With the advent of gravitational wave astronomy, the characterization of the source properties is a key task for the astrophysical community. The accurate theoretical modeling of the waveforms emitted by different sources is fundamental in this respect. The aim of our project is to introduce techniques from the field of deep learning into gravitational waveform modeling. In particular, we propose to exploit specific neural network architectures known as variational autoencoders: they are generative models, meaning that they learn to reconstruct and reproduce complex patterns inside observed fiducial data. The main goal is to use numerical relativity waveforms as a benchmark for an autoencoder to produce novel approximate numerical waveforms, without the need of running actual numerical simulations. The key motivation comes from the fact that numerical simulations are extremely costly, both in terms of time and computational resources. Neural networks are known to approximate with high efficiency arbitrary nonlinear correlations: therefore, we expect that a deep learning based approach to waveform modeling will be able to match and eventually exceed the accuracy of the current waveform approximants. Moreover, neural networks reconstruct correlations virtually without any external input: this diminishes the risk of biases and systematics, which might come from enforcing an a priori physically informed waveform structure. The proposed project is cross-disciplinary, as it lies at the interplay of deep learning and gravitational waves: this is an expanding research area, and we wish to actively contribute to it in the development of our project.
(NOTE: When citing bibliographical items, we will refer to their arxiv number: for example, [2005.03745] refers to the paper at the web link "https://arxiv.org/abs/2005.03745".)
a) Advantages over traditional waveform approximants
The model we propose to build is a surrogate, i.e., an approximate model to accelerate the evaluation of a previously existing fiducial model. In our case, the fiducial model is constituted by ab initio numerical simulations of gravitational waveforms. The potential of such an approach can be better appreciated from the following consideration. The current phenomenological approximants, as given by the effective-one-body and the Phenom families, assume a priori a physically informed waveform structure and enforce several approximations to general relativity: therefore they can be susceptible to biases and systematic errors. Indeed, their continuous improvement is an ongoing research program: see for example [1803.10701] and [2003.12079], in which an improved effective-one-body model and a corresponding surrogate were constructed. The advantage of surrogates based directly on numerical waveforms is that the algorithm is let free to learn the optimal correlations among the parameters, without feeding in external assumptions about the nature of such correlations. Therefore, the risk of systematics is diminished.
b) Advantages over non-deep learning based surrogates
Previous attempts in the direct modeling of numerical waveforms, as presented in [1502.07758, 1701.00550, 1705.07089, 1812.07865], resulted in an accuracy improvement by about one order of magnitude, when compared to phenomenological approximants. Our approach is original, in that previous works never exploited the full generalization power of deep learning. For example, in [1811.05491] the authors use a fully connected neural network to approximate the map between the parameter space and the latent space, but in order to construct the latter they rely upon a conventional reduced-basis decomposition. The advantage of an approach completely based on deep learning, such as the one we propose, is that neural networks supersede ordinary algorithms in the task of identifying complex patterns in the data. Therefore a deep learning surrogate is expected to achieve an even better faithfulness to the original numerical solutions.