg, researchers at the University of Dundee in the UK, mapped the wave equations onto the structure of a recurrent neural network. Its minimal memory requirements allowed them to scale up wave scattering calculations by two orders of magnitude or more. The “scattering network” design was published Aug. 5 in Intelligent Computing, a Science Partner Journal, in an article titled “Scaling Up Wave Calculations with a Scattering Network.”

The method developed by Valantinas and Vettenburg is based on the convergent Born series method for efficient numerical calculations of the wave equation, but can compute wave scattering in a volume 655 times larger than had been achieved previously. Instead of using finite differences to approximate derivatives, which demands oversampling to minimize numerical errors, a convolutional neural network layer was used to determine accurate derivates without oversampling. This allowed the researchers to compute multiple scattering throughout a volume of 175 μm-cubed, corresponding to 21 million cubic wavelengths. Moreover, the network can be used to deposit light on a target volume while minimizing the exposure of other regions. This is of particular importance to minimize sample exposure when focusing through biological tissue for deep-tissue microscopy.

The cloud-based scattering network is specifically designed to efficiently encode the reality of light scattering using relevant physics, rather than approximating it loosely. It embodies Maxwell’s equations, which describe the behavior of electric and magnetic fields such as light waves.

Earlier, a two-layer physics-encoded network was found to require intensive training, even for very small problems. Adding a preconditioning layer shortened the training time by more than 80%. The final version of the network, given the correct recurrent form and physics-defined weights, computes the equations' solutions through deterministic optimization, without relying on deep learning backpropagation at all. It is this version of the network that confers the highest efficiency benefits.

The scattering network was implemented in the machine learning library PyTorch and demonstrated on Google Colab. It was integrated with the open source wave-solver MacroMax so that it can be easily used for a variety of materials, including those with birefringent and chiral properties. This puts the ability to tackle large-scale scattering calculations in the hands of any researcher with an internet connection.