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Recent developments in the computational automated design of electromagnetic devices, otherwise known as inverse design, have significantly enhanced the design process for nanophotonic systems. Inverse design can both reduce design time considerably and lead to high-performance, nonintuitive structures that would otherwise have been impossible to develop manually. Despite the successes enjoyed by structure optimization techniques, most approaches leverage electromagnetic solvers that require significant computational resources and suffer from slow convergence and numerical dispersion. Recently, a fast simulation and boundary-based inverse design approach based on boundary integral equations was demonstrated for two-dimensional nanophotonic problems. In this work, we introduce a new full-wave three-dimensional simulation and boundary-based optimization framework for nanophotonic devices also based on boundary integral methods, which achieves high accuracy even at coarse mesh discretizations while only requiring modest computational resources. The approach has been further accelerated by leveraging GPU computing, a sparse block-diagonal preconditioning strategy, and a matrix-free implementation of the discrete adjoint method. As a demonstration, we optimize three different devices: a 1:2 1550 nm power splitter and two nonadiabatic mode-preserving waveguide tapers. To the best of our knowledge, the tapers, which span 40 wavelengths in the silicon material, are the largest silicon photonic waveguiding devices to have been optimized using full-wave 3D solution of Maxwell’s equations.
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This content will become publicly available on September 25, 2026
Coefficient-to-Basis Network: a fine-tunable operator learning framework for inverse problems with adaptive discretizations and theoretical guarantees
We propose a Coefficient-to-Basis Network (C2BNet), a novel framework for solving inverse problems within the operator learning paradigm. C2BNet efficiently adapts to different discretizations through fine-tuning, using a pre-trained model to significantly reduce computational cost while maintaining high accuracy. Unlike traditional approaches that require retraining from scratch for new discretizations, our method enables seamless adaptation without sacrificing predictive performance. Furthermore, we establish theoretical approximation and generalization error bounds for C2BNet by exploiting low-dimensional structures in the underlying datasets. Our analysis demonstrates that C2BNet adapts to low-dimensional structures without relying on explicit encoding mechanisms, highlighting its robustness and efficiency. To validate our theoretical findings, we conducted extensive numerical experiments that showcase the superior performance of C2BNet on several inverse problems. The results confirm that C2BNet effectively balances computational efficiency and accuracy, making it a promising tool to solve inverse problems in scientific computing and engineering applications. This article is part of the theme issue ‘Frontiers of applied inverse problems in science and engineering’.
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- Award ID(s):
- 2145167
- PAR ID:
- 10667285
- Publisher / Repository:
- The Royal Society
- Date Published:
- Journal Name:
- Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
- Volume:
- 383
- Issue:
- 2305
- ISSN:
- 1364-503X
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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