temperature are successfully rescaled in the range [0, 1], with all physical parameters explicitly represented in the mathematical expression of the equations.

This transformation can significantly enhance the efficiency and ease of dataset creation for deep learning.

For instance, when studying different comets, the original model for the radiation flux functions leads to varying domains of definition due to differences in rotational velocities.

Additionally, the range of values fluctuates with variable parameters such as Bond albedo AB and heliocentric distance r.

This variability complicates the construction of a comprehensive set of radiation flux functions.

However, the normalized model can effectively address this issue through the parameter extraction.

Excluding the radiation flux, we have identified and summarized all the independent parameters that influence the equations:
p1 = (1 −AB)F⊙, p2 = ϵ, p3 = X, p4 = ρdCd, p5 = ω, p6 = κd, p7 = κm, p8 = f. (13)
In the subsequent discussions, we treat all these parameters as variable within a physically reasonable range in order to obtain a generalized model.

The radiation flux needs to be calculated before solving the equations.

It is a periodic function about time, determined by the angle between the normal vector of the surface element and the solar direction, incorporating both the horizon and projected shadows.

The calculation method is consistent with our previous work for asteroids (secondary radiation and self-heating are not considered in this work), as described in Section 2.1.2 of Zhao et al. (2024).

It is worth noting that the radiation flux used to train the network should be randomly generated, which will be detailed in Section 3, while the illumination and shadow mentioned here are just specific to real-world situations.

The backward finite difference method is utilized to solve the partial differential equations, considering its computational efficiency.

First we divide the continuous variables into a set of space-time grids, where the i-th grid of depth is denoted by i∆x and the j-th grid of time is denoted by j∆t.

As a result, the heat conduction equation is discretized into T i,j+1 = (1 −2 ∆t
∆x2 )T i,j + ∆t
∆x2 (T i+1, j + T i−1, j).
(14)
The thickness of the dust mantle is much smaller than that of the dust-ice mixture.

To improve computational efficiency while ensuring accuracy, different spatial step sizes are applied in two layers, with a smaller step size ∆xd = 1 mm for the dust mantle and a larger one ∆xm = 1 cm for the dust-ice mixture. ∆xd and ∆xm are then obtained through dividing ∆xd and ∆xm by the skin depth lsd, lsm.

The time step is taken as ∆t = 2π/1200.

We denote the temperature at the interface between the two layers as Tm, j, then the three boundary conditions are expressed in the finite difference scheme as follows:
T 1, j −T 0,j
0,j −Φd
T
∆xd = E( j∆t),
T m,j −T m−1, j
T m+1,j −T m,j
(15)
−Φd
∆xd
+ Φm
∆xm = lZ(X), T n,j = T n−1, j.

The surface temperature T0, j and the interface temperature Tm,j can be determined from the known T1, j, Tm−1, j, Tm+1, j by taking
advantage of Newton–Raphson iterative algorithm to solve the boundary conditions.

The overall temperature need to exhibit a stable and static distribution due to the rotation of the comet.

After one complete spin of the nucleus, the temperature should be invariant at the subsolar point, which holds at all depths.

This static condition is used as a convergence criterion for the iteration.

In this work, the criterion is for the mean absolute error of the normalized temperature between iterations to be below 1 × 10−4.
2.4.

Water activity The water activity of the comet is effectively represented by the sublimation flux in the model.

The global total outgassing flux of water from the comet nucleus is the integral of the sublimation flux over the entire surface.

In the polyhedral shape model, this can be expressed as follows (Hu et al. 2017):
Ztotal = �
ZkS k
(16)
k
where Zk indicates the sublimation flux of k-th facet and its area is denoted as S k.