Aging Stars with Confidence: How Neural Networks and Uncertainty Help Date the Cosmos

In the study lead author Víctor Tamames Rodero and collaborators present an innovative approach to estimating stellar ages. Their focus is on applying artificial intelligence, particularly Bayesian Neural Networks (BNNs), to address a fundamental challenge in astronomy: dating stars with both accuracy and well-quantified uncertainty.

Why Dating Stars Is So Difficult

Stellar dating is essential for understanding the history of our galaxy, but it’s notoriously hard to do. Traditional methods—like comparing stars to models of stellar evolution (called isochrones), using their rotation (gyrochronology), vibrations (asteroseismology), or even their surface chemistry (chemical clocks)—all come with limitations. Some stars have overlapping characteristics that make their ages hard to separate, and observational data is often noisy or incomplete. Moreover, most AI models don’t natively handle uncertainty, which is key when making scientific predictions. The authors aim to fix that.

Building a Better Predictor

To tackle this, the team turns to Bayesian Neural Networks, which are like regular neural networks but with a twist: they treat the network’s inner parameters as probabilities instead of fixed numbers. This allows them to express how uncertain they are about each prediction. Even better, they embed these networks into a hierarchical Bayesian model (HBM). This type of model has multiple layers of inference, helping the system learn both the relationships among stellar properties and the uncertainties from the data itself.

Their key innovation is swapping out a traditional mathematical relationship between inputs and outputs with flexible neural networks that can “learn” from the data. This hybrid model is designed to predict not just a star’s age, but also give a probability distribution showing how confident the model is in its result.

A Chemical Approach to Time

For this study, the authors focus on main sequence (MS) stars—stars like our Sun that are steadily burning hydrogen. They use a method called chemical clocks, which estimates age based on ratios of certain elements in a star’s atmosphere. These chemical signatures, like the ratio of Yttrium to Magnesium ([Y/Mg]), act as a timestamp of when the star formed, since the elements accumulate in the galaxy over time. MS stars are ideal for this because their surface chemistry doesn’t change much as they age.

The Data and the Model

To train their model, the authors used a dataset of 328 well-studied stars from a project called HARPS-GTO. Each star came with detailed chemical measurements and previously estimated ages. They validated their model on 23 separate stars, including the Sun, stars from the well-known M67 cluster, and stars studied through asteroseismology—some of the most accurate benchmarks available. This helped them test how well their model generalizes to new data.

The model is trained in two steps: first, it uses a method called Markov Chain Monte Carlo (MCMC) to explore the range of possible parameter values in the training data. Then, it uses those insights to predict the ages of new stars, providing not just a number but a full distribution—essentially a range of likely ages.

Results: Accurate and Cautious Predictions

After testing different model designs, the best-performing architecture was surprisingly simple: a single hidden layer neural network with six nodes. It achieved a mean absolute error of less than 1 billion years (Ga) on the test data. This level of accuracy is competitive with traditional methods, but with the added benefit of conservative and transparent uncertainty estimates. For example, if the model isn't sure about a prediction, it doesn't pretend otherwise—it reports a wider range of possible ages.

Looking Ahead

This work shows how combining machine learning with Bayesian statistics can lead to better tools for astrophysics. The authors’ model is flexible enough to be adapted to other types of stars or problems—like studying how the ages of stars vary across the Milky Way or exploring the role of magnetic fields in stellar evolution. While future improvements could make the method faster or more scalable, this paper marks a promising step toward more reliable, data-driven stellar dating.

Source: Rodero