Figure 1.
Figure 2.
Figure 3.
Figure 4.
Figure 5.
Periodic inputs selected for the model and their ranges for dataset generation
| DOY Sin and Cos | Seconds Sin and Cos | Long Sin and Cos | LST Sin and Cos | Lat Sin | Lat Cos |
|---|---|---|---|---|---|
| [−1;1] | [−1;1] | [−1;1] | [−1; 1] | [−1;1] | [0;1] |
Quantile summary (K) of temperature outputs used for network training_ Exospheric and altitude temperature quantile data are the same in taken precision_
| Min | 5th | 25th | 50th | 75th | 95th | Max | |
|---|---|---|---|---|---|---|---|
| Temp. | 4.51e+02 | 8.41e+02 | 1.03e+03 | 1.19e+03 | 1.37e+03 | 1.64e+03 | 2.24e+03 |
Final relative percentage loss for each restored number density output_
| He | O | N2 | O2 | Ar | H | N | O (anom) |
|---|---|---|---|---|---|---|---|
| 0.171% | 0.414% | 0.560% | 0.648% | 0.850% | 0.137% | 0.401% | 0.168% |
Neural network structure_ Biases enabled in each layer_
| Layer index | Layer type | Input shape | Output shape | Parameters | Activation function |
|---|---|---|---|---|---|
| 0 | Dense | 14 | 64 | 960 | Hardswish |
| 1 | Dense | 64 | 64 | 4160 | Hardswish |
| 2 | Dense | 64 | 64 | 4160 | Hardswish |
| 3 | Dense | 64 | 64 | 4160 | Hardswish |
| 4 | Dense | 64 | 10 | 650 | No activation |
| Total parameter numbers | 14 090 | ||||
Quantile summary (cm−3) of neutral number-density outputs used for network training_ O(anom) is anomalous atomic oxygen_
| He | O | N2 | O2 | Ar | H | N | O (anom) | |
|---|---|---|---|---|---|---|---|---|
| Min | 2.99e+02 | 1.25e-08 | 1.19e-23 | 3.42e-29 | 1.11e-40 | 1.37e+03 | 6.84e-10 | 3.58e+01 |
| 5th | 6.63e+04 | 5.70e+01 | 2.75e-05 | 1.24e-08 | 2.23e-14 | 8.56e+03 | 4.05e+00 | 1.00e+03 |
| 25th | 2.16e+05 | 5.02e+03 | 1.05e-01 | 1.18e-04 | 3.29e-09 | 1.67e+04 | 3.58e+02 | 4.57e+03 |
| 50th | 4.76e+05 | 1.01e+05 | 2.52e+01 | 5.58e-02 | 9.26e-06 | 2.96e+04 | 7.40e+03 | 1.38e+04 |
| 75th | 1.08e+06 | 2.08e+06 | 5.06e+03 | 2.40e+01 | 1.86e-02 | 5.63e+04 | 1.16e+05 | 4.03e+04 |
| 95th | 2.83e+06 | 3.77e+07 | 8.74e+05 | 7.98e+03 | 3.17e+01 | 1.56e+05 | 2.49e+06 | 1.69e+05 |
| Max | 1.04e+07 | 4.45e+08 | 9.67e+07 | 2.19e+06 | 1.40e+05 | 9.57e+06 | 2.65e+08 | 2.35e+06 |
Non-periodic inputs selected for the model and their ranges for dataset generation before normalization
| Alt, km | F10.7, sfu | F10.7 81a, sfu | Ap, nT |
|---|---|---|---|
| [500;1500] | [56;504] | [61;300] | [0;208] |
Final relative percentage loss for restored temperatures and total mass density
| Temp. exospheric | Temp. at height | Total mass density (ρTotal) |
|---|---|---|
| 0.0469% | 0.0475% | 0.245% |
Evaluation times of compared models for different data_ M stands for million_
| Number of NRLMSISE calculations | C++ NRLMSISE time, seconds | Neural network NRLMSISE time, seconds | ||
|---|---|---|---|---|
| CPU 1 thread | CPU 1 thread | CPU 12 threads | GPU CUDA | |
| 100 000 | 0.262 (1× reference) | 0.087 (3.0× boost) | 0.079 (3.3× boost) | 0.142 (1.85× boost) |
| 500 000 | 1.314 (1× reference) | 0.310 (4.2× boost) | 0.192 (6.8× boost) | 0.143 (9.19× boost) |
| 1M | 2.566 (1× reference) | 0.596 (4.3× boost) | 0.324 (7.9× boost) | 0.157 (16.3× boost) |
| 1M × 10 times | 25.598 (1× reference) | 5.646 (4.5× boost) | 2.709 (9.5× boost) | 0.166 (154.2× boost) |
| 1M × 100 times | 258.448 (1× reference) | 57.424 (4.5× boost) | 26.68 (9.7× boost) | 1.034 (250.0× boost) |