EAS Doctoral Proposal Defense by Pranav Vinod
Abstract:
One important astrophysical application of general relativity is modeling binary black hole systems, whose orbital evolution and merger generate gravitational waves (GWs). While numerical relativity provides accurate solutions to Einstein's equations for these systems, it is computationally expensive, motivating faster data-driven alternatives. Previous work has shown that neural ordinary differential equations (NODEs) can learn the underlying dynamics directly from GW data through constrained optimization over plausible physical models. However, this approach requires repeatedly solving costly ODEs during training, limiting model size and accuracy. To address this, we propose a modified two-stage approach based on feed-forward neural networks. First, the network is trained to approximate the right-hand side of the governing ODEs without enforcing physical constraints. This pre-trained model is then refined using a physics-informed constrained optimization with waveform data. Preliminary results demonstrate successful training across a range of orbits, with errors approaching numerical round-off. The resulting NODE accurately extrapolates to long-time evolutions, performs well near dynamical separatrix, and captures complex dynamics such as zoom-whirl orbits involving multiple timescales. We apply this new technique to learn binary black hole dynamics from numerical relativity data and showcase potentially new applications, such as determining initial data for black hole simulations. We will present preliminary results in this new direction and highlight the advantages and challenges of this approach.
Advisor:
Dr. Scott Field, Department of Mathematics
Committee members:
- Dr. Zheng Chen, Department of Mathematics
- Dr. Alfa Heryudono, Department of Mathematics
- Dr. Firas Khatib, Department of Computer & Information Science
Note: All EAS Students are encouraged to attend.
TXT 105 – CSCDR
: Zoom
Dr. Scott Field
sfield@umassd.edu
https://umassd.zoom.us/j/92743420577?pwd=ihOdwW6zRCHUQqSCwg1xz369i6B2XB.1