Generative Adversarial Learning from Deterministic Processes
Provides theoretical justification for the empirical success of GANs on non-i.i.d. data from physical systems, addressing a gap in statistical learning theory.
The paper proves that generative adversarial learning can learn the invariant distribution of a chaotic dynamical system from a single deterministic time series, with explicit convergence rates in Jensen-Shannon divergence.
Physical AI is being successfully applied to data which does not follow the traditional paradigm of independent and identically distributed (i.i.d.) samples. In fact, physical AI is often trained on data which is not random at all, and is instead derived from chaotic dynamical systems like turbulence. We aim to explain the empirical success of these methods using the example of generative adversarial networks (GANs), whose statistical learning theory under the i.i.d. assumption is generally well understood. We prove that it is possible, using an infinite-dