Anin Puthukkudy

This project explores emulating the 6SV (Second Simulation of the Satellite Signal in the Solar Spectrum) radiative transfer simulator at the Top-Of-Atmosphere (TOA). The goal is to train a surrogate deep neural network model that can rapidly emulate radiative transfer computations across a wide range of aerosol types and loadings, replacing computationally expensive physics-based simulations with near-instantaneous neural network inference.

The primary focus is on producing the apparent reflectance and Degree of Linear Polarization (DoLP) at the TOA. To achieve this, we created a 16-million datapoint training dataset using Latin Hypercube Sampling (LHS) over the full range of sun-satellite geometry, aerosol properties, and surface properties. The dataset is generated separately for Land and Ocean surfaces, and individual surrogate models are trained for each surface type.

The 6SV-NN training experiments showed that the largest gains in emulator accuracy came from improving the training setup rather than making major changes to network size. Across the saved experiments, the most important factors were increasing dataset size, using physically meaningful input features, and choosing loss functions and target transforms that matched the behavior of the radiative transfer outputs. The final workflow consistently used a moderate multilayer perceptron architecture (15-256-256-128-64-3), which suggests that model capacity was sufficient and that later improvements came mainly from better data representation and optimization strategy.

For land cases, increasing the amount of training data produced the clearest and most consistent improvements. In the multi-wavelength setup, performance improved from an RMSE of about 2.50×10^-3 with 1M samples to 7.87×10^-4 with 4M samples, and then to a best value of 5.15×10^-4 with the 16M-sample configuration. At the same time, the fraction of predictions within 0.002 absolute error increased from 47.1% at 1M samples to 98.3% at 4M, and to 99.7% in the best 16M run. The best land models also used engineered physical inputs, including angular terms, aerosol descriptors, wavelength, and BRDF parameters (k₀, k₁, k₂), indicating that feature design was an important part of the final performance.

Ocean cases were more difficult and highlighted a different limitation. Larger datasets still helped, with ocean RMSE improving from about 7.05×10^-3 in an early 200k single-wavelength setup to 2.57×10^-3 for the 4M multi-wavelength configuration, and further to 2.23×10^-3 in a 16M multi-wavelength run. However, ocean accuracy did not improve as uniformly as land, because ocean reflectances include many very small values that make relative error unstable. To address this, later ocean experiments added domain-specific features such as pigment concentration, wind speed, and wind azimuth, along with a log-transformed target of the form log(R + 10^-4). This change greatly reduced mean relative error from very large values to about 7–9% in the log-target runs, though with some tradeoff in absolute RMSE.

Overall, the experiments showed that the most effective path to improving 6SV-NN performance was not a larger or deeper neural network, but a better formulation of the problem. For land, the combination of larger datasets, physics-informed features, and robust tail-aware training produced excellent emulator accuracy. For ocean, domain-specific features and log-target training were necessary to stabilize relative error. The main lesson is that feature engineering, data scaling, and target/loss design were the dominant drivers of accuracy improvement in the 6SV-NN training workflow.

Architecture & Initial Results

Figure 1: 6SV-NN emulator architecture (15-256-256-128-64-3). Inputs include sun-satellite geometry (angular terms), aerosol properties (AOD, SSA, size distribution), surface BRDF parameters (k₀, k₁, k₂), and wavelength. Outputs are I (apparent reflectance), DoLP (Degree of Linear Polarization), and AoLP (Angle of Linear Polarization).

Total Polarization Ratio

Figure 2a: Truth vs. prediction for total polarization ratio. Left: 1:1 scatter plot (RMSD = 0.001, N = 10,000, 99.9% within ±0.003). Right: Difference plot (MAE = 4.62×10^-4, Max|err| = 4.80×10^-3).

Figure 2b: Residual distribution (NN − mini6sv) for total polarization ratio. Near-zero centered distribution with MAE = 4.62×10^-4.

Apparent Reflectance

Figure 3a: Truth vs. prediction for apparent reflectance. Left: 1:1 scatter plot (RMSD = 0.001, MAPD = 0.09%, Bias = −0.06%, 100% within ±0.5% rel.). Right: Difference plot (MAE = 5.00×10^-4, Max|err| = 7.16×10^-3).

Figure 3b: Residual distribution (NN − mini6sv) for apparent reflectance. Near-zero centered distribution with MAE = 5.00×10^-4.

