Turbulence Scaling from Deep Learning Diffusion Generative Models

Complex spatial and temporal structures are inherent characteristics of turbulent fluid flows and comprehending them poses a major challenge. This comprehesion necessitates an understanding of the space of turbulent fluid flow configurations. We employ a diffusion-based generative model to learn the distribution of turbulent vorticity profiles and generate snapshots of turbulent solutions to the incompressible Navier-Stokes equations. We consider the inverse cascade in two spatial dimensions and generate diverse turbulent solutions that differ from those in the training dataset. We analyze the statistical scaling properties of the new turbulent profiles, calculate their structure functions, energy power spectrum, velocity probability distribution function and moments of local energy dissipation. All the learnt scaling exponents are consistent with the expected Kolmogorov scaling and have lower errors than the training ones. This agreement with established turbulence characteristics provides strong evidence of the model's capability to capture essential features of real-world turbulence.

Neural Network Complexity of Chaos and Turbulence

We study the complexity of chaos and turbulence as viewed by deep neural networks by considering network classification tasks of distinguishing turbulent from chaotic fluid flows, noise and real world images of cats or dogs. We analyze the relative difficulty of these classification tasks and quantify the complexity of the computation at the intermediate and final stages. We analyze incompressible as well as weakly compressible fluid flows and provide evidence for the feature identified by the neural network to distinguish turbulence from chaos.

Using machine learning to parametrize postmerger signals from binary neutron stars

There is growing interest in the detection and characterization of gravitational waves from postmerger oscillations of binary neutron stars. These signals contain information about the nature of the remnant and the high-density and out-of-equilibrium physics of the postmerger processes, which would complement any electromagnetic signal. However, the construction of binary neutron star postmerger waveforms is much more complicated than for binary black holes: (i) there are theoretical uncertainties in the neutron-star equation of state and other aspects of the high-density physics, (ii) numerical simulations are expensive and available ones only cover a small fraction of the parameter space with limited numerical accuracy, and (iii) it is unclear how to parametrize the theoretical uncertainties and interpolate across parameter space. In this work, we describe the use of a machine-learning method called a conditional variational autoencoder (CVAE) to construct postmerger models for hyper/massive neutron star remnant signals based on numerical-relativity simulations. The CVAE provides a probabilistic model, which encodes uncertainties in the training data within a set of latent parameters. We estimate that training such a model will ultimately require $\sim 10^4$ waveforms. However, using synthetic training waveforms as a proof-of-principle, we show that the CVAE can be used as an accurate generative model and that it encodes the equation of state in a useful latent representation.