The DOI matches its Crossref record; 37 of the 37 references it cites were found in a registry or an index.
Physics-Informed Neural Networks with Hard Constraints for Inverse Design
Abstract
Inverse design arises in a variety of areas in engineering such as acoustic, mechanics, thermal/electronic transport, electromagnetism, and optics. Topology optimization is an important form of inverse design, where one optimizes a designed geometry to achieve targeted properties parameterized by the materials at every point in a design region. This optimization is challenging, because it has a very high dimensionality and is usually constrained by partial differential equations (PDEs) and additional inequalities. Here, we propose a new deep learning method---physics-informed neural networks with hard constraints (hPINNs)---for solving topology optimization. hPINN leverages the recent development of PINNs for solving PDEs, and thus does not require a large dataset (generated by numerical PDE solvers) for training. However, all the constraints in PINNs are soft constraints, and hence we impose hard constraints by using the penalty method and the augmented Lagrangian method. We demonstrate the effectiveness of hPINN for a holography problem in optics and a fluid problem of Stokes flow. We achieve the same objective as conventional PDE-constrained optimization methods based on adjoint methods and numerical PDE solvers, but find that the design obtained from hPINN is often smoother for problems whose solution is not unique. Moreover, the implementation of inverse design with hPINN can be easier than that of conventional methods because it exploits the extensive deep-learning software infrastructure.
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Cites
Raissi, M., Perdikaris, P., & Karniadakis, G. E. (2019) · Journal of Computational Physics · doi:10.1016/j.jcp.2018.10.045 · Cited by 20,384
Physics-informed machine learning
Karniadakis, G. E., Kevrekidis, I. G., Lu, L., Perdikaris, P., Wang, S., & Yang, L. (2021) · Nature Reviews Physics · doi:10.1038/s42254-021-00314-5 · Cited by 8,718
Self-citationA Limited Memory Algorithm for Bound Constrained Optimization
Byrd, R. H., Lu, P., Nocedal, J., & Zhu, C. (1995) · SIAM Journal on Scientific Computing · doi:10.1137/0916069 · Cited by 6,221
Topology optimization approaches: A comparative review
Sigmund, O., & Maute, K. (2013) · Structural and Multidisciplinary Optimization · doi:10.1007/s00158-013-0978-6 · Cited by 2,890
DeepXDE: A Deep Learning Library for Solving Differential Equations
Lu, L., Meng, X., Mao, Z., & Karniadakis, G. E. (2021) · SIAM Review · doi:10.1137/19m1274067 · Cited by 2,512
Self-citationArtificial neural networks for solving ordinary and partial differential equations
Lagaris, I. E., Likas, A., & Fotiadis, D. I. (1998) · IEEE Transactions on Neural Networks · doi:10.1109/72.712178 · Cited by 2,412
Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations
Raissi, M., Yazdani, A., & Karniadakis, G. E. (2020) · Science · doi:10.1126/science.aaw4741 · Cited by 2,103
Inverse design in nanophotonics
Molesky, S., Lin, Z., Piggott, A. Y., Jin, W., Vucković, J., & Rodriguez, A. W. (2018) · Nature Photonics · doi:10.1038/s41566-018-0246-9 · Cited by 1,818
AutoML: A survey of the state-of-the-art
He, X., Zhao, K., & Chu, X. (2021) · Knowledge-Based Systems · doi:10.1016/j.knosys.2020.106622 · Cited by 1,691
Topology optimization of fluids in Stokes flow
Borrvall, T., & Petersson, J. (2003) · International Journal for Numerical Methods in Fluids · doi:10.1002/fld.426 · Cited by 1,234
Cited by
Physics-informed neural networks (PINNs) for fluid mechanics: a review
Cai, S., Mao, Z., Wang, Z., Yin, M., & Karniadakis, G. E. (2021) · Acta Mechanica Sinica · doi:10.1007/s10409-021-01148-1 · Cited by 2,084
Self-citationGradient-enhanced physics-informed neural networks for forward and inverse PDE problems
Yu, J., Lu, L., Meng, X., & Karniadakis, G. E. (2022) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/j.cma.2022.114823 · Cited by 722
Self-citationRoadmap for Optical Metasurfaces
Kuznetsov, A. I., Brongersma, M. L., Yao, J., Chen, M. K., Levy, U., Tsai, D. P., Zheludev, N. I., Faraon, A., Arbabi, A., Yu, N., et al. (2024) · ACS Photonics · doi:10.1021/acsphotonics.3c00457 · Cited by 420
Empowering Metasurfaces with Inverse Design: Principles and Applications
Li, Z., Pestourie, R., Lin, Z., Johnson, S. G., & Capasso, F. (2022) · ACS Photonics · doi:10.1021/acsphotonics.1c01850 · Cited by 283
Self-citationInverse design enables large-scale high-performance meta-optics reshaping virtual reality
Li, Z., Pestourie, R., Park, J.-S., Huang, Y.-W., Johnson, S. G., & Capasso, F. (2022) · Nature Communications · doi:10.1038/s41467-022-29973-3 · Cited by 280
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Metadata
- Authors
- Lu, L., Pestourie, R., Yao, W., Wang, Z., Verdugo, F., & Johnson, S. G.
- Venue
- SIAM Journal on Scientific Computing
- Published
- 2021-01
- Volume
- 43
- Issue
- 6
- Pages
- B1105-B1132
- ISSN
- 1064-8275 (ISSN-L)
- 1095-7197
- OpenAlex
- W3128157635
- Cited by
- 771
- References
- 37
- FWCI
- 32.58
- Type
- journal article
- Language
- en
- Open access
- closed
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