CfA Seminar Oct 29 2024

Speaker 1: Lisa Drummond - MIT
Gyroscopes orbiting gargantuan black holes: spinning secondaries in EMRIs

Extreme mass ratio inspirals (EMRIs) are unique LISA sources which offer unprecedented accuracy in measuring black hole properties and conducting tests of general relativity. At lowest order, the smaller black hole follows a geodesic of the larger black hole's spacetime. Accurate models of large mass-ratio systems must include post-geodesic corrections, which account for forces driving the small body away from the geodesic. When a spinning body orbits a black hole, its spin couples to the curvature of the background spacetime due to a post-geodesic effect called the spin-curvature force. To harness the full potential of EMRIs, it is essential to construct waveform models to include this effect, in order to match the phase of gravitational-wave signals across hundreds of thousands of orbits. Another important post-geodesic effect is gravitational self-force, which describes the small body's interaction with its own spacetime curvature. This effect includes the backreaction due to gravitational-wave emission that leads to the inspiral of the small body into the black hole. We use osculating element integration to generate a spinning-body inspiral that includes both the backreaction due to gravitational waves and spin-curvature forces. Fully-relativistic EMRI waveforms are computationally expensive to evaluate, posing a challenge for performing Bayesian inference of astrophysical properties. We use near-identity transformations (NITs) to accelerate trajectory evaluation for inspirals with arbitrary orbital and spin configurations and calculate the gravitational waveforms and examine the dephasing of the waveform due to the presence of spin-curvature forces.

Speaker 2: Congyue Deng - Stanford University
Representing and Enforcing Geometric Relations in Deep Neural Networks

”The reality of the universe is geometrical.” – E. A. Burtt. The Metaphysical Foundations of Modern Physical Science.

Deep learning frameworks, whether supervised or unsupervised, have achieved remarkable success in a large variety of problems in astrophysics. However, despite their ability to extract high-level information from data, they often struggle to capture exact geometric relationships. Even in the simplest cases, for example, point cloud networks trained on well-aligned objects (e.g. chairs in an upright position) can fail when tested on objects in arbitrary poses (e.g. chairs in random orientations under an SE(3) transformation). This highlights the networks’ lack of geometric understanding of pose changes and, more broadly, group actions and geometric relations. These limitations are common across many learning frameworks, impacting their robustness and generalizability – particularly in real-world applications where explainability and trustworthiness are critical, such as processing data from scientific experiments. On the other hand, geometry is a language that is widely adopted in describing physical laws. Incorporating and enforcing geometric relations in neural networks paves a way of building deep learning systems that can understand and follow physical laws. In this talk, I will demonstrate how naively constructed neural networks fail to understand geometric transformations in a variety of scenarios. I will then introduce a series of works on incorporating geometric operators into the latent spaces of neural networks, enabling them to expressively represent different classes of geometric transformations, from the simplest linear transformations to the more complex multi-body movements and continuous diffeomorphism. In the end, I will briefly discuss the possible future directions of applying geometric-aware deep learning to astrophysical problems.