Towards the Habitable Worlds Observatory: Retrieval of Reflection Spectra from Evolving Earth Analogues using 1D CNNs

The gist The one-dimensional convolutional neural network (1D CNN), trained on over one million synthetic, noise-injected spectra simulating Archean, Proterozoic, and Modern Earth analogs, can rapidly retrieve key planetary parameters and molecular abundances from reflection spectra to serve as a mission-ready retrieval engine for direct-imaging missions like the Habitable Worlds Observatory (HWO) <ref:2508.00076#pg14>.

Methodology

The synthetic reflection spectra dataset was generated using NASA’s PSG2, which is a radiative transfer model that synthesizes planetary spectra by coupling atmospheric radiative transfer equations with high-resolution spectroscopic databases. Building the training set involved two integrated steps: (1) Habitability screening and (2) Sample realization <ref:2508.00076#pg5>. The dataset was generated using PSG, which forward-modeled spectra as observed by LUVOIR-B and HabEx/SS at low spectral resolution <ref:2508.00076#pg14>. The synthetic reflection spectra dataset was generated using NASA’s PSG2, which is a radiative transfer model that synthesizes planetary spectra by coupling atmospheric radiative transfer equations with high-resolution spectroscopic databases.

Data Generation and Filtering

The training set comprised 1,086,914 exoplanets that met all the requirements after imposing physical and observational filters. This selection process involved applying physical criteria to ensure long-term atmospheric retention and the potential for surface liquid water, followed by sample realization. The noise is modeled as Gaussian, and any spectrum for which the noise at any wavelength exceeds the 3sigma threshold is rejected. Out of more than 3.7 million computed samples, only 1,086,914 exoplanets met all the requirements, forming the final dataset used in this work.

Model Architecture and Training

The model adopts a one-dimensional Convolutional Neural Network (1D CNN) architecture designed to capture spectral correlations along the wavelength axis. The network uses residual convolutional blocks, where each block consists of two convolutions with 1-D filters, each convolution followed by batch normalization (BN), the SiLU activation function, and a spatial dropout (SD1D) mask. To address broader dependencies, the network is followed by a multi-head self-attention (MHA) layer. The data flow ends with dense layers that branch into three heads for Physical Features (PF), Main Chemical Features (MCF), and Other Chemical Features (OCF). Normalization is applied using three complementary scaling strategies tailored to the statistical properties of spectra, PF targets, and MCF/OCF targets.

Retrieval Performance and Interpretation

The model performs best where spectral signatures are prominent, such as for CH4 and CO2 in the Archean era, but performance degrades as spectral lines weaken. Planetary radius, gravity, and surface pressure are recovered with low bias and dispersion-limited scatter. The model correctly outputs numerically negligible values for true zero-abundance cases, demonstrating its ability to avoid false positives. Integrated Gradients confirm that the model bases its predictions on physically meaningful features, including the Fraunhofer A band for O2 and the Hartley–Huggins band for O3.

Uncertainty and Credibility

Uncertainty estimation is performed via Monte Carlo Dropout, which transforms the deterministic model into a stochastic ensemble by keeping dropout layers active during inference. The analysis of the Monte Carlo Dropout posteriors reveals that while the fraction of test points inside the predicted interval increases monotonically with sigma, the coverage remains consistently below the ideal Gaussian level, especially for temperature. Credibility curves show that O3 proves almost indifferent to stellar type or distance, maintaining a probability greater than 0.85 across the full explored range of log-abundances.

Conclusion and Limitations

The CNN establishes the architecture as a viable and practical alternative to traditional Bayesian methods, achieving inference in mere seconds for 5,000 Monte Carlo Dropout samples on a single RTX 2060 GPU. The study's main limitations stem from the simplifications made in the training set, specifically assuming a vertically uniform atmospheric composition and a complete absence of clouds or hazes. Future work must incorporate vertical atmospheric gradients and the effects of multiple scattering by clouds and hazes. The CNN is capable of processing direct-imaging spectra with HWO on an operational cadence.

How it works

The model simultaneously infers six molecular abundances (including biosignatures O2 and O3) along with radius, gravity, surface pressure, and temperature. Inference on unseen test data is performed via Monte Carlo Dropout, enabling uncertainty estimation across thousands of realizations within seconds. The network performs best where spectral features are prominent, accurately recovering CH4 and CO2 in Archean atmospheres and O2 and O3 in Modern cases, while avoiding false positives and outputting near-zero abundances in scenarios of true absence such as Archean O2 and O3.

