# 45th place solution

NeurIPS Ariel Data Challenge 2025: A Hybrid Approach to Exoplanet Transit Spectroscopy
We express our gratitude to the organizers and participants of the NeurIPS Ariel Data Challenge 2025 for creating this valuable scientific competition.
Executive Summary
Notebook:
[https://www.kaggle.com/code/devadevam/fork-of-fork-of-fork-of-fork-of-notebookfc5-e6859d](https://www.kaggle.com/code/devadevam/fork-of-fork-of-fork-of-fork-of-notebookfc5-e6859d)
main ideas:
estimating sigma as difference between the base non-ML model's prediction and the target value of mu (check the
SafeMLCalibrator
class)
Astrophysical features through dimensional analysis (the
add_interaction_features
function)
atmospheric physics-based features: equilibrium temperature modeling, stellar insolation calculations, Rayleigh scattering slope analysis, and molecular absorption signatures (the
add_atmospheric_physics_features
function)
Core Methodology
Our solution architecture employs a multi-layered approach combining:
Foundation Layer
: Analytical transit modeling providing physically-motivated baseline predictions
Enhancement Layer
: Machine learning calibration for systematic bias correction and prediction refinement
Feature Layer
: Physics-informed engineering incorporating stellar and atmospheric physics
Validation Layer
: Robust uncertainty quantification with proper statistical calibration
New ideas first:
Feature Engineering
Temporal and Spectral Characterization
We extract comprehensive statistical descriptors from preprocessed time series:
Statistical Moments
: Complete characterization including central tendencies, dispersion measures, asymmetry (skewness), and tail behavior (kurtosis)
Distributional Features
: Multi-percentile analysis (5th, 25th, 50th, 75th, 95th percentiles) and root-mean-square calculations
Temporal Correlations
: Autocorrelation function analysis at multiple lag intervals for time-domain pattern recognition
Frequency Domain Analysis
: Fast Fourier Transform decomposition with energy partitioning across low, mid, and high-frequency bands, spectral centroid computation, and zero-crossing rate analysis
Astrophysical Feature Engineering
We incorporate domain-specific features derived from fundamental stellar and planetary physics:
Orbital Mechanics
: Impact parameter calculations, orbital velocity estimates, mean motion derivations, and Keplerian mass-radius relationships
Atmospheric Physics
: Equilibrium temperature modeling, stellar insolation calculations, Rayleigh scattering slope analysis, and molecular absorption signatures (H₂O, CO₂, CO, CH₄)
Cross-Parameter Interactions
: Systematically constructed interaction terms, logarithmic transformations for scale invariance, and trigonometric mappings of orbital geometry
Spectroscopic Analysis Features
Drawing from established atmospheric retrieval methodologies:
Spectral Modeling
: Blackbody correlation analysis and continuum characterization
Morphological Analysis
: Spectral slope, curvature measurements, and absorption feature detection
Coherence Metrics
: Transmission spectrum consistency analysis across wavelength channels
Multi-Scale and Quality Metrics
Hierarchical Analysis
: Feature computation across multiple smoothing scales (3, 7, 15, 31 data points)
Signal Quality
: Transit signal-to-noise ratio quantification and V-shaped morphology assessment
Data Integrity
: Completeness scoring and quality assurance metrics
Machine Learning Enhancement Framework
Safe ML Calibrator Design
Our primary methodological contribution centers on conservative machine learning integration:
Scale Calibration Module
:
Linear regression framework:
depth_calibrated = α + β × depth_analytical
Rigorous out-of-fold cross-validation preventing information leakage
Spectral Shape Calibration
:
Principal Component Analysis on normalized transmission spectra
Regularized regression on principal components using Ridge methodology
Full spectral reconstruction with uncertainty propagation
Uncertainty Calibration System
:
Instrument-specific Ridge regression models for FGS and AIRS uncertainty estimation
Geometric blending in logarithmic space for numerical stability
Integration time weighting for observation quality assessment
Statistical Regularization
Feature Curation
: Systematic removal of constant and near-constant predictors
Multicollinearity Management
: Correlation-based pruning with threshold τ = 0.95
Selection Methodology
: Permutation importance-based feature ranking
Conservative Blending
: Strictly constrained combination weights (α ≤ 0.3, β ≤ 0.3, γ = 0.55)
Quality-Aware Training Protocol
We implement sophisticated quality assessment for optimal training sample weighting:
Malformation Detection
: Automated identification of corrupted transit signals
Signal-to-Noise Quantification
: Comprehensive SNR-based scoring methodology
Adaptive Cross-Validation
: Quality-weighted fold construction for robust model evaluation
Uncertainty Quantification
Sigma is estimated as the difference between base model's extimation of mu and the target value.
