Tobias Buck

D. Huppenkothen, M. Ntampaka, M. Ho et al. · princeton

Machine learning has rapidly become a tool of choice for the astronomical community. It is being applied across a wide range of wavelengths and problems, from the classification of transients to neural network emulators of cosmological simulations, and is shifting paradigms about how we generate and report scientific results. At the same time, this class of method comes with its own set of best practices, challenges, and drawbacks, which, at present, are often reported on incompletely in the astrophysical literature. With this paper, we aim to provide a primer to the astronomical community, including authors, reviewers, and editors, on how to implement machine learning models and report their results in a way that ensures the accuracy of the results, reproducibility of the findings, and usefulness of the method.

Robin Janssen, Immanuel Sulzer, Tobias Buck

We introduce CODES, a benchmark for comprehensive evaluation of surrogate architectures for coupled ODE systems. Besides standard metrics like mean squared error (MSE) and inference time, CODES provides insights into surrogate behaviour across multiple dimensions like interpolation, extrapolation, sparse data, uncertainty quantification and gradient correlation. The benchmark emphasizes usability through features such as integrated parallel training, a web-based configuration generator, and pre-implemented baseline models and datasets. Extensive documentation ensures sustainability and provides the foundation for collaborative improvement. By offering a fair and multi-faceted comparison, CODES helps researchers select the most suitable surrogate for their specific dataset and application while deepening our understanding of surrogate learning behaviour.

Luca Wolf, Tobias Buck, Bjoern Malte Schaefer

Neural ODEs are a widely used, powerful machine learning technique in particular for physics. However, not every solution is physical in that it is an Euler-Lagrange equation. We present Helmholtz metrics to quantify this resemblance for a given ODE and demonstrate their capabilities on several fundamental systems with noise. We combine them with a second order neural ODE to form a Lagrangian neural ODE, which allows to learn Euler-Lagrange equations in a direct fashion and with zero additional inference cost. We demonstrate that, using only positional data, they can distinguish Lagrangian and non-Lagrangian systems and improve the neural ODE solutions.

Berkay Gunes, Sven Buder, Tobias Buck

We present COMPASS, a novel simulation-based inference framework that combines score-based diffusion models with transformer architectures to jointly perform parameter estimation and Bayesian model comparison across competing Galactic Chemical Evolution (GCE) models. COMPASS handles high-dimensional, incomplete, and variable-size stellar abundance datasets. Applied to high-precision elemental abundance measurements, COMPASS evaluates 40 combinations of nucleosynthetic yield tables. The model strongly favours Asymptotic Giant Branch yields from NuGrid and core-collapse SN yields used in the IllustrisTNG simulation, achieving near-unity cumulative posterior probability. Using the preferred model, we infer a steep high-mass IMF slope and an elevated Supernova Ia normalization, consistent with prior solar neighbourhood studies but now derived from fully amortized Bayesian inference. Our results demonstrate that modern SBI methods can robustly constrain uncertain physics in astrophysical simulators and enable principled model selection when analysing complex, simulation-based data.

Christian Kleiber, William H. Oliver, Tobias Buck

We present $\texttt{LAMINAR}$, a novel unsupervised machine learning pipeline designed to enhance the representation of structure within data via producing a more-informative distance metric. Analysis methods in the physical sciences often rely on standard metrics to define geometric relationships in data, which may fail to capture the underlying structure of complex data sets. $\texttt{LAMINAR}$ addresses this by using a continuous-normalising-flow and inverse-transform-sampling to define a Riemannian manifold in the data space without the need for the user to specify a metric over the data a-priori. The result is a locally-adaptive-metric that produces structurally-informative density-based distances. We demonstrate the utility of $\texttt{LAMINAR}$ by comparing its output to the Euclidean metric for structured data sets.

Immanuel Sulzer, Tobias Buck

In astrophysics, solving complex chemical reaction networks is essential but computationally demanding due to the high dimensionality and stiffness of the ODE systems. Traditional approaches for reducing computational load are often specialized to specific chemical networks and require expert knowledge. This paper introduces a machine learning-based solution employing autoencoders for dimensionality reduction and a latent space neural ODE solver to accelerate astrochemical reaction network computations. Additionally, we propose a cost-effective latent space linear function solver as an alternative to neural ODEs. These methods are assessed on a dataset comprising 29 chemical species and 224 reactions. Our findings demonstrate that the neural ODE achieves a 55x speedup over the baseline model while maintaining significantly higher accuracy by up to two orders of magnitude reduction in relative error. Furthermore, the linear latent model enhances accuracy and achieves a speedup of up to 4000x compared to standard methods.