Key Findings

[The model simultaneously infers six molecular abundances (including biosignatures O2 and O3) along with radius, gravity, surface pressure, and temperature]

[Inference on unseen test data is performed via Monte Carlo Dropout, enabling uncertainty estimation across thousands of realizations within seconds]

[The network performs best where spectral features are prominent, accurately recovering CH4 and CO2 in Archean atmospheres and O2 and O3 in Modern cases, while avoiding false positives and outputting near-zero abundances in scenarios of true absence such as Archean O2 and O3]

How it works

The CNN architecture uses residual convolutional blocks where each block consists of two convolutions with 1-D filters, each convolution followed by batch normalization (BN), the SiLU activation function, and a spatial dropout (SD1D) mask. To address broader dependencies, the network is followed by a multi-head self-attention (MHA) layer. The data flow ends with dense layers that branch into three heads for Physical Features (PF), Main Chemical Features (MCF), and Other Chemical Features (OCF).

Key Findings

[The network performs best where spectral features are prominent, accurately recovering CH4 and CO2 in Archean atmospheres and O2 and O3 in Modern cases, while avoiding false positives and outputting near-zero abundances in scenarios of true absence such as Archean O2 and O3]

How it works

Integrated Gradients shed light on the model’s decision-making process by attributing the prediction for each gas to individual input features (i.e., wavelengths). For Modern Earth, the network correctly weights the Fraunhofer A band for O2 and the Hartley–Huggins UV band for O3. Under Proterozoic conditions, the LUVOIR-B retrieval path effectively nullifies the importance of O2/O3, whereas HabEx/SS still assigns some weight to O2 in the UV.

Key Findings

[Integrated Gradients shed light on the model’s decision-making process by attributing the prediction for each gas to individual input features (i.e., wavelengths)]

[For Modern Earth, the model correctly weights the Fraunhofer A band for O2, and the Hartley–Huggins UV band for O3]

[Under Proterozoic conditions, the LUVOIR-B retrieval path effectively nullifies the importance of O2/O3, whereas HabEx/SS still assigns some weight to O2 in the UV]

How it works

Credibility curves help to quantify the detection horizons by defining a credibility probability Pε(by) that is greater than 1-δ. For O3, every slice maintains Pr(error ≤ 0.5) ≳ 0.85 across the full explored range of log-abundances.

1. Precise molecular abundance retrieval for biosignatures: The 1D CNN can simultaneously infer six molecular abundances (including biosignatures O2 and O3) along with radius, gravity, surface pressure, and temperature. This allows the system to accurately distinguish between true absence and low-abundance scenarios in unseen data.

2. Uncertainty quantification via Monte Carlo Dropout: The system can estimate parameter uncertainties by performing T stochastic forward passes and calculating the predictive variance, providing a measure of model confidence across thousands of realizations within seconds.

3. Physical constraint enforcement through tailored normalization: The system employs three complementary scaling strategies, including the Hellinger transform for chemical species, to handle distributions spanning up to 150-fold enhancement over the baseline value, ensuring that true zeros are discarded before taking the logarithm.

4. Feature importance mapping for diagnostic identification: Using Integrated Gradients, the system can map which spectral features are most influential, such as identifying that the network assigns greater importance to the Fraunhofer A band for O2 in Modern Earth cases.

5. Credibility horizon assessment: The system provides a quantitative measure of trust by calculating the credibility probability, defining a limit where photometric noise, rather than model bias, becomes the limiting factor.

The Habitable Worlds Observatory (HWO) will characterize Earth-like exoplanets from low-resolution reflected-light spectra. To assess how atmospheric evolution shapes what can be recovered, we trained a convolutional neural network on 109,945 spectra generated with the Planetary Spectrum Generator for Archean, Proterozoic, and Modern atmospheres under LUVOIR-B and HabEx/SS observing assumptions, separating the contributions of observational noise and model variability. We find that recovery depends jointly on abundance and spectral structure. Across eras, O 2 recovery weakens in Proterozoic atmospheres and CH 4 becomes reliable only when abundant, while an isolated UV band yields robust Modern O 3 recovery (R 2 0.98) despite poor Modern CH 4 recovery (R 2=0.32 - 0.35). Without being supplied feature locations, the network assigns 58 - 71% of total attribution to visible wavelengths, while the ultraviolet remains decisive for O 3 and the near-infrared for CH 4 and CO 2. Aggregate retrieval leverage declines beyond approximately 1.7,μ m, supporting a practical long-wavelength boundary in this setup. These wavelength dependencies also shape detectability. At baseline noise, 83 - 85% of Modern O 2 cases satisfy a 3σ criterion, while Proterozoic O 2 remains below 50% when noise is halved and Modern CH 4 remains below 3σ as observational noise approaches zero because model uncertainty caps its significance. Together, these results imply molecule-specific priorities for HWO trade studies. Low-abundance O 2 retains considerable leverage from improved observational quality while motivating better inference, whereas at the 1,000-hour benchmark O 3 and Modern CH 4 show predominantly model-associated uncertainty in these networks, motivating broader training coverage and improved uncertainty calibration.