Training Deep Neural Networks for the Inverse Design of Nanophotonic Structures
TL;DR: A tandem neural network architecture is demonstrated that tolerates inconsistent training instances in inverse design of nanophotonic devices and provides a way to train large neural networks for the inverseDesign of complex photonic structures.
Abstract: Data inconsistency leads to a slow training process when deep neural networks are used for the inverse design of photonic devices, an issue that arises from the fundamental property of nonuniqueness in all inverse scattering problems. Here we show that by combining forward modeling and inverse design in a tandem architecture, one can overcome this fundamental issue, allowing deep neural networks to be effectively trained by data sets that contain nonunique electromagnetic scattering instances. This paves the way for using deep neural networks to design complex photonic structures that require large training data sets.
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TL;DR: A deep-learning-based model is reported, comprising two bidirectional neural networks assembled by a partial stacking strategy, to automatically design and optimize three-dimensional chiral metamaterials with strong chiroptical responses at predesignated wavelengths.
Abstract: Deep-learning framework has significantly impelled the development of modern machine learning technology by continuously pushing the limit of traditional recognition and processing of images, speech, and videos. In the meantime, it starts to penetrate other disciplines, such as biology, genetics, materials science, and physics. Here, we report a deep-learning-based model, comprising two bidirectional neural networks assembled by a partial stacking strategy, to automatically design and optimize three-dimensional chiral metamaterials with strong chiroptical responses at predesignated wavelengths. The model can help to discover the intricate, nonintuitive relationship between a metamaterial structure and its optical responses from a number of training examples, which circumvents the time-consuming, case-by-case numerical simulations in conventional metamaterial designs. This approach not only realizes the forward prediction of optical performance much more accurately and efficiently but also enables one to i...
619 citations
TL;DR: In this paper, artificial neural networks are used to approximate light scattering by multilayer nanoparticles. But the network needs to be trained on only a small sampling of the data to approximate the simulation to high precision.
Abstract: We propose a method to use artificial neural networks to approximate light scattering by multilayer nanoparticles. We find that the network needs to be trained on only a small sampling of the data to approximate the simulation to high precision. Once the neural network is trained, it can simulate such optical processes orders of magnitude faster than conventional simulations. Furthermore, the trained neural network can be used to solve nanophotonic inverse design problems by using back propagation, where the gradient is analytical, not numerical.
576 citations
TL;DR: This work identifies a solution to circumvent this conventional design procedure by means of a deep learning architecture to expedite the discovery and design of metasurfaces for tailored optical responses in a systematic, inverse-design manner.
Abstract: The advent of metasurfaces in recent years has ushered in a revolutionary means to manipulate the behavior of light on the nanoscale. The design of such structures, to date, has relied on the expertise of an optical scientist to guide a progression of electromagnetic simulations that iteratively solve Maxwell's equations until a locally optimized solution can be attained. In this work, we identify a solution to circumvent this conventional design procedure by means of a deep learning architecture. When fed an input set of customer-defined optical spectra, the constructed generative network generates candidate patterns that match the on-demand spectra with high fidelity. This approach reveals an opportunity to expedite the discovery and design of metasurfaces for tailored optical responses in a systematic, inverse-design manner.
536 citations
TL;DR: Recent progress in deep-learning-based photonic design is reviewed by providing the historical background, algorithm fundamentals and key applications, with the emphasis on various model architectures for specific photonic tasks.
Abstract: Innovative approaches and tools play an important role in shaping design, characterization and optimization for the field of photonics. As a subset of machine learning that learns multilevel abstraction of data using hierarchically structured layers, deep learning offers an efficient means to design photonic structures, spawning data-driven approaches complementary to conventional physics- and rule-based methods. Here, we review recent progress in deep-learning-based photonic design by providing the historical background, algorithm fundamentals and key applications, with the emphasis on various model architectures for specific photonic tasks. We also comment on the challenges and perspectives of this emerging research direction. The application of deep learning to the design of photonic structures and devices is reviewed, including algorithm fundamentals.
446 citations
TL;DR: This work proposes to represent metamaterials and model the inverse design problem in a probabilistically generative manner, enabling to elegantly investigate the complex structure–performance relationship in an interpretable way, and solve the one‐to‐many mapping issue that is intractable in a deterministic model.
Abstract: The research of metamaterials has achieved enormous success in the manipulation of light in a prescribed manner using delicately designed subwavelength structures, so-called meta-atoms. Even though modern numerical methods allow for the accurate calculation of the optical response of complex structures, the inverse design of metamaterials, which aims to retrieve the optimal structure according to given requirements, is still a challenging task owing to the nonintuitive and nonunique relationship between physical structures and optical responses. To better unveil this implicit relationship and thus facilitate metamaterial designs, it is proposed to represent metamaterials and model the inverse design problem in a probabilistically generative manner, enabling to elegantly investigate the complex structure-performance relationship in an interpretable way, and solve the one-to-many mapping issue that is intractable in a deterministic model. Moreover, to alleviate the burden of numerical calculations when collecting data, a semisupervised learning strategy is developed that allows the model to utilize unlabeled data in addition to labeled data in an end-to-end training. On a data-driven basis, the proposed deep generative model can serve as a comprehensive and efficient tool that accelerates the design, characterization, and even new discovery in the research domain of metamaterials, and photonics in general.
