Selecting Pulsars using ANN

Introduction :

Since the discovery of pulsars in 1967, pulsar searching has evolved significantly. Modern surveys employ high-performance computing and advanced signal processing algorithms to detect weak pulsar signals amidst radio frequency interference and binary systems. However, the final stage of selecting credible pulsar candidates still relies on human judgment, which can be time-consuming and inefficient for large-scale surveys producing millions of candidates.

Large-scale pulsar surveys have greatly increased our knowledge of pulsars and their properties. Future surveys will utilize next-generation radio telescopes like LOFAR, FAST, and SKA, benefiting from their large collecting areas and wide fields of view. The sheer number of pulsar candidates detected by these instruments necessitates multi-person or machine-based candidate selection.

In some cases, machine solutions have been developed, such as candidate ranking based on likelihoods or sorting based on similarity scores. Researchers in 2010 presented an alternative method using an Artificial Neural Network (ANN) trained on specific scores to automatically identify credible pulsar candidates from the Parkes multi-beam pulsar survey (PMPS) data. ANNs have been successfully used in various areas of astronomy, including galaxy classification and event selection in large surveys.

What is ANN?

An Artificial Neural Network (ANN) is a computational technique inspired by the human central nervous system. ANNs are used for non-parametric estimation, where data cannot be modeled using known theories. They find applications in areas like speech and pattern recognition.

ANNs consist of nodes organized into layers, including an input layer, hidden layers, and an output layer. The architecture is defined by the number of nodes in each layer. Inputs are passed to the input layer, and calculations are performed in each node of the hidden layer based on weighted sums of the values from the previous layer. An activation function is then applied to control the output amplitude of each node. The process continues until the output layer is reached, producing the final output values of the ANN.

In supervised learning, the ANN is trained by comparing the output values with a desired output vector determined by a human. This is done by evaluating an error function, which measures the discrepancy between the output and the desired values. The weights of the ANN are then adjusted through a process called backpropagation, starting from the output layer and moving backward through the layers. The weight modifications are determined by the chosen learning model, such as Resilient backPROPagation (RPROP), which uses partial derivatives to guide the weight updates.

The RPROP learning function minimizes the error function, which includes a weight decay term. Once the training is complete, the weights of the ANN are fixed, allowing it to process input vectors and produce output vectors similar to the desired outputs seen during training.

Overall, ANNs provide a flexible framework for solving complex problems without relying on explicit theoretical models. They learn patterns and make predictions based on training data, enabling them to excel in tasks like speech recognition, pattern classification, and more.

Discovering Pulsars:

In research by R.P.Eatough, Artificial Neural Network (ANN) was utilized to analyze a subset of candidates generated from a re-analysis of the Parkes Multi-beam Pulsar Survey (PMPS). This re-analysis involved conducting acceleration searches in order to improve the identification of potential pulsar signals.

The re-analysis of the PMPS data resulted in the discovery of 14 pulsars using traditional candidate selection methods. In addition to these discoveries, one pulsar was found by employing an ANN with an architecture represented as 8:8:2. This architecture indicates that the ANN consisted of an input layer with eight nodes, a hidden layer with eight nodes, and an output layer with two nodes.

The newly discovered pulsar, provisionally named PSR J1926+0739, exhibits a spin period of approximately 318 milliseconds and a dispersion measure (DM) of around 160 cm^−3 pc. The detection of this pulsar achieved a signal-to-noise ratio (SNR) of roughly 10, indicating the strength and reliability of the detected pulsar signal.

The timing solution for PSR J1926+0739 was also analyzed. This solution involves determining various astrometric parameters (related to the position and motion of the pulsar) as well as spin-down parameters (related to the pulsar's rotational dynamics) with sufficient accuracy. The finalized timing solution and all the determined parameters were presented in a publication by Eatough.

To summarize, applying an ANN to the re-analysis of the PMPS data led to the discovery of an additional pulsar named PSR J1926+0739. Ongoing observations and timing measurements at the Jodrell Bank Observatory aim to further characterize the pulsar and provide accurate astrometric and spin-down parameters.

