Estimating Orbital Parameters of Direct Imaging Exoplanet Using Neural Network

TL;DR

This work introduces FM-MCMC, a flow-matching enhanced MCMC framework that combines continuous normalizing flows trained with a flow-matching objective to generate high-quality initial proposals for traditional MCMC samplers. Applied to direct-imaging exoplanetary systems, specifically $\beta$ Pictoris b, FM-MCMC achieves large speedups (e.g., ~ $77.8\times$ over PTMCMC and $365.4\times$ over nested sampling) while preserving posterior accuracy, outperforming neural posterior estimation in precision. The method fuses deep generative modeling with classical sampling to handle high-dimensional, potentially multimodal posteriors and is scalable to future survey-scale datasets and multi-planet/instrument inference. Beyond exoplanets, the framework offers a general paradigm for fast, uncertainty-aware inference across cosmology, biomedical imaging, and particle physics.

Abstract

In this work, we propose a new flow-matching Markov chain Monte Carlo (FM-MCMC) algorithm for estimating the orbital parameters of exoplanetary systems, especially for those only one exoplanet is involved. Compared to traditional methods that rely on random sampling within the Bayesian framework, our approach first leverages flow matching posterior estimation (FMPE) to efficiently constrain the prior range of physical parameters, and then employs MCMC to accurately infer the posterior distribution. For example, in the orbital parameter inference of beta Pictoris b, our model achieved a substantial speed-up while maintaining comparable accuracy-running 77.8 times faster than Parallel Tempered MCMC (PTMCMC) and 365.4 times faster than nested sampling. Moreover, our FM-MCMC method also attained the highest average log-likelihood among all approaches, demonstrating its superior sampling efficiency and accuracy. This highlights the scalability and efficiency of our approach, making it well-suited for processing the massive datasets expected from future exoplanet surveys. Beyond astrophysics, our methodology establishes a versatile paradigm for synergizing deep generative models with traditional sampling, which can be adopted to tackle complex inference problems in other fields, such as cosmology, biomedical imaging, and particle physics.

Figures (4)

• Figure 1: Flow-matching MCMC framework. In the Training section, there is first a prior distribution $p(\theta)$, from which the parameter $\theta$ is extracted, and the data is generated by a model $x$. These generated data are fed into the training process along with the parameters. The inference section is based on the trained model, input the real observation data, and use the trained model to infer the initial proposals. The initial proposal is then provided to PTMCMC for likelihood calculations.
• Figure 2: FM‑MCMC vs PTMCMC vs NPE posterior comparison for $\beta$ Pictoris b orbital elements. Comparative analyses reveal that NPE produces broader posterior distributions, whereas FM‑MCMC delivers more concentrated estimates, underscoring its superior statistical precision.
• Figure 3: FM‑MCMC vs PTMCMC vs Nested sampling posterior comparison for $\beta$-Pictoris b orbital elements. Posterior distributions of $\beta$-Pictoris b’s orbital parameters inferred by FM‑MCMC (blue), PTMCMC (orange), and nested sampling (red) show statistical consistency, with nearly identical $1-\sigma$ and $2-\sigma$ credible regions. This overlap demonstrates that FM‑MCMC accurately reproduces the full posterior structure obtained by conventional sampling methods.
• Figure 4: P-P plot validating the unbiasedness of the CNF model. The near-perfect alignment of all CDF curves (colored lines) with the theoretical diagonal y=x (black dashed line) indicates statistical consistency between the CNF posterior estimates and the true distribution.