Surrogate-Accelerated Bayesian Inversion for Exoplanet Interior Characterization

TL;DR

The paper tackles the computational bottleneck in Bayesian exoplanet interior inference caused by expensive forward models. It introduces a surrogate-accelerated framework using polynomial chaos-Kriging (PCK) trained on a manageable number of forward-model evaluations and embedded within an Adaptive Metropolis MCMC to achieve significant speedups while maintaining rigorous uncertainty quantification. Validation across 1,000 synthetic cases and real targets like TOI-270 d demonstrates high surrogate fidelity (R^2 > 0.99) and credible intervals with near-nominal coverage, with speedups of approximately 2–3 orders of magnitude (days to minutes). The approach enables population-scale interior studies, rapid adaptation to model updates, and seamless integration of atmospheric constraints from upcoming missions, marking a substantial advance in exoplanet interior characterization.

Abstract

Characterizing the interior structure of exoplanets is an inverse problem often solved using Bayesian inference, but this approach is hampered by the high computational cost of planetary structure models. To overcome this barrier, we present a robust framework that accelerates inference by replacing the computationally expensive physics-based forward model with a fast polynomial chaos-Kriging (PCK) surrogate directly within a Markov chain Monte Carlo (MCMC) sampling loop. We rigorously validate our approach using a suite of tests, including a direct comparison against a benchmark MCMC inference using the full forward model, and a large-scale coverage study with 1000 synthetic test cases to demonstrate the statistical reliability of our inferred credible intervals. Our surrogate-assisted framework achieves a computational speedup of over 2 orders of magnitude (factor of $\sim$320), reducing single-CPU inference times from days to minutes. This efficiency is achieved with a surrogate that requires only a few hundred forward model evaluations for training \rev{for a single planet}. This data efficiency provides significant flexibility for model developments and a clear advantage over common machine learning approaches, which typically demand vast training sets ($>10^6$ model runs) and intensive pre-computation. The PCK surrogate maintains high fidelity with $R^2 > 0.99$ for most scenarios, and root-mean-square errors typically an order of magnitude smaller than observational uncertainties. This efficiency enables large scale population studies while preserving statistical robustness, which is computationally impractical with traditional methods.

Figures (6)

• Figure 1: A schematic of our surrogate-assisted inversion framework. (a) One-Time Training Phase: A computationally expensive forward model is run $N_{\text{train}}$ times to generate a training database. This database is used to train a fast Polynomial Chaos-Kriging (PCK) surrogate model. This is a one-time computational cost. (b) Rapid Inference Phase: For a given exoplanet with observational data ($y_{\text{obs}}$), the fast surrogate is placed inside an MCMC sampling loop to efficiently explore the posterior distribution of the interior structure parameters ($\theta$).
• Figure 2: Validation of the PCK surrogate's predictive performance on the held-out test set for two representative cases: (a) the Earth (Setting 1) and (b) the TOI-270 d (Setting 5). The surrogate's mean prediction (blue dot) shows agreement with the true forward model outputs (red dotted line). Results for the remaining experimental settings are shown in Appendix \ref{['app:PCK_val_plots']}.
• Figure 3: Posterior distributions for the interior structure parameters inferred via MCMC, shown for two representative cases: (a) the constrained Earth case (Setting 1) and (b) the TOI-270 d exoplanet (Setting 5). The results demonstrate the framework's ability to produce well-behaved posteriors that reflect the strength of the observational constraints. Corner plots for all other scenarios are available in Appendix \ref{['app:corner_plots']}.
• Figure 4: Side-by-side comparison of posterior distributions for the Sub-Neptune (T) scenario obtained using (a) our surrogate-based approach and (b) the full forward model. The computational times highlight the dramatic efficiency gain achieved by our framework.
• Figure 5: Residual plots showing the predictive performance of the PCK surrogate on the held-out test sets for the Super-Earth, tightly constrained Sub-Neptune, and loosely constrained Sub-Neptune scenarios. The residuals (Predicted - True) are tightly scattered around zero, confirming the surrogate's high fidelity.