Accelerating Posterior Inference from Pulsar Light Curves via Learned Latent Representations and Local Simulator-Guided Optimization

TL;DR

Experiments on the observed light curve of PSR J0030+0451, captured by NASA's Neutron Star Interior Composition Explorer (NICER), show that the method closely matches posterior estimates obtained using traditional MCMC methods while achieving 120 times reduction in inference time.

Abstract

Posterior inference from pulsar observations in the form of light curves is commonly performed using Markov chain Monte Carlo methods, which are accurate but computationally expensive. We introduce a framework that accelerates posterior inference while maintaining accuracy by combining learned latent representations with local simulator-guided optimization. A masked U-Net is first pretrained to reconstruct complete light curves from partial observations and to produce informative latent embeddings. Given a query light curve, we identify similar simulated light curves from the simulation bank by measuring similarity in the learned embedding space produced by pretrained U-Net encoder, yielding an initial empirical approximation to the posterior over parameters. This initialization is then refined using a local optimization procedure using hill-climbing updates, guided by a forward simulator, progressively shifting the empirical posterior toward higher-likelihood parameter regions. Experiments on the observed light curve of PSR J0030+0451, captured by NASA's Neutron Star Interior Composition Explorer (NICER), show that our method closely matches posterior estimates obtained using traditional MCMC methods while achieving 120 times reduction in inference time (from 24 hours to 12 minutes), demonstrating the effectiveness of learned representations and simulator-guided optimization for accelerated posterior inference.

Figures (6)

• Figure 1: Method overview for accelerated posterior inference from pulsar light curves. (a) Masked U-Net pretraining: Training light curves $\textbf{x}_i$ undergo 75% random masking and are processed by a 1D U-Net consisting of an encoder $f_\phi$ and decoder $g_\psi$. The model is trained end-to-end to reconstruct the original unmasked light curves via masked reconstruction loss, learning multi-scale representations. (b) Embedding extraction: After pretraining is complete, each light curve $\textbf{x}_i$ from the simulation bank is passed through the pretrained (frozen) encoder $f_\phi$ to extract 768-dimensional embeddings $\textbf{z}_i$, which are stored with their corresponding parameters as $\{\textbf{z}_i, \boldsymbol{\theta}_i\}$ pairs in a database. (c) k-NN retrieval: For a query observation $\textbf{x}^*$, we encode to $\textbf{z}^* = f_\phi(\textbf{x}^*)$ and perform k-NN retrieval in the learned embedding space by computing cosine similarity $\cos(\textbf{z}_i, \textbf{z}^*)$, retrieving the top-$K=4{,}000$ most similar samples to form an initial empirical posterior $\hat{p}_0(\boldsymbol{\theta} \mid \textbf{x}^*)$ that preserves multimodal parameter structure. (d) Local refinement: Starting from the initial posterior $\hat{p}_0(\boldsymbol{\theta} \mid \textbf{x}^*)$, local hill climbing with forward simulator $F(\boldsymbol{\theta})$ refines each retrieved mode by minimizing Poisson negative log-likelihood $\mathcal{L}(\boldsymbol{\theta}) = F(\boldsymbol{\theta} - \textbf{x}^* \log F(\boldsymbol{\theta})$, producing the refined posterior $\hat{p}_{\textit{ref}}(\boldsymbol{\theta} \mid \textbf{x}^*)$ with increased density at high-likelihood regions.
• Figure 2: Average KL divergence versus retrieval size $K$ for $P{=}1$ (orange) and $P{=}5$ (blue) refinement. KL divergence decreases monotonically and levels off at $K\approx 3000$ (KL $\approx 0.01$), justifying the use of $K{=}4{,}000$.
• Figure 3: Left: Posterior distributions of pulsar parameters comparing results from (i) the embedding retrieval and hill climbing refinement over 5 parameters approach in the work (in orange) and (ii) a traditional MCMC informed by a nested sampling approach (in green). Right: Predicted light curves corresponding to parameter posterior configurations from this work (orange) compared to those from the baseline MCMC pipeline (green). The predicted posteriors align well with the observed light curve and are in agreement with the predictions from MCMC.
• Figure 4: Visual diagnostic of retrieval fidelity. For each query (row), the spread of retrieved curves across ranks reflects how well the similarity space concentrates around the observed morphology; multi-level embeddings show the smallest spread, whereas raw-space cosine similarity exhibits larger deviations in peak and baseline structure.
• Figure 5: Predictions on gamma-ray spectroscopy data using the refinement framework in this work. The first 4 columns in each row show predicted posteriors of parameters describing a photopeak for a sample Ba-133. The last column shows the predicted photopeak profiles corresponding to the predicted parameters compared to the observed photopeak. The NLL improves as number of parameters are increased in the refinement and converges at the 3-parameter stage ($P$ =3).