The Eclipsing Binaries via Artificial Intelligence. II. Need for Speed in PHOEBE Forward Models

TL;DR

This work tackles the heavy computational burden of forward-modeling eclipsing binaries by training a six-input, fully connected ANN to predict PHOEBE light curves with high speed. Using a training set exceeding $10^6$ synthetic light curves and a final architecture of six hidden layers with 512 nodes each, the PHOEBAI framework delivers over $10^4\times$ speedups while maintaining systematic errors around $\sim 10^{-3}$ and occasional statistical improvements. The authors rigorously assess robustness via cross-validation, data uncertainties, sample size, and dilution effects, demonstrating the critical role of dilution and presenting methods to incorporate it as a fitting parameter. The approach promises rapid estimation of EB parameters across large surveys (e.g., OGLE, TESS, Kepler/K2), enabling scalable Bayesian inference, provided the network is trained across appropriate parameter ranges and validated against the physics-driven PHOEBE model.

Abstract

In modern astronomy, the quantity of data collected has vastly exceeded the capacity for manual analysis, necessitating the use of advanced artificial intelligence (AI) techniques to assist scientists with the most labor-intensive tasks. AI can optimize simulation codes where computational bottlenecks arise from the time required to generate forward models. One such example is PHOEBE, a modeling code for eclipsing binaries (EBs), where simulating individual systems is feasible, but analyzing observables for extensive parameter combinations is highly time-consuming. To address this, we present a fully connected feedforward artificial neural network (ANN) trained on a dataset of over one million synthetic light curves generated with PHOEBE. Optimization of the ANN architecture yielded a model with six hidden layers, each containing 512 nodes, provides an optimized balance between accuracy and computational complexity. Extensive testing enabled us to establish ANN's applicability limits and to quantify the systematic and statistical errors associated with using such networks for EB analysis. Our findings demonstrate the critical role of dilution effects in parameter estimation for EBs, and we outline methods to incorporate these effects in AI-based models. This proposed ANN framework enables a speedup of over four orders of magnitude compared to traditional methods, with systematic errors not exceeding 1\%, and often as low as 0.01\%, across the entire parameter space.

Figures (20)

• Figure 1: A schematic of the feedforward neural network. The IL (leftmost collection of nodes $p_{1}, \dots, p_{n}$) takes EB parameters as input; these parameters are then propagated to the hidden layer (middle collection of nodes $h_{1} \dots h_{m}$) and, in turn, to the OL (rightmost collection of nodes $o_{1} \dots o_{q}$). The mapping is uniquely defined by the set of weights $w_{11} \dots w_{nm}$, $v_{11} \dots v_{mq}$, and biases $b_{1}\dots b_{m}$, $c_{1}\dots c_{q}$ added after summation of weighted connections. These weights and biases are determined by backpropagation from the known combinations of model parameters and synthesized observables.
• Figure 2: Overlay of light curves generated for a test sample. For each phase, the median and 18th–84th percentile range of fluxes were computed. The red solid line represents the median light curve, while the shaded region between the red dashed lines indicates the percentile range. Each thin black line represents an individual light curve. Although only 5000 out of the 1,250,000 generated light curves are shown here, the statistics were computed for the entire sample. See Section \ref{['sec:training_set_generation']} for more details.
• Figure 3: A diagnostic figure illustrating the results from RSCV. The figure consists of $N$ plots, where $N$ corresponds to the number of unique values for a given hyperparameter. Each plot features two histograms: the first histogram (solid black line) represents the entire sample, while the second (dashed red line) represents the subset with the specific value of the hyperparameter, shown above each histogram (in this case, the AF in the OL). The $x$-axis indicates the values of the chosen metric (here, the MAE averaged across all folds). The lower the value of the metric, the better the performance.
• Figure 4: Density histograms comparing the initial and filtered distributions of the main set of parameters during the step of generating forward models using PHOEBE.
• Figure 5: (Top) Phase-folded light curve of one synthetic dataset with fitted models. The dashed red line represents the model obtained using an ANN, while the solid blue line represents the model obtained with PHOEBE. (Bottom) Residuals after subtracting the ANN model fluxes from the observed data.