Building on the surrogate modeling approach, this project employs the GRASP (Generalized Retrieval of Aerosol and Surface Properties) radiative transfer code instead of 6SV to simulate TOA observations. The key distinction is that the GRASP RT forward model simulates the full polarimetric signal — the Stokes parameters I, Q, and U — at the Top-Of-Atmosphere, enabling complete characterization of both intensity and polarization state of the scattered radiation. This surrogate model is particularly suited for multi-angle polarimetric retrievals from instruments such as HARP2 and SPEXOne aboard NASA's PACE satellite, where computational speed of the forward model is a critical bottleneck.

The most important result came from the March 2026 hyperparameter sweep on a 2M-sample land dataset. That search reduced the best validation loss from 0.012198 to 0.010494, about a 14% improvement. Secondary accuracy metrics moved in the same direction: I<1% improved from 12.5% to 13.8%, P<1% improved from 11.0% to 12.4%, and test I(rel≤1%) improved from 12.57% to 13.61%.

The strongest lesson was that a smaller and cleaner model worked better than a larger one. The baseline hidden-layer layout of 512-256-256-128 was outperformed by a compact 256-256-128-64 architecture, which improved validation loss by another 4.7% after batch-size tuning. Larger alternatives such as 1024-512-256-128 and 512-512-512-256-128 were clearly worse, and enabling residual connections also hurt performance significantly. This suggests the model was somewhat over-parameterized for this training regime, and that extra depth or complexity did not translate into better generalization.

On the optimization side, smaller batch size helped. Reducing batch size from 2048 to 1024 gave the single largest early gain, improving validation loss by 6.25%. Larger batch sizes did not help: 4096 was slightly worse and 8192 was much worse. The learning-rate sweep also showed that the original LR=0.001 was already near-optimal. Tested alternatives (0.003, 0.0005, 0.0003) all regressed.

In terms of feature representation, the clearest win was Fourier features. Enabling FOURIER=32 improved validation loss by another 3.7% on top of the better batch size and smaller architecture. A later full-dataset follow-up confirmed this was not just a small-subset effect: FOURIER=32 beat FOURIER=64 throughout training, and by epoch 30 the full-data run reached val=0.00662, with I<1%=20.5% and P<1%=19.0%, substantially better than the earlier 2M-sample experiments. This strongly suggests that moderate Fourier expansion helps the network represent angular structure efficiently, but more Fourier capacity is not necessarily better.

The loss design also mattered. Keeping loss_weights="1 2 1 1" was important — changing to uniform weights (1 1 1 1) caused the largest regression in the sweep, about 48% worse validation loss. That indicates the extra emphasis on polarized radiance was important for overall model quality. Likewise, switching activation from SiLU to GELU hurt performance, so the simpler baseline activation remained the better choice.

Several feature-engineering and target-definition changes were scientifically important. Adding sphere_frac as an input fixed a missing physical dependency and restored sensitivity in Jacobians. Moving to log(P_rad) and relative polarization metrics improved target conditioning and made evaluation more physically meaningful.

Overall, the project learned that better GRASP-NN-RT performance came from better conditioning and better inductive bias, not from a larger network. The best tested recipe was: LR=0.001, BATCH_SIZE=1024, hidden layers 256-256-128-64, ACTIVATION=SiLU, FOURIER=32, no residual connections, and loss_weights="1 2 1 1". The broad conclusion is that compact architecture, moderate Fourier features, balanced loss weighting, and physically aligned targets gave the most reliable gains in accuracy.

Architecture & Training Configuration

Figure 1: GRASP-NN-RT architecture. Inputs pass through Fourier Feature Expansion (F=32), then through hidden layers (256→256→128→64, SiLU activation). Outputs are Stokes parameters I, Q, and U. Training uses LR=0.001, batch size=1024, and weighted loss (1:2:1:1).

Predicted vs. True (Transformed & Recovered Stokes)

Figure 2: Predicted vs. True for transformed and recovered Stokes parameters. Top row: transformed outputs — log_I, pol_rad, sin(2χ), cos(2χ), where χ is the angle of linear polarization (AoLP = ½ arctan(U/Q)), transformed to sin/cos to eliminate the discontinuity at ±90° and provide a smooth, bounded representation for the network. Bottom row: recovered physical Stokes parameters (I, Q, U) and degree of polarization (P). N = 1,818,242 test samples. I within ±0.5% relative: 24.38%, Q within ±0.5%: 15.28%, U within ±0.5%: 13.13%.