Conclusion and Future Directions:

ANNs have been developed to assist in the search for radio pulsars within a database containing approximately 16 million pulsar candidates. These candidates were generated through a recent re-analysis of the PMPS. The ANNs were trained using small sets of characteristic scores obtained from pulsar candidate plots, which were initially generated for human inspection.

In the evaluation of a test sample comprising around 2.5 million pulsar candidates, the ANNs successfully recovered approximately 92% of the known pulsars present in the sample. However, it was noted that some pulsars may have been missed due to three possible reasons: inadequate training of the ANNs on millisecond pulsars (MSPs), abnormal candidate plots generated by the search software, or unbalanced training sets. Future implementations should aim to avoid unbalanced training sets or bias the training sets towards the objects of interest, such as pulsars. 

Having a higher number of false positives from the ANN can be advantageous for identifying the rare objects in the dataset, namely pulsars.

To reduce the "contamination" from non-pulsars in the results set, the threshold for pulsar identification (referred to as z1) was increased to 0.7, 0.8, and 0.9, respectively. With each increment in the threshold, the number of genuine pulsar candidates recovered by the ANN decreased compared to non-pulsar candidates. However, the corresponding fraction of recovered pulsars was still substantial, at 89%, 86%, and 81% for the respective thresholds. These few percentage points could potentially represent new discoveries in a pulsar search. 

Higher thresholds should only be used when the number of candidates produced by the ANN becomes unmanageable. Improving the detection efficiency of ANNs will be a focus of future work, likely involving better representation of two-dimensional diagnostic plots in the input vectors. These diagnostic plots are useful for distinguishing against narrow-band and impulsive radio frequency interference (RFI).

It is important to recognize that ANNs can only classify inputs based on the training they receive. By training ANNs using pulsars exhibiting a wide range of properties and phenomena, such as scintillation, scattering, intermittency, and binary motion, the likelihood of uncovering atypical or unexpected pulsar phenomena is reduced. Special attention should be given to training sets that include millisecond pulsars, as they display different candidate plots compared to standard pulsars. 

Additionally, for more exotic pulsars, such as relativistic binary pulsars, training sets based on real data may be limited in size, and simulated pulsar signals covering a range of parameters could be employed. However, ANNs trained with simulated data may not perform as well as those trained with real data due to subtle instrumental and RFI effects. In new pulsar surveys, dedicated observations of known pulsars will be necessary to build a training database specifically for millisecond pulsars and the standard population of pulsars.

Another class of ANNs, known as unsupervised ANNs, does not require a desired or target vector during training. An example of such an ANN is the Kohonen Self-Organizing Map (SOM). SOMs provide a way to represent multi-dimensional data in a lower number of dimensions, typically as a two-dimensional map. Input vectors with similar properties are mapped to nearby regions on the SOM. 

Utilizing such ANNs could help classify pulsar candidates into sub-classes, including millisecond pulsars, standard pulsars, noise signals, and common RFI signals. While unsupervised ANNs may not be optimal for candidate selection, they will be explored in future work.

Future pulsar surveys, such as those conducted with the Square Kilometer Array (SKA), will cover larger volumes of real and parameter space associated with radio pulsars. The sensitivity of the SKA is expected to enable the discovery of 20,000 to 30,000 pulsars that are beaming toward Earth and visible from the designated sites. Analyzing the resulting candidates from such surveys will be a significant data analysis task. 

Scaling up the PMPS to an all-sky survey would lead to a roughly 40-fold increase in the number of pulsar candidates. If each candidate is inspected for one second, reviewing all the candidates would take over 20 years. However, by employing ANNs and assuming a recovered fraction of 0.5%, the total inspection time could be reduced to just over one month, greatly reducing the workload on human observers. 

Nonetheless, it is important to note that ANNs should not yet replace human inspection entirely, as humans are better equipped to identify unusual or interesting features in individual pulsar candidates. ANNs, such as those discussed in this work, could be employed initially for rapid analysis of search output data before conducting more detailed manual inspections using graphical selection tools.