Baseline Uncertainty Modeling
FGS Photometric Uncertainties
:
In-transit versus out-of-transit variance estimation with robust statistical measures
Dataset-wide median scaling with conservative clipping bounds
AIRS Spectroscopic Uncertainties
:
Wavelength-dependent variance modeling accounting for detector characteristics
Integration time normalization with conservative scaling factors
Uncertainty Estimation
Predictive Modeling
: Ridge regression on engineered uncertainty features
Robust Combination
: Geometric blending with baseline uncertainty estimates
Planet-Specific Calibration
: Optimal uncertainty multiplier (c*) determination
Physical Constraints
: Spectral smoothness requirements ensuring realistic uncertainty profiles
Model Training and Validation
Cross-Validation Architecture
Stratification Strategy
: 8-fold cross-validation with quality-aware stratification
Sample Weighting
: Quality-based importance weighting during training
Unbiased Evaluation
: Strict out-of-fold prediction protocols
Independent Validation
: Hold-out testing on reserved training data
Hyperparameter Optimization
Regularization Strategy
: Conservative Ridge penalties (α = 0.5-1.0) preventing overfitting
Dimensionality Control
: Limited principal component retention (2-4 components)
Safety Constraints
: Maximum blending weights capped at 0.3 for methodological conservatism
Data Processing Pipeline
This part has been mostly taken from this public code:
[https://www.kaggle.com/code/antonsibilev/very-fast-1h-optimized-nb-with-0-333](https://www.kaggle.com/code/antonsibilev/very-fast-1h-optimized-nb-with-0-333)
Instrumental Calibration
AIRS-CH0 Spectroscopic Data:
Applied instrument-specific linear correction coefficients to mitigate systematic offsets
Implemented correlated double sampling (CDS) for readout noise suppression
Performed wavelength-dependent flat field correction with hot pixel identification and masking
Executed robust statistical binning with iterative sigma-clipping for outlier rejection
Applied adaptive smoothing algorithms with phase-aware processing to preserve transit signals while reducing noise
FGS1 Photometric Data:
Optimized CDS processing for single-channel detector characteristics
Implemented spatial binning across detector arrays to improve signal-to-noise ratio
Established comprehensive quality assurance protocols for data completeness validation
Transit Signal Processing
Noise Reduction
: Savitzky-Golay filtering with optimized window sizes and polynomial orders
Feature Detection
: Piecewise polynomial fitting algorithms for precise ingress/egress identification
Phase-Aware Processing
: Adaptive transit masking that preserves astrophysical signals
Quality Assessment
: Multi-metric evaluation system for identifying low signal-to-noise or malformed transits
Analytical Transit Modeling Framework
Mathematical Formulation
An extended transit model that captures the fundamental physics of planetary occultation:
F() = F₀() × [ - δ × ()]
Where:
F₀(t) represents the stellar flux continuum modeled through polynomial detrending
δ quantifies the wavelength-dependent transit depth
T(t) describes the normalized transit light curve profile
Optimization Strategy
Parameter Estimation
: Nelder-Mead simplex optimization with robust convergence criteria
Constraint Management
: Delta-margin constraints preventing boundary effects and ensuring physical validity
Phase Analysis
: Gradient-based algorithms for precise transit timing determination
Systematic Correction
: Third-order polynomial detrending for instrumental and stellar variability removal