CoordGate: Efficiently Computing Spatially-Varying Convolutions in Convolutional Neural Networks

Optical imaging systems are inherently limited in their resolution due to the point spread function (PSF), which applies a static, yet spatially-varying, convolution to the image. This degradation can be addressed via Convolutional Neural Networks (CNNs), particularly through deblurring techniques. However, current solutions face certain limitations in efficiently computing spatially-varying convolutions. In this paper we propose CoordGate, a novel lightweight module that uses a multiplicative gate and a coordinate encoding network to enable efficient computation of spatially-varying convolutions in CNNs. CoordGate allows for selective amplification or attenuation of filters based on their spatial position, effectively acting like a locally connected neural network. The effectiveness of the CoordGate solution is demonstrated within the context of U-Nets and applied to the challenging problem of image deblurring. The experimental results show that CoordGate outperforms conventional approaches, offering a more robust and spatially aware solution for CNNs in various computer vision applications.

A Tensor Network Implementation of Multi Agent Reinforcement Learning

Recently it has been shown that tensor networks (TNs) have the ability to represent the expected return of a single-agent finite Markov decision process (FMDP). The TN represents a distribution model, where all possible trajectories are considered. When extending these ideas to a multi-agent setting, distribution models suffer from the curse of dimensionality: the exponential relation between the number of possible trajectories and the number of agents. The key advantage of using TNs in this setting is that there exists a large number of established optimisation and decomposition techniques that are specific to TNs, that one can apply to ensure the most efficient representation is found. In this report, these methods are used to form a TN that represents the expected return of a multi-agent reinforcement learning (MARL) task. This model is then applied to a 2 agent random walker example, where it was shown that the policy is correctly optimised using a DMRG technique. Finally, I demonstrate the use of an exact decomposition technique, reducing the number of elements in the tensors by 97.5%, without experiencing any loss of information.

Hyperspectral Compressive Wavefront Sensing

Presented is a novel way to combine snapshot compressive imaging and lateral shearing interferometry in order to capture the spatio-spectral phase of an ultrashort laser pulse in a single shot. A deep unrolling algorithm is utilised for the snapshot compressive imaging reconstruction due to its parameter efficiency and superior speed relative to other methods, potentially allowing for online reconstruction. The algorithm's regularisation term is represented using neural network with 3D convolutional layers, to exploit the spatio-spectral correlations that exist in laser wavefronts. Compressed sensing is not typically applied to modulated signals, but we demonstrate its success here. Furthermore, we train a neural network to predict the wavefronts from a lateral shearing interferogram in terms of Zernike polynomials, which again increases the speed of our technique without sacrificing fidelity. This method is supported with simulation-based results. While applied to the example of lateral shearing interferometry, the methods presented here are generally applicable to a wide range of signals, including Shack-Hartmann-type sensors. The results may be of interest beyond the context of laser wavefront characterization, including within quantitative phase imaging.

Data-driven Science and Machine Learning Methods in Laser-Plasma Physics

Laser-plasma physics has developed rapidly over the past few decades as lasers have become both more powerful and more widely available. Early experimental and numerical research in this field was dominated by single-shot experiments with limited parameter exploration. However, recent technological improvements make it possible to gather data for hundreds or thousands of different settings in both experiments and simulations. This has sparked interest in using advanced techniques from mathematics, statistics and computer science to deal with, and benefit from, big data. At the same time, sophisticated modeling techniques also provide new ways for researchers to deal effectively with situation where still only sparse data are available. This paper aims to present an overview of relevant machine learning methods with focus on applicability to laser-plasma physics and its important sub-fields of laser-plasma acceleration and inertial confinement fusion.