Physics-informed neural networks for inverse problems in nano-optics and metamaterials.

By Yuyao Chen, Lu Lu, G. Em Karniadakis, L. Dal Negro. 2019

681 citations recorded by the source corpus.

In this paper, we employ the emerging paradigm of physics-informed neural networks (PINNs) for the solution of representative inverse scattering problems in photonic metamaterials and nano-optics technologies. In particular, we successfully apply mesh-free PINNs to the difficult task of retrieving the effective permittivity parameters of a number of finite-size scattering systems that involve many interacting nanostructures as well as multi-component nanoparticles. Our methodology is fully validated by numerical simulations based on the finite element method (FEM). The development of physics-informed deep learning techniques for inverse scattering can enable the design of novel functional nanostructures and significantly broaden the design space of metamaterials by naturally accounting for radiation and finite-size effects beyond the limitations of traditional effective medium theories.

Subfields: Atomic and Molecular Physics, and Optics, Electrical and Electronic Engineering, Electronic, Optical and Magnetic Materials

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

In Electrical and Electronic Engineering

In Electronic, Optical and Magnetic Materials

Citations in the corpus

Physics informed deep learning for computational elastodynamics without labeled data (2020, background): “…ﬂuid ﬂows and Navier-Stokes equations [10, 17–21], solving stochastic PDEs [22], ﬂows transport in porous media [23–25], cardiovascular systems [26–28], design of metamaterials [29– 31], metamodeling of nonlinear structural systems [32, 33], and discovery of physical laws [34–36], among others.”
Characterizing possible failure modes in physics-informed neural networks (2021, background): “This has garnered interest and shown successful results in a wide variety of science and engineering problems and applications [3, 11, 16, 29–31 However, there have also been issues observed with this formulation.”
Physics-informed graph neural Galerkin networks: A unified framework for solving PDE-governed forward and inverse problems (2021, background): “Its merit and effectiveness has been demonstrated over a plethora of scientific applications in many areas [3–7].”
Physics-informed neural networks with hard constraints for inverse design (2021, methodology): “Moreover, PINNs have been successfully employed to solve diverse inverse problems , including in optics [8], ﬂuid mechanics [45, 55], systems biology [60], biomedicine [46, 24], and even inverse problems of stochastic PDEs [62] and fractional PDEs [38].”
MIONet: Learning multiple-input operators via tensor product (2022, neutral): “These methods have shown promising results in diverse applications, such as fluid mechanics [38], optics [4], systems biology [44, 5], and biomedicine [14].”
CAN-PINN: A Fast Physics-Informed Neural Network Based on Coupled-Automatic-Numerical Differentiation Method (2021, methodology): “Interesting applications include quantification of cardiovascular flows from visualization or sensor data [31–33], metamaterials design [34], and nondestructive quantification of cracks [35].”
Learning the solution operator of parametric partial differential equations with physics-informed DeepONets (2021, neutral): “Nevertheless, these approaches have found wide applicability across diverse applications including fluid mechanics [19, 20], heat transfer [21], bio-engineering [22, 23], materials [24, 25, 26], and finance [27, 28], showcasing the remarkable effectiveness of ML techniques in learning black-box func”
DeepXDE: A Deep Learning Library for Solving Differential Equations (2019, background): “An attractive feature of PINNs is that it can be used to solve inverse problems with minimum change of the code for forward problems [47, 48, 51, 21, 13].”
Analyses of internal structures and defects in materials using physics-informed neural networks (2022, methodology): “4 of 12 can be directly estimated using the standard formulation of PINNs for inverse problems (12, 18, 41, 42).”
A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks (2022, methodology): “PINNs have been applied to tackle diverse problems in computational science and engineering, such as inverse problems in nano-optics, metamaterials [5], and ﬂuid dynamics [2], parameter estimation in systems biology [6, 7], and problems of inverse design and topology optimization [8].”
Scientific Machine Learning Through Physics–Informed Neural Networks: Where we are and What’s Next (2022, methodology): “It consists of two NN components: an encoder that translates the data from the input layer to a finite number of hidden units, and a decoder that has an output layer with the same number of nodes as the input layer (Chen et al, 2018).”
Estimates on the generalization error of physics-informed neural networks for approximating a class of inverse problems for PDEs (2020, background): “They are particularly successful for approximating the so-called inverse problems involving PDEs, see [15, 44, 53,54] and references therein.”
When and why PINNs fail to train: A neural tangent kernel perspective (2020, background): “Thanks to the approximation capabilities of neural networks, physics-informed neural networks (PINNs) have already led to a series of remarkable results across a range of problems in computational science and engineering, including fluids mechanics [1, 2, 4, 5], bio-engineering [6, 7], meta-material”
Physics-informed neural networks for inverse problems in supersonic flows (2022, methodology): “In recent years physics-informed neural networks (PINNs) [1] emerged as an alternative simple method to solve many problems in computational science and engineering, see, for example [2, 3, 4, 5, 6, 7, 8, 9, 10, 4, 11, 12, 13, 14, 15].”