ThermoONet -- a deep learning-based small body thermophysical network: applications to modelling water activity of comets

TL;DR

ThermoONet addresses the computational bottleneck in cometary thermophysical modeling by replacing costly numerical simulations with a DeepONet-based surrogate that predicts subsurface temperature and water ice sublimation flux. It achieves around $MAPE \approx 2\%$ accuracy and roughly six orders of magnitude speedup, while generalizing to irregular shapes such as 67P and enabling fitting of observed water curves via global optimization (e.g., Simulated Annealing). The approach uses parameter grouping and attention within DeepONet to handle eight scalar parameters plus a diurnal insolation input $E$, supporting efficient exploration of parameter space. This work provides a scalable tool for interpreting cometary activity and can be integrated into broader physical models or optimization pipelines.

Abstract

Cometary activity is a compelling subject of study, with thermophysical models playing a pivotal role in its understanding. However, traditional numerical solutions for small body thermophysical models are computationally intensive, posing challenges for investigations requiring high-resolution or repetitive modeling. To address this limitation, we employed a machine learning approach to develop ThermoONet - a neural network designed to predict the temperature and water ice sublimation flux of comets. Performance evaluations indicate that ThermoONet achieves a low average error in subsurface temperature of approximately 2% relative to the numerical simulation, while reducing computational time by nearly six orders of magnitude. We applied ThermoONet to model the water activity of comets 67P/Churyumov-Gerasimenko and 21P/Giacobini-Zinner. By successfully fitting the water production rate curves of these comets, as obtained by the Rosetta mission and the SOHO telescope, respectively, we demonstrate the network's effectiveness and efficiency. Furthermore, when combined with a global optimization algorithm, ThermoONet proves capable of retrieving the physical properties of target bodies.

Figures (9)

• Figure 1: Architecture of $ThermoONet$. The network consists of three branch networks with distinct inputs, parameter group $p_1$, $p_{2-8}$ and the radiation flux function $E$, where $E$ is presented as some discrete locations with $m$ elements sampled on $[\overline{t}_1,\overline{t}_2,...,\overline{t}_m]$. A layer incorporating the attention mechanism processes the Hadamard product of the outputs from branch net$_1$ and branch net$_2$. The resulting output from this layer $[b_1^1,b_2^1,...,b_p^1]$ is then element-wise multiplied (Hadamard product) with the output from branch net$_3$$[b_1^2,b_2^2,...,b_p^2]$. The average of the resulting values is taken as the final output.
• Figure 2: Detailed architectures of branch net$_n$ and attention mechanism, where FC is the full connected layer. The input of branch net$_n$ experiences the initial feature extraction through a FC layer and then carries out the feature amplification by attention mechanism, where $i$ represents the layer number. 3, 6, and 6 layers are respectively used in branch networks from net$_1$ to net$_3$.
• Figure 3: Comparison of computational cost between $ThermoONet$ and traditional numerical simulation for the shape models with varying number of facets. The error bars represent the maximum and minimum time costs in the repeated calculation for over 20 times.
• Figure 4: Differences in the output subsurface temperature between $ThermoONet$ and numerical simulation as functions of obliquity $\beta$ and heliocentric distance $r$. The left panels present the error functions for different thicknesses of dust mantle, with the blue, black, and red lines respectively representing 5 mm, 10 mm, and 15 mm respectively. The right panels illustrate the error functions for varying icy area fractions, with the blue, black, and red lines respectively corresponding to 1$\%$, 10$\%$, and 20$\%$. The panels fix $r=2$ au for the top panels and $\beta=0^{\circ}$ for the bottom panels, $f=10\%$ for the left panels and $X=10$ mm for the right panels. For the settings of other parameters, please refer to Table \ref{['tab:pa0']}.
• Figure 5: Differences in global water production rate derived from $ThermoONet$ and the numerical simulation at different orbital phases of comet 67P. The top panel is the temperature calculation errors, where the black line was derived with $X=5$ mm, $f=1\%$, and the red line with $X=10$ mm, $f=1\%$, the blue line with $X=5$ mm, $f=10\%$. The asterisks denote specific examples of temperature distributions shown in Fig. \ref{['fig:67P_detail']}. The bottom panel is the water production rate, where the real lines stand for the results from $ThermoONet$, the circles are these from the numerical solutions, with the same parameters as in the top one.