JuanCastillo29/space-mission-intelligence-data huggingface dataset:
exhibiting heterogeneous sensitivity to the solutions of the model, so direct adoption of the parameter encoding scheme for asteroids proves ineffective.

A single branch network collectively encoding all parameters can reduce sensitivity to each individual parameter, especially for those parameters significantly influencing the results.

Conversely, constructing separate branch networks for individual parameters would result in excessive computational memory allocation and time cost.

To resolve this challenge, we propose a parameter grouping method based on sensitivity analysis.

Parameters governing the thermal processes are partitioned into two distinct categories, high-sensitivity and moderate-sensitivity parameters.

Each category is encoded through dedicated branch network, achieving an optimal balance between parameter sensitivity and computational efficiency.

The schematic architecture of the neural network adapted for this work is shown in Fig. 1, where the branch networks are presented in Fig. 2.

Parameter group1 consists of the highsensitivity parameters p1 which exhibits dominant influence over system behavior (more details are shown in the Appendix A), while parameter group2 consists of the remaining parameters.

The neural network encodes these grouped parameters through dedicated branch networks (branch net1 and branch net2), followed by a Hadamard product operation between their respective outputs.

This combined tensor undergoes transformation through an attention mechanism layer, designed to amplify the features through adaptive weight allocation (Vaswani et al. 2017; Woo et al. 2018; Wang et al. 2020).

Notably, each branch network incorporates internal attention mechanisms to perform hierarchical feature enhancement.

The target subsurface temperature is derived from a averaging operation to the Hadamard product between the amplified features and branch net3 output.
3.2.

Dataset and training The neural network developed in this work focuses on the diurnal water ice activity.

Seasonal variations in thermal conditions are reflected through variations in insolation.

As mentioned above, the neural network will be trained with a 9-dimensional parameter space, comprising scalar parameters p1-p8 and one functional input E representing the normalized diurnal insolation curve.

To ensure ThermoONet generalizing well across different cometary environments, we should design Parameter Group1 Branch net1

1b
1p
2b
Function
Branch net3
) (
t E
2 p
b
) (
t E
) ( ...
mt
E

[Figure: Fig. 1. Architecture of ThermoONet. The network consists of three branch networks with distinct inputs, parameter group p1, p2−8 and the radiation flux function E, where E is presented as some discrete locations with m elements sampled on [t1, t2, ..., tm]. A layer incorporating the attention mechanism processes the Hadamard product of the outputs from branch net1 and branch net2. The resulting output from this layer [b1 1, b1 2, ..., b1 p] is then element-wise multiplied (Hadamard product) with the output from branch net3 [b2 1, b2 2, ..., b2 p]. The average of the resulting values is taken as]
requirements. The only difference is that all eight parameters un-
dergo simultaneous joint randomization to maintain proper pa-
rameter covariance structures. Special treatment is implemented
with a similar number in each range. This balanced multi-range
generation mechanism, grounded in prior knowledge of the non-
tures the substantial influence of various ranges on the resulting
temperature. In the practical training process, we have generated
a dataset with 36,000 sets of data.
random pairs of the radiation flux function E and the thermal pa-
were calculated by the numerical simulation. Random functions
are generated by the mean-zero Gaussian random field (GRF)
(Lu et al. 2021), then rescaled in the range [0,1] through the sig-
distance along the y axis in order to ensure the completeness of
the function space (Zhao et al. 2024). For the network of this
work, the training process employs a modified stochastic sam-
The cost of computation time and the level of accuracy are used to assess the performance of ThermoONet.
4.1. Computational cost We compare the computational time consumed by three approaches, ThermoONet with GPU, ThermoONet with CPU, and traditional numerical simulation, for calculating the global ice front temperature distribution of a spherical nucleus with varying number of facets. It is worth mentioning that dataset construction required approximately 6 hours, while the neural network training process was completed within 20 minutes. Once trained, the network is ready for immediate application and does not require further adjustment, so we only analyze the inference time of the network. The ThermoONet calculations were carried out on both GPU and CPU for over 20 times to get an estimate on the uncertainty. The time consumption of the numerical simulation is evaluated by multiplying the average time cost per facet (calculated based on the temperature of a large number of facets) by the total number of facets. All of the computations were performed on a personal computer1 and under the environment of Python 3.8. Results show that (Fig. 3):
• Calculation using ThermoONet is approximately six orders of magnitude faster than the numerical simulation.
• Computational time costs by numerical and CPU-based ThermoONet increase almost linearly with number of facets, while the computation cost by GPU-based ThermoONet stays almost constant against increasing number of facets.
When we need to calculate a large number of global temperature distributions, it is worth noting that the vectorized operations can be further used to ensure that the computation time does not increase linearly with the number of facets.
production rate

