We demonstrate that incorporating physics-based intuition and Maxwell-equation-based constraints into machine learning process reduces the required amount of the training data and improves prediction accuracy and physics consistency. In addition, physics-based provides an avenue to extend the range of the model applicability outside the space of the original labeled dataset. The proposed approaches are illustrated on examples of photonic composites, from photonic crystals to hyperbolic metamaterials.
Machine learning is widely used for optimization or classification tasks. Unfortunately, extensive labeled datasets are often required for training machine learning models. In this work we demonstrate that incorporating physics-driven constraints into machine learning algorithms can dramatically improve both accuracy and extendibility of resulting models, simultaneously reducing the size of the required training set and enabling training on unlabeled data. Physics-informed machine learning is illustrated on example of predicting optical modes supported by periodic layered composites. The approach can be readily utilized for analysis of electromagnetic modes in composites with 2D periodic geometry or in complex waveguiding structures.
Optical microscopy provides unparalleled tools for understanding and characterization of small-scale objects. We have recently developed an approach that combines diffractive imaging and machine learning to characterize wavelength-scale objects with subwavelength resolution based on few (or, often, single) measurement. The technique relies on the diffraction interaction between finite-sized diffraction grating and an object to outcouple information about both sub-wavelength and wavelength-scale features of the object into the far field and on machine learning to characterize the object based on its diffractive signature. In this work we aim to understand the flow of information through the image recognition process. We parameterize the diffractive signatures in Bessel and Fourier representations and analyze the performance of the recovery routines dependent on the choice of the harmonics in these expansions. Separately, we analyze the subset of the harmonics that are used by the machine learning algorithms in identifying the objects. Performance of the recovery routines as a function of noise is also analyzed. Our study provides an insight into the dynamics of machine learning and it helps identify the information channels that are crucial for optimal recovery of complex objects with high resolution, fidelity, and speed.
We develop an approach that enables characterization of wavelength-scale objects with deep subwavelength resolution. The technique combines diffractive imaging that out-couples the information about the subwavelength features of the object into the far-field zone with machine learning that analyzes the resulting patterns. Recovery of complex objects with 120-nm resolution with ~530-nm light is demonstrated experimentally. Our theoretical analysis suggests that the same objects can be recovered with up to 2-micron-wavelength light. Our work opens the door for new characterization tools that combine high spatial resolution, fast data acquisition, and artificial intelligence
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