A scalable and accurate framework for self-calibrating null depth retrieval using neural posterior estimation

TL;DR

This work targets the challenge of accurate null depth retrieval in nulling interferometry, proposing neural posterior estimation (NPE) within a simulation-based inference (SBI) framework to achieve high precision with improved efficiency. A flow-based posterior estimator is trained on simulations that incorporate real auxiliary data, enabling rapid amortized inference on observations from the LBTI nuller. The results show retrieval accuracies at the $\sim10^{-4}$ level, with substantial speedups compared to traditional NSC methods, and robust validation through predictive checks. A key finding is that tailoring models to specific pointings yields higher accuracy than a universal model, highlighting a scalability-accuracy trade-off and guiding future improvements in time correlations, simulator realism, and robustness against simulation-to-reality gaps. The approach holds promise for accelerating data reduction in current and next-generation nulling interferometers and may be adaptable to broader interferometric applications.

Abstract

Accurate null depth retrieval is critical in nulling interferometry. However, achieving accurate null depth calibration is challenging due to various noise sources, instrumental imperfections, and the complexity of real observational environments. These challenges necessitate advanced calibration techniques that can efficiently handle such uncertainties while maintaining a high accuracy. This paper aims to incorporate machine-learning techniques with a Bayesian inference to improve the accuracy and efficiency of null depth retrieval in nulling interferometry. Specifically, it explores the use of neural posterior estimation (NPE) to develop models that overcome the computational limitations of conventional methods, such as numerical self-calibration (NSC), providing a more robust solution for accurate null depth calibration. An NPE-based model was developed, with a simulator that incorporates real data to better represent specific conditions. The model was tested on both synthetic and observational data from the LBTI nuller for evaluation. The NPE model successfully demonstrated improved efficiency, achieving results comparable to current methods in use. It achieved a null depth retrieval accuracy down to a few $10^{-4}$ on real observational data, matching the performance of conventional approaches while offering significant computational advantages, reducing the data retrieval time to one-quarter of the time required by self-calibration methods. The NPE model presents a practical and scalable solution for null depth calibration in nulling interferometry, offering substantial improvements in efficiency over existing methods with a better precision and application to other interferometric techniques.

Figures (7)

• Figure 1: Workflow diagram NPE. The process consists of data generation, neural network training, and inference-making.
• Figure 2: Comparison of the posterior distributions obtained with the NPE (blue) and NSC (orange) methods on the same synthetic dataset. The retrieved parameters are $N_a$, $\mu_{OPD}$, and $\sigma_{OPD}$. The histograms along the diagonal show the marginalized distributions of each parameter, while the off-diagonal plots display the joint distributions between pairs of parameters. The black dashed crosses mark the ground truth values.
• Figure 3: Retrieval of the null depth using NPE (blue) and NSC via MCMC (orange) for mock datasets with true null depths ranging from 0.001 to 0.010 and fixed $\mu_{OPD} = 300$ nm and $\sigma_{OPD} = 250$ nm. The gray line indicates the one-to-one correspondence. Error bars correspond to the $16^{\mathrm{th}}$ and $84^{\mathrm{th}}$ percentiles of the posterior distributions.
• Figure 4: Null depth of the science star $\beta$ Leo over time retrieved by the NPE model, calibrated using reference stars.
• Figure 5: Prior (left) and posterior (right) predictive check for the NPE model. Left: The grey semi-transparent lines represent data generated from the prior predictive distribution, indicating the range of data the model might encounter during training. The red solid line represents the validation data to be inferred by the model, specifically for the measured null. Right: The grey semi-transparent lines represent the posterior predictive samples for each model. The red solid line represents the validation data during the inference.