333 citations
Cites methods from "Training Deep Neural Networks for t..."
...To remedy this issue, tandem training strategy has been used to avoid instable training loss and force the inverse network to converge to one possible solution [53], but this operation sacrifices the design varieties and leads to limited generalization ability....
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References
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TL;DR: Back-propagation repeatedly adjusts the weights of the connections in the network so as to minimize a measure of the difference between the actual output vector of the net and the desired output vector, which helps to represent important features of the task domain.
Abstract: We describe a new learning procedure, back-propagation, for networks of neurone-like units. The procedure repeatedly adjusts the weights of the connections in the network so as to minimize a measure of the difference between the actual output vector of the net and the desired output vector. As a result of the weight adjustments, internal ‘hidden’ units which are not part of the input or output come to represent important features of the task domain, and the regularities in the task are captured by the interactions of these units. The ability to create useful new features distinguishes back-propagation from earlier, simpler methods such as the perceptron-convergence procedure1.
23,814 citations
TL;DR: It is rigorously established that standard multilayer feedforward networks with as few as one hidden layer using arbitrary squashing functions are capable of approximating any Borel measurable function from one finite dimensional space to another to any desired degree of accuracy, provided sufficiently many hidden units are available.
18,794 citations
TL;DR: A model of a system having a large number of simple equivalent components, based on aspects of neurobiology but readily adapted to integrated circuits, produces a content-addressable memory which correctly yields an entire memory from any subpart of sufficient size.
Abstract: Computational properties of use of biological organisms or to the construction of computers can emerge as collective properties of systems having a large number of simple equivalent components (or neurons). The physical meaning of content-addressable memory is described by an appropriate phase space flow of the state of a system. A model of such a system is given, based on aspects of neurobiology but readily adapted to integrated circuits. The collective properties of this model produce a content-addressable memory which correctly yields an entire memory from any subpart of sufficient size. The algorithm for the time evolution of the state of the system is based on asynchronous parallel processing. Additional emergent collective properties include some capacity for generalization, familiarity recognition, categorization, error correction, and time sequence retention. The collective properties are only weakly sensitive to details of the modeling or the failure of individual devices.
16,652 citations
TL;DR: This Review focuses on recent developments on flat, ultrathin optical components dubbed 'metasurfaces' that produce abrupt changes over the scale of the free-space wavelength in the phase, amplitude and/or polarization of a light beam.
Abstract: Metamaterials are artificially fabricated materials that allow for the control of light and acoustic waves in a manner that is not possible in nature. This Review covers the recent developments in the study of so-called metasurfaces, which offer the possibility of controlling light with ultrathin, planar optical components. Conventional optical components such as lenses, waveplates and holograms rely on light propagation over distances much larger than the wavelength to shape wavefronts. In this way substantial changes of the amplitude, phase or polarization of light waves are gradually accumulated along the optical path. This Review focuses on recent developments on flat, ultrathin optical components dubbed 'metasurfaces' that produce abrupt changes over the scale of the free-space wavelength in the phase, amplitude and/or polarization of a light beam. Metasurfaces are generally created by assembling arrays of miniature, anisotropic light scatterers (that is, resonators such as optical antennas). The spacing between antennas and their dimensions are much smaller than the wavelength. As a result the metasurfaces, on account of Huygens principle, are able to mould optical wavefronts into arbitrary shapes with subwavelength resolution by introducing spatial variations in the optical response of the light scatterers. Such gradient metasurfaces go beyond the well-established technology of frequency selective surfaces made of periodic structures and are extending to new spectral regions the functionalities of conventional microwave and millimetre-wave transmit-arrays and reflect-arrays. Metasurfaces can also be created by using ultrathin films of materials with large optical losses. By using the controllable abrupt phase shifts associated with reflection or transmission of light waves at the interface between lossy materials, such metasurfaces operate like optically thin cavities that strongly modify the light spectrum. Technology opportunities in various spectral regions and their potential advantages in replacing existing optical components are discussed.
4,613 citations
01 May 1999
TL;DR: A model of a system having a large number of simple equivalent components, based on aspects of neurobiology but readily adapted to integrated circuits, produces a content-addressable memory which correctly yields an entire memory from any subpart of sufficient size.
Abstract: Computational properties of use to biological organisms or to the construction of computers can emerge as collective properties of systems having a large number of simple equivalent components (or neurons). The physical meaning of content-addressable memory is described by an appropriate phase space flow of the state of a system. A model of such a system is given, based on aspects of neurobiology but readily adapted to integrated circuits. The collective properties of this model produce a content-addressable memory which correctly yields an entire memory from any subpart of sufficient size. The algorithm for the time evolution of the state of the system is based on asynchronous parallel processing. Additional emergent collective properties include some capacity for generalization, familiarity recognition, categorization, error correction, and time sequence retention. The collective properties are only weakly sensitive to details of the modeling or the failure of individual devices.
2,865 citations