Deep learning for the modeling and inverse design of radiative heat transfer

TL;DR

The paper addresses the challenge of modeling and optimizing radiative heat transfer across near-field, far-field, and subwavelength regimes by leveraging deep neural networks as fast surrogates and as engines for inverse design. It demonstrates three proof-of-principle applications—NFRHT in multilayer hyperbolic metamaterials, passive radiative cooling in photonic-crystal slabs, and thermal emission of subwavelength objects—each paired with custom numerical data-generation methods to train compact NN models. The key contributions include accurate forward surrogates (with percent-level errors), efficient inverse-design via backpropagation, and transfer-learning strategies that improve data efficiency across related problems. The results suggest substantial potential for rapid design-space exploration in thermal radiation and motivate future work on generative models and time-dependent or many-body extensions to broaden applicability and impact.

Abstract

Deep learning is having a tremendous impact in many areas of computer science and engineering. Motivated by this success, deep neural networks are attracting an increasing attention in many other disciplines, including physical sciences. In this work, we show that artificial neural networks can be successfully used in the theoretical modeling and analysis of a variety of radiative heat transfer phenomena and devices. By using a set of custom-designed numerical methods able to efficiently generate the required training datasets, we demonstrate this approach in the context of three very different problems, namely, (i) near-field radiative heat transfer between multilayer systems that form hyperbolic metamaterials, (ii) passive radiate cooling in photonic-crystal slab structures, and (iii) thermal emission of subwavelength objects. Despite their fundamental differences in nature, in all three cases we show that simple neural network architectures trained with datasets of moderate size can be used as fast and accurate surrogates for doing numerical simulations, as well as engines for solving inverse design and optimization in the context of radiative heat transfer. Overall, our work shows that deep learning and artificial neural networks provide a valuable and versatile toolkit for advancing the field of thermal radiation.

Figures (11)

• Figure 1: (a) Schematic representation of a neuron, the basic component of a neural network. The value of a neuron is determined by a linear transformation that weights the importance of various inputs, followed by a nonlinear activation function. Two typical nonlinear activation functions are also shown: sigmoid and ReLU. (b) Feed-forward neural network with neurons arranged into layers with the output of one layer serving as the input to the next layer.
• Figure 2: (a) Sketch of two identical multilayer systems separated by a vacuum gap of size $d_0$. The two reservoirs feature $N$ total layers alternating between a Drude metal (grey areas) with permittivity $\epsilon_\mathrm{m}$ and a dielectric (white areas) with permittivity $\epsilon_\mathrm{d}$. The last layer in both cases is made of metal and the thickness of layer $i$ is denoted by $d_i$. (b) The transmission of the evanescent waves as a function of the frequency $\omega$ and the magnitude of the parallel wave vector $k$ for the bulk system, i.e., two parallel plates made of the metal, and $d_0 = 10$ nm. (c) The same as in panel (b), but for the multilayer system with $N= 160$ and $d_i = 10$ nm for all layers.
• Figure 3: Results for the spectral heat transfer coefficient $h_\omega$ between two multilayers with $N=4$ and a gap size $d_0 = 10$ nm. (a) Comparison between real $h_\omega$-spectra computed with fluctuational electrodynamics (solid lines) and the prediction of the NN (dashed lines). The layer thicknesses (in nm) are indicated in the legend. (b) Comparison of the NN approximation to the target spectrum (layer thicknesses in nm are indicated in the legend) following the inverse design problem described in the text. (c) Result of the optimization problem in which the total heat transfer coefficient is maximized. (d) Result of the optimization problem where $h_\omega$ is minimized in the frequency region indicated by the dashed vertical lines.
• Figure 4: (a-d) Same as in Fig. \ref{['fig-multilayer2']} but now for $N=6$. (e-h) Same as in Fig. \ref{['fig-multilayer2']} but for $N=8$.
• Figure 5: (a) Schematics of the silica mirror used as a passive radiative cooler in Ref. Kou2017. It consists of a SiO$_2$ slab of thickness $d_\mathrm{SiO_2}$ and a silver thin film of thickness $d_\mathrm{Ag}$. (b) A nanostructured version of the cooler of panel (a), but featuring a periodic array of circular holes of radius $R$ with a lattice parameter $a$ (square lattice). (c) Emissivity as a function of the wavelength for a silica photonic crystal (black solid line) and a silica mirror (red solid line) for $d_\mathrm{SiO_2} = 500$$\mu$m and $d_\mathrm{Ag} = 120$ nm. For the photonic crystal: $a = 100$ nm and $R = 50$ nm ($f = 0.785$). The cyan solid line corresponds to the AM1.5 solar spectrum $I_{\rm AM1.5}$ (see right vertical axis), the orange curve to the atmospheric emissivity/absorptivity spectrum $\varepsilon_{\rm atm}$, and the gray dashed line to the blackbody radiation curve $I_{\rm BB}$ (50 times enlarged in spectral irradiance) at 300 K.