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Physics-guided Neural Networks (PGNNs) represent an emerging class of neural networks that are trained using physics-guided (PG) loss functions (capturing violations in network outputs with known physics), along with the supervision contained in data. Existing work in PGNNs has demonstrated the efficacy of adding single PG loss functions in the neural network objectives, using constant trade-off parameters, to ensure better generalizability. However, in the presence of multiple PG functions with competing gradient directions, there is a need to adaptively tune the contribution of different PG loss functions during the course of training to arrive at generalizable solutions. We demonstrate the presence of competing PG losses in the generic neural network problem of solving for the lowest (or highest) eigenvector of a physics-based eigenvalue equation, which is commonly encountered in many scientific problems. We present a novel approach to handle competing PG losses and demonstrate its efficacy in learning generalizable solutions in two motivating applications of quantum mechanics and electromagnetic propagation. All the code and data used in this work are available at https://github.com/jayroxis/Cophy-PGNN. 

Far-field analysis of small objects is severely constrained by the diffraction limit. Existing tools achieving sub-diffraction resolution often utilize point-by-point image reconstruction via scanning or labelling. Here, we present a new technique capable of fast and accurate characterization of two-dimensional structures with at least wavelength/25 theoretical resolution, based on a single far-field intensity measurement. Experimentally, we realized this technique resolving the smallest-available to us 180-nm-scale features with 845-nm laser light, reaching a resolution of wavelength/5. A comprehensive analysis of machine learning algorithms was performed to gain insight into the learning process and to understand the flow of subwavelength information through the system. Image parameterization, suitable for diffractive configurations and highly tolerant to random noise was developed. The proposed technique can be applied to new optical characterization tools with high spatial resolution, fast data acquisition and artificial intelligence, such as high-speed nanoscale metrology and quality control, and can be further developed to high-resolution spectroscopy