Deep Physical Informed Neural Networks for Metamaterial Design

By Zhiwei Fang, Justin Zhijun Zhan. 2020

156 citations recorded by the source corpus.

In this paper, we propose a physical informed neural network approach for designing the electromagnetic metamaterial. The approach can be used to deal with various practical problems such as cloaking, rotators, concentrators, etc. The advantage of this approach is the flexibility that we can deal with not only the continuous parameters but also the piecewise constants. As our best knowledge, there is no other faster and much efficient method to deal with these problems. As a byproduct, we propose a method to solve high frequency Helmholtz equation, which is widely used in physics and engineering. Some benchmark problems have been solved in numerical tests to verify our method.

Subfields: Biomedical Engineering, Electronic, Optical and Magnetic Materials, Signal Processing

How researchers see this paper

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

In Biomedical Engineering

1. Luning Sun
2. Yew-Soon Ong
3. Chengping Rao
4. Jian-Xun Wang
5. Han Gao
6. Paris Perdikaris
7. Yang Liu

In Electronic, Optical and Magnetic Materials

1. Luning Sun
2. Chengping Rao
3. Jian-Xun Wang
4. Han Gao
5. Yang Liu

In Signal Processing

1. Luning Sun
2. Yew-Soon Ong
3. Jian-Xun Wang
4. Han Gao
5. Paris Perdikaris
6. Yang Liu

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.”
• CAN-PINN: A Fast Physics-Informed Neural Network Based on Coupled-Automatic-Numerical Differentiation Method (2021, background): “PINNs have been demonstrated for various physics phenomena, including heat transfer [23,24], fluid dynamics [25–27] and electromagnetic propagation [28–30].”
• PhyGeoNet: Physics-informed geometry-adaptive convolutional neural networks for solving parameterized steady-state PDEs on irregular domain (2020, methodology): “This weakly-supervised method has been applied to solve various PDEs with limited training data in many scientific problems, including subsurface flows [20], vortex-induced vibrations [21], turbulent flows [22, 23], cardiovascular systems [14, 24–26], metamaterial design [27–29], geostatistical mode”
• 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”
• On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks (2020, background): “The results of this experiment are summarized in figure 18.”