Various astronomical observations provide mass and radius information about compact stellar objects that are generally thought to be neutron stars. This mass-versus-radius curve reveals information about the equation of state of the dense matter constituting the neutron star. An alternative explanation for some of these objects is that they are actually boson stars -- hypothetical compact objects made up of exotic matter. For boson stars, the mass-radius curve would reveal information about their scalar potential, the analog of a neutron star's equation of state. An important question is to what extent neutron stars and boson stars can be observationally distinguished based on their mass-versus-radius curves, or conversely to what extent these two types of object can produce the same mass-versus-radius curves.
Inferring the properties of a neutron star or boson star from its mass-versus-radius curve is the inverse of the usual "forward" approach of solving the stellar structure equations with the equation of state / scalar potential to compute this curve. By parameterizing a wide class of equations of state and scalar potentials, we plan to train neural networks to predict these properties from a given mass-versus-radius curve. The question of distinguishability can then be investigated directly by studying the resulting networks and their predictions.
We will first generate thousands of examples of mass-versus-radius curves corresponding to a range of neutron-star equations of state and boson-star scalar potentials by solving the Tolman-Oppenheimer-Volkoff (TOV) equations, a system of ODEs that describe the structure of these stars. We will rely on two open-source TOV solver packages for this step, though we also plan investigate a fast, GPU-enabled TOV solver written by a current graduate student at Princeton. We will then train and test neural networks that, given a mass-versus-radius curve, will predict the underlying equation of state or scalar potential that gave rise to it. The infrastructure developed in the course of this project will support future exploration of the primary scientific questions of neutron/boson star distinguishability.
A previous student worked briefly on this problem and produced an initial implementation that handles a severely limited range of mass-versus-radius curves and runs on a single processor. For this project, we will need to scale both production of mass-versus-radius curves and neural network training/inference to HPC platforms. We anticipate using PyTorch for the machine-learning aspects of the project.
Project Information Subsection
(1) a large set of mass-versus-radius curves generated from known neutron-star equations of state and boson-star scalar potentials. These will be the training and test data for our networks
(2) one or more neural networks designed to infer the underlying equation of state/scalar potential from a given mass-versus-radius curve.
(3) characterization of the networks on the data produced in item (1).
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We are seeking an undergraduate or graduate student with sufficient math and/or physics background to work with TOV equation solvers and sufficient Python or related programming skills to distribute the generation of mass-versus-radius curves and to implement and use neural networks in PyTorch. Some prior knowledge of applied machine learning would be a strong plus.
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Some hands-on experience
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Long Island University - Post
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CR-Rensselaer Polytechnic Institute
10/01/2023
Yes
Already behind3Start date is flexible
6
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Milestone Title: Background preparation Milestone Description: The student will familiarize themselves with neutron star equations of state, boson star scalar potentials, and the TOV equations. Give launch presentation. Completion Date Goal: 2024-05-08
Milestone Title: Validation of TOV solvers Milestone Description: Verify that we are correctly using the two open-source TOV equation solvers (in particular, that the inputs provided are correctly formatted); tweak the solvers if necessary to fit our application. Evaluate whether the alternative GPU-based TOV solver can provide a more efficient alternative to the open-source solves. Completion Date Goal: 2024-05-15
Milestone Title: Generate training and test data Milestone Description: Produce training and test sets of thousands of mass-versus-radius curves from known neutron star equations of state and boson star scalar potentials. Completion Date Goal: 2024-05-29
Milestone Title: Develop neural network architecture Milestone Description: Design and implement neural networks that can take a mass-versus radius curve and predict the underlying equation of state/scalar potential. Completion Date Goal: 2024-06-14
Milestone Title: Train and test networks Milestone Description: Train the networks on the data produced in earlier milestones and test to what extent they can recover EOS's/scalar potentials. Completion Date Goal: 2024-06-30
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The project needs a cluster suitable for distributing generation of mass-versus-radius curves (ODE solving) and neural network training and inference. Availability of GPUs would be a strong plus, particularly if the Princeton TOV code proves feasible to use, and in any case to accelerate neural network training.
Potential computing resources:
(1) 13-node CPU cluster local to LIU
(2) Frontera (both CPU and GPU nodes) and ACCESS machines
(3) the Unity cluster (URI and UMass Dartmouth)
(4) RPI CCI cluster