Deep operator neural network applied to efficient computation of asteroid surface temperature and the Yarkovsky effect

TL;DR

Results show that the trained network is able to predict temperature with an accuracy of sim 1 on average, while the computational cost is five orders of magnitude lower, enabling thermal property analysis in a multidimensional parameter space.

Abstract

Surface temperature distribution is crucial for thermal property-based studies about irregular asteroids in our Solar System. While direct numerical simulations could model surface temperatures with high fidelity, they often take a significant amount of computational time, especially for problems where temperature distributions are required to be repeatedly calculated. To this end, deep operator neural network (DeepONet) provides a powerful tool due to its high computational efficiency and generalization ability. In this work, we applied DeepONet to the modelling of asteroid surface temperatures. Results show that the trained network is able to predict temperature with an accuracy of ~1% on average, while the computational cost is five orders of magnitude lower, hence enabling thermal property analysis in a multidimensional parameter space. As a preliminary application, we analyzed the orbital evolution of asteroids through direct N-body simulations embedded with instantaneous Yarkovsky effect inferred by DeepONet-based thermophysical modelling.Taking asteroids (3200) Phaethon and (89433) 2001 WM41 as examples, we show the efficacy and efficiency of our AI-based approach.

Figures (11)

• Figure 1: Architecture of the modified DeepONet adopted in this work. The network learning the operator $G:(E,\Phi)\rightarrow G(E,\Phi)$ includes three inputs, the function $E$, the parameter $\Phi$. $E$ is presented as some discrete locations with $m$ elements sampled on $[\overline{t}_1,\overline{t}_2,...,\overline{t}_m]$. In this work, $\overline{z}$ limited in a small range is considered as the only variable input to trunk net. The input of SELayer receives the Hadamard product of the outputs from branch net$_1$ and branch net$_2$. The final output is the dot product of $[b_1,b_2,...,b_p]$ and $[t_1,t_2,...,t_p]$ with a bias.
• Figure 2: Detail architectures of branch net$_1$, branch net$_2$ and SELayer adopted in this work, where FC is the fully-connected layer, BN is the batch normalization layer. The input of branch net$_{1(2)}$ experiences the initial feature extraction through a fully-connected layer and then is carried out the feature amplification by 4(2) SELayer. Trunk net is similar but it should be noted that there is an activation function before output. SELayer in this work is a modified Squeeze-and-Excitation Layer specially for fully-connected architecture.
• Figure 3: Time cost of DeepONet and traditional numerical simulation as a function of number of facets. The red line consisting of error bars centered around circles represents the time cost required by DeepONet in GPU and the red line consisting of error bars centered around squares represents the time cost required by DeepONet in CPU. The black line is the time cost required by traditional numerical simulation.
• Figure 4: Error between the results from DeepONet and numerical simulation. The panels describe the mean absolute error of $\Delta T/T$ as a function of $\beta$ (left panel) and of $\Phi$ (right panel), where the black lines represent the spherical asteroid, the blue lines are the biaxial ellipsoid and the red lines are the triaxial ellipsoid. The left panels fix $\Phi=5$ and the right panels fix $\beta=90^{\circ}$.
• Figure 5: Surface temperatures of two irregular asteroids from DeepONet and traditional simulation, and the relative errors between them. The top-row panels are for a main belt asteroid (Lutetia) and the bottom-row panels are for a Amor-class asteroid (1996 HW1). The left-column panels describe the results from DeepONet, the middle-column panels are the results from traditional simulation and the right-column panels are relative errors between the two methods.