Source-linked AI summary
Training deep neural networks for the inverse design of nanophotonic structures
Dianjing Liu, Yixuan Tan, Erfan Khoram, Zongfu Yu
TL;DR
Inverse-design neural networks can fail to train accurately when datasets are inconsistent, even when output instances are unique. The paper analyzes this issue through forward and inverse modeling, showing that data consistency matters for effective training.
Problem
Inverse-design neural networks face data inconsistency that prevents accurate training, beyond the presence of non-unique instances.
Method
The paper analyzes inverse design by contrasting well-defined forward modeling with inverse mappings represented by alternative operators.
Results
Inconsistent dataset D3 cannot train an accurate inverse neural network even though all its Y values are unique.
Takeaways & Limitations
Effective inverse-design training requires attention to data consistency, not merely uniqueness of the training instances.
Abstract
from arXiv · showhide
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 non-uniqueness 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 non-unique electromagnetic scattering instances. This paves the way for using deep neural networks to design complex photonic structures that requires large training sets.
II. Training forward neural network. · III. Training neural network to design transmission phase delay of 2D structure.
The supplied passages consist of related-work citations associated with training a neural network to design transmission phase delay in 2D structures; they do not provide substantive details about the forward-network training section.
- III. Training neural network to design transmission phase delay of 2D structure.: Prior work cited for 2D photonic-structure design includes level-set optimization, inverse design, and optimization of aperiodic dielectric structures.The passages list Kao et al., Piggott et al., and Seliger et al. as related work.
- III. Training neural network to design transmission phase delay of 2D structure.: The cited literature includes deep learning with coherent nanophotonic circuits and trainable hardware using error backpropagation through physical media.These works are listed in the related-work references.
- III. Training neural network to design transmission phase delay of 2D structure.: Nanophotonic inverse design using artificial neural networks is also cited as related work.The passage identifies Peurifoy et al. and their contribution in Frontiers in Optics.
- III. Training neural network to design transmission phase delay of 2D structure.: Related references include bidirectional neural-network models for reverse modeling of microwave circuits and neural-network inverse modeling for microwave filter design.The cited works are by Vai et al. and Kabir et al.
- III. Training neural network to design transmission phase delay of 2D structure.: The references connect neural-network applications in microwave-device design with designer metasurfaces and metasurface holograms.The passages cite Selleri et al., Yu and Capasso, and Zheng et al.
- III. Training neural network to design transmission phase delay of 2D structure.: The cited technical background includes a free electromagnetic solver for layered periodic structures.The solver is identified as S4 by Liu and Fan.
I. Data consistency in inverse design problems
Inverse design fails when training data combine multiple inverse mappings, even if every target instance is unique. A controlled example shows that self-consistent datasets train accurate inverse networks, whereas their inconsistent union does not.
- Problem setup: A many-to-one nonlinear operator maps 8-dimensional real vectors X to 4-dimensional real vectors Y, making the forward problem well-defined but inverse design non-unique.The mapping is expressed as Y = ÔX.
- Training consequence: D1 and D2 train inverse networks well, whereas inconsistent D3 cannot train an accurate network despite containing unique instances with different Y values.The experiment identifies dataset inconsistency, in addition to non-unique instances, as the cause of inaccurate inverse-network training.
- Problem setup: Two different inverse operators can produce distinct X values for the same Y, establishing multiple valid inverse mappings.For every Y in R^4, both operators satisfy the forward relation when applied inversely.
- Data consistency: Datasets D1 and D2 are each self-consistent because their instances come from one inverse mapping, but their union D3 is not self-consistent.D3 = D1 ∪ D2 combines instances generated by two different inverse operators.