[Table: Table 1. Fixed parameters in the error analysis.]

| Table 1. Fixed parameters in the error analysis. |  |
| --- | --- |
| ϵ | 1 |
| ρi (kg m−3) | 920 |
| Ci (J kg−1 K−1) | 2100 |
| ρd (kg m−3) | 500 |
| Cd (J kg−1 K−1) | 1000 |
| ω (rad s−1) | 1.4× 10−4 |
| κd (W m−1 K−1) | 2× 10−3 |
| κm (W m−1 K−1) | 2.4× 10−3 |

The loss function is the mean square error (MSE) between the temperature calculated with numerical simulation and the output from the neural network, and the adaptive moment estimation method (Adam) is used as the optimization algorithm. Same as in the training process of the asteroid network in Zhao et al. (2024), the learning rate decay approach is utilized to mitigate issues related to wide oscillations of the loss function and slow convergence. We term the trained neural network ThermoONet, a model designed based on the core principles of DeepONet and specifically tailored for cometary thermophysical modelling.

[Figure: Fig. 4 shows the results. The overall error in temperature fluctuates as the radiation flux function or parameters change. With the inclusion of more parameters, the error inevitably increases compared to that of the deep learning model for asteroids (Zhao et al. 2024). However, it is still maintained at a reasonably low level, with maximum below 4% and an average around 2%. We notice that the error does not show significant correlation with varying heliocentric distances, which confirms the effectiveness of the specially designed training dataset. As shown in Eq. 5-7, the sublimation flux of water ice exhibits an exponential relationship with the temperature, meaning that any error in temperature has an even more significant impact on the calculated sublimation flux. Moreover, given that many cometary nucleus show a concave shape, the projected shadows between facets complicate the radiation flux function, which presents a great challenge for the generalization of the neural network, even more severe than in the case of asteroid (Zhao et al. 2024). In order to validate the generalization capability of ThermoONet, it is applied to a real comet with irregular shape. In practice, we take comet 67P as the example and simulate its temperature with a shape model of 2868 facets (Jorda et al. 2016). Ephemerides of 67P is retrieved using Rosetta SPICE kernels (Acton 1996; ESA SPICE Service 2017). We evaluate both the temperature and water production rate at different orbital phases by comparing them with the results from numerical solutions (see Fig. 5). We also examine the temperature distributions at three specific orbital locations before, near and after the perihelion (Fig. 6). Other parameters are the same as in Table 1. The average temperature errors are about 2.5%, and the global water production rates from two methods are showing the same trend. The average relative errors are respectively 5.04% for (X = 5 mm, f = 1%), 19.25% for (X = 5 mm, f = 10%), and 10.26% for (X = 10 mm, f = 1%). The patterns of error distribution shown in Fig. 5 suggest that the temperature error is the smallest in the high-temperature region, typically below 3K. The primary source of error lies in the mid-temperature regions. However, only a few facets exhibit errors exceeding 10K.]