Multi-View Symbolic Regression

Symbolic regression (SR) searches for analytical expressions representing the relationship between a set of explanatory and response variables. Current SR methods assume a single dataset extracted from a single experiment. Nevertheless, frequently, the researcher is confronted with multiple sets of results obtained from experiments conducted with different setups. Traditional SR methods may fail to find the underlying expression since the parameters of each experiment can be different. In this work we present Multi-View Symbolic Regression (MvSR), which takes into account multiple datasets simultaneously, mimicking experimental environments, and outputs a general parametric solution. This approach fits the evaluated expression to each independent dataset and returns a parametric family of functions f(x; \theta) simultaneously capable of accurately fitting all datasets. We demonstrate the effectiveness of MvSR using data generated from known expressions, as well as real-world data from astronomy, chemistry and economy, for which an a priori analytical expression is not available. Results show that MvSR obtains the correct expression more frequently and is robust to hyperparameters change. In real-world data, it is able to grasp the group behaviour, recovering known expressions from the literature as well as promising alternatives, thus enabling the use SR to a large range of experimental scenarios.

Toward an understanding of the properties of neural network approaches for supernovae light curve approximation

The modern time-domain photometric surveys collect a lot of observations of various astronomical objects, and the coming era of large-scale surveys will provide even more information. Most of the objects have never received a spectroscopic follow-up, which is especially crucial for transients e.g. supernovae. In such cases, observed light curves could present an affordable alternative. Time series are actively used for photometric classification and characterization, such as peak and luminosity decline estimation. However, the collected time series are multidimensional, irregularly sampled, contain outliers, and do not have well-defined systematic uncertainties. Machine learning methods help extract useful information from available data in the most efficient way. We consider several light curve approximation methods based on neural networks: Multilayer Perceptrons, Bayesian Neural Networks, and Normalizing Flows, to approximate observations of a single light curve. Tests using both the simulated PLAsTiCC and real Zwicky Transient Facility data samples demonstrate that even few observations are enough to fit networks and achieve better approximation quality than other state-of-the-art methods. We show that the methods described in this work have better computational complexity and work faster than Gaussian Processes. We analyze the performance of the approximation techniques aiming to fill the gaps in the observations of the light curves, and show that the use of appropriate technique increases the accuracy of peak finding and supernova classification. In addition, the study results are organized in a Fulu Python library available on GitHub, which can be easily used by the community.

Supernova Light Curves Approximation based on Neural Network Models

Photometric data-driven classification of supernovae becomes a challenge due to the appearance of real-time processing of big data in astronomy. Recent studies have demonstrated the superior quality of solutions based on various machine learning models. These models learn to classify supernova types using their light curves as inputs. Preprocessing these curves is a crucial step that significantly affects the final quality. In this talk, we study the application of multilayer perceptron (MLP), bayesian neural network (BNN), and normalizing flows (NF) to approximate observations for a single light curve. We use these approximations as inputs for supernovae classification models and demonstrate that the proposed methods outperform the state-of-the-art based on Gaussian processes applying to the Zwicky Transient Facility Bright Transient Survey light curves. MLP demonstrates similar quality as Gaussian processes and speed increase. Normalizing Flows exceeds Gaussian processes in terms of approximation quality as well.

Photometric Data-driven Classification of Type Ia Supernovae in the Open Supernova Catalog

We propose a novel approach for a machine-learning-based detection of the type Ia supernovae using photometric information. Unlike other approaches, only real observation data is used during training. Despite being trained on a relatively small sample, the method shows good results on real data from the Open Supernovae Catalog. We also demonstrate that the quality of a model, trained on PLASTiCC simulated sample, significantly decreases evaluated on real objects.