4.2. Accuracy assessment We first use a spherical comet to assess the accuracy of temperature predictions with varying obliquity β (the angle between the spin axis and the normal vector of the orbital plane) and heliocentric distance r. We also investigate how errors change with different key model parameters such as the thickness of the dust mantle X and icy area fraction f, where fixed parameters are listed in Table 1. We measure the mean absolute percentage error (MAPE) of temperature between the neural network and numerical simulation, denoted as MAPE (T).
Interpreting the water production rate as a function of the heliocentric distance using thermophysical models has been an intriguing topic in cometary science as it helps us understand the nature of cometary activity (Keller et al. 2015; Hu et al. 2017; Attree et al. 2019; Marshall et al. 2019; Skorov et al. 2020). It is a time-consuming process to calculate the water production rate curve (hereafter water curve) using traditional numerical simulation, which requires computations of global temperature distribution at different orbital phases and it needs to be recalculated whenever the parameters are adjusted. Due to the large number of physical parameters involved, previous studies often fix cen-
1 A laptop equipped with AMD Ryzen 9 6900HX with Radeon Graphics and NVIDIA GeForce RTX 3070Ti Laptop GPU Article number, page 6 of 13

Simulation ThermoONet (GPU) ThermoONet (CPU)
Time (s)
0 2500 5000 7500 10000 12500 15000 17500 20000 N Fig. 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.
3.5
X=5mm X=10mm X=15mm
f=1% f=10% f=20%
2.5
3.0
2.0
2.5
MAPE(T) (%)
MAPE(T) (%)
2.0
1.5
1.5
1.0
1.0
0.5
0.5
0 20 40 60 80 ( )
0 20 40 60 80 ( )
3.0
4.0
2.8
3.5
2.6
3.0
MAPE(T) (%)
MAPE(T) (%)
2.4 2.2
2.5
2.0
2.0
1.8
1.5
1.6 1.4
1.0
1.0 1.5 2.0 2.5 3.0 3.5 4.0 r (au)
1.0 1.5 2.0 2.5 3.0 3.5 4.0 r (au)

[Figure: Fig. 4. Differences in the output subsurface temperature between ThermoONet and numerical simulation as functions of obliquity β 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 β = 0◦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 1.]
hence enabling the application of global optimization algo-

Article number, page 7 of 13

3.56 2.24 1.3 2.33 3.66 Heliocentric Distance (au) 5mm-10% 5mm-1% 10mm-1%
3.5
MAPE(T) (%)
3.0 2.5 2.0
Global Water Production Rate (mol/s)
ThermoONet (5mm-10%)
Simulation (5mm-10%) ThermoONet (5mm-1%)
Simulation (5mm-1%) ThermoONet (10mm-1%)
Simulation (10mm-1%) 2014-08-12 2015-02-24 2015-09-10 2016-02-09 2016-08-29 UTC

[Figure: Fig. 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. 6. 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.]

[Table: Table 2. Initial values and the results derived from SA and BGD for the variable parameters in fitting the water curve of 67P.]
through Möller-Trumbore algorithms and interpolation algo-
rithms.
• eight scalar parameters are computed based on the physical
properties of the comet and orbital ephemerides, the radia-
tion flux for each facet then is retrieved from the precom-
puted lookup table.
• the derived 9-dimensional parameters serve as input to
T hermoONet, which outputs subsurface temperature at the
ice front of each facet. The results subsequently drive the
calculation of water ice sublimation rates and associated ac-
tivity levels.

Parameters Initial values Fitting results X (mm) 5 3.61 f (%) 5 0.644
κd (W m−1 K−1) 1× 10−3 2.18× 10−3
κm (W m−1 K−1) 1× 10−3 2.20× 10−3
ρdCd (J m−3 K−1) 2× 105 5.68× 105
optimized parameter combination is shown in Table 2.
The overall fitting performance is satisfactory with MAPE
= 37.08%, capturing the asymmetrical trend before and after
perihelion. A slight underestimation is observed near the peri-
helion, which is consistent with the finding in Hu et al. (2017).
This phenomenon may be explained by several factors, including
the varying levels of activity across different regions of 67P (At-
tree et al. 2019), the gradual exposure of water ice as the comet
approaches perihelion (Fornasier et al. 2016; Filacchione et al.
2020), and the temperature-dependent changes in thermal con-
ductivity (Skorov et al. 2020). It is worth mentioning that the
advantage of T hermoONet in computation efficiency could be
of help in assessing aforementioned mechanisms.
We combine T hermoONet with SA to fit the observed water
curve of comet 67P from Läuter et al. (2020), the shape model
with 23788 facets is used (Jorda et al. 2016).
We chose five parameters to be fitted, including the thick-
ness of the dust mantle X, the icy area fraction f , the product
selected as in Table 2 and the corresponding water curve is gen-
erated by applying T hermoONet at every observation time. The
loss function is MAPE between the predicted results and the av-
erage observed data, and SA is applied to search for the pre-
liminary optimal parameter combination that minimizes MAPE.
Finally, Batch Gradient Descent (BGD) is utilized to refine the
parameters, converging to a solution that further reduces the loss
There is a growing database of water curves of different types
of comets retrieved using observations by solar observatories
Combi et al. (2019, 2021b, 2023). Most of these comets still lack
well-defined parameters such as size, shape, rotation characteris-

Article number, page 8 of 13 tics, and thermophysical parameters.

[Figure: Fig. 6. The subsurface temperature distribution of comet 67P modelled by ThermoONet and the numerical simulation at three specific positions marked by asterisks in the top panel of Fig. 5. The top row shows the normalized radiation flux, and the second to fourth rows show the results calculated with ThermoONet, the numerical simulation, and the differences between them.]

It could prove difficult for traditional numerical simulations to fit these data by searching a large parameter space. However, by combining trial-and-error testing with ThermoONet, exploring a large parameter space becomes feasible. We take comet 21P as an example to demonstrate the application of the trial-and-error testing. The water curve of 21P is significantly different from that of 67P, remaining essentially flat before perihelion and exhibiting an obvious decline after perihelion (see more from Combi et al. (2021a)). A preliminary consideration is that the solar illumination area of 21P gradually decreases during the observation period, which could be the combined effect of its shape and the orientation of its spin axis, which was shown in Marshall et al. (2019). We can iteratively adjust the parameters based on trial-and-error results by taking advantage of ThermoONet.
tain with a wide range from 9.5 to 19 h (Leibowitz & Brosch 1986; Moulane et al. 2020)). Parameters to be fitted are shown in Table 3. The test shapes are respectively sphere with ax = ay = az = 3.5 km, biaxial ellipsoid with ax = 2ay = 2az = 5.2 km and triaxial ellipsoid ax = 2ay = 4az = 5.2 km. As shown in Fig. 8, the evolutionary trend of the triaxial ellipsoid better matches the observational data, confirming our previous hypothesis regarding the solar illumination area, meaning that the farther the comet is before the perihelion, the larger the region with higher temperature.
In this work, we developed ThermoONet, a DeepONet-based neural network for modelling cometary activity. Due to the high-dimensional parameter space in cometary thermophysical model, we tailored the architecture of DeepONet by removing

[Figure: Fig. 8 shows preliminary fitting results. The fixed parameters are ϵ = 1, ω = 1.74 × 10−4 rad s−1 (the rotation period is uncer-]

Article number, page 9 of 13

3.56 2.24 1.3 2.33 3.66 Heliocentric Distance (au)
UTC
Fitting from SA and BGD
Observations

[Figure: Fig. 7. Fitting the global water production rate of 67P as a function of time. The blue rectangles represent the observation data from Läuter et al. (2020), and the red line corresponds to the best fit curve achieved by combining ThermoONet with the optimization algorithm. The black dashed line indicates the epoch of the perihelion. A detailed description of the observation data and sources thereof can be found in Läuter et al. (2020).]

1.28 1.12 1.03 1.03 1.13 Heliocentric Distance (au)
ax = ay = az ax = 2ay = 2az ax = 2ay = 4az 1998 2005 2012 2018
56.57 33.72 11.56 12.79 34.65 Days Relative to Perihelion

[Figure: Fig. 8. Fitting the global water production rate of 21P as a function of days from perihelion by applying ThermoONet to different shapes. The black line corresponds to a sphere model, the blue line is a ellipsoid model with ax = 2ay = 2az and the red line is a ellipsoid with ax = 2ay = 4az. Other parameters are as stated in Table 3. The scatter points with different colors and shapes represent observational data at different apparitions (Combi et al. 2019), where purple circles from 1998, blue triangles from 2005, green squares from 2012, and black asterisks from 2018. The detailed description about the observation data and sources thereof can be found in Combi et al. (2019).]

[Table: Table 3. Parameters for fitting the water curve of 21P.]
performance, including its computation time, accuracy, and
generalization ability. The results show that T hermoONet de-
ployed on GPU has the highest efficiency, and generates the
global sublimation flux approximately six orders of magni-
tude faster than using numerical simulation. The accuracy of
T hermoONet varies with parameters, with an average of around
2%. T hermoONet can be successfully applied to irregular
comets as exemplified by comet 67P, with the water production
rate curve closely matching the numerical simulation, demonstrating strong generalization ability and practicability. We tested the capability of ThermoONet in computationally demanding tasks by fitting global water production rate curves of comets using global optimization algorithms. By applying Simulated Annealing, we successfully fit the observed water production rate curve of comet 67P derived with Rosetta mission data, and obtained a set of optimized physical parameters of 67P. Additionally, we fit the water curve of comet 21P to demonstrate the capability of combining ThermoONet with trial-and-error testing. Although limited knowledge is available for 21P, we managed to reconstruct the unique trend observed in its water production rate by adjusting the shape, rotation, and thermal parameters. We anticipate a broad range of application for ThermoONet in various research topics concerning small body activities. In addition to analyzing large-scale and high-resolution data analysis, it can also serve as an efficient model to be embedded into more complex physical systems.
Article number, page 11 of 13

Table A.1. Parameters and their reference values used in the parameter sensitivity analysis.
p1 (W m−2) 64 p2
1 p3 (mm) 5
p4 (J m−3 K−1) 5 × 105 p5 (h) 10
p6 (W m−1 K−1) 2× 10−3
p7 (W m−1 K−1) 2× 10−3 p8 (%) 10
trolled variable approach with a fixed radiation flux as an ex-
ample. When modifying a single parameter, the remaining pa-
rameters maintain their reference values specified in Table A.1.
tation period. Fig. A.1 shows the resultant variations in temper-
primarily influences the value range of temperature distributions,
whereas the remaining parameters affect the shape of tempera-
ture curves within this established range.

Acknowledgements. The authors thank Prof. Groussin for the insightful review comments that helped to significantly improve the manuscript. The authors thank Dr. Xuanyu Hu for extensive discussions on the thermophysical modelling for comets. XS thanks members of the ISSI International Team "Timing and Processes of Planetesimal Formation and Evolution" for inspirational discussions. This work is financially supported by the National Natural Science Foundation of China (No. 12233003 and 12073011).
Assessing Interstellar Flight Challenges and Prospects
NASA Grant No. NNX17AE81G First Year Report Prepared by:
Marc G. Millis, Jeff Greason, Rhonda Stevenson Tau Zero Foundation Business Office: 1053 East Third Avenue Broomfield, CO 80020 Prepared for:
Millis 2018 Grant NNX17AE81G_for_CR.docx

pg 1 of 69
Progress toward developing an evaluation process for interstellar propulsion and power options is described. The goal is to contrast the challenges, mission choices, and emerging prospects for propulsion and power, to identify which prospects might be more advantageous and under what circumstances, and to identify which technology details might have greater impacts. Unlike prior studies, the infrastructure expenses and prospects for breakthrough advances are included. This first year's focus is on determining the key questions to enable the analysis. Accordingly, a work breakdown structure to organize the information and associated list of variables is offered. A flow diagram of the basic analysis is presented, as well as more detailed methods to convert the performance measures of disparate propulsion methods into common measures of energy, mass, time, and power. Other methods for equitable comparisons include evaluating the prospects under the same assumptions of payload, mission trajectory, and available energy. Missions are divided into three eras of readiness (precursors, era of infrastructure, and era of breakthroughs) as a first step before proceeding to include comparisons of technology advancement rates. Final evaluation "figures of merit" are offered. Preliminary lists of mission architectures and propulsion prospects are provided.
ACS Attitude Control System NIAC NASA Innovative Advanced Concepts AI Artificial Intelligence PMAD Power Management and Distribution BPP Breakthrough Propulsion Physics RF Radio Frequency (Electromagnetic Waves) C&DH Control and Data Handling RP-OM Received Power – Onboard Reaction Mass CY Calendar Year RP-XM Received Power – External Reaction Mass ESO European Southern Observatory RTG Radioisotope Thermal Generator FTL Faster Than Light SMTD Space Mission Technology Directorate GNC Guidance Navigation and Control SRL Scientific Readiness Levels IP-OM Internal Power – Onboard Reaction Mass TRL Technology Readiness Levels IP-XM Internal Power – External Reaction Mass TVIW Tennessee Valley Interstellar Workshop JBIS Journal of the British Interplanetary Society WBS Work Breakdown Structure
Millis 2018 Grant NNX17AE81G_for_CR.docx

pg 5 of 69
This work was supported by NASA under grant No. NNX17AE81G, under the direction of Dr. Jay Falker, Jason Derleth, and Dr. Mike LaPointe of NASA Headquarters. The authors would like to acknowledge their encouragement and support for this effort.
Additional assistance came from Jim Gilland of the Ohio Aerospace Institute, Paul Gilster of the Tau Zero Foundation, Les Johnson of NASA, and the staff who helped run the 2017 Tennessee Valley Interstellar Workshop.
Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Aeronautics and Space Administration.
pg 2 of 69

Millis 2018 Grant NNX17AE81G_for_CR.docx TABLE OF CONTENTS LIST
of	
  Information	
  from	
  Subject	
  Matter	
  Experts............................ 62 10.2. Analysis	
  Portal................................................................................................................................. 63 10.3. General	
  Audience	
  Website .......................................................................................................... 63 10.4. Concluding	
  Remarks ..................................................................................................................... 63
11.	
   REFERENCES..............................................................................................................................64
11.1. Sequentially	
  Cited........................................................................................................................... 64 11.2. Bibliography..................................................................................................................................... 65
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Millis 2018 Grant NNX17AE81G_for_CR.docx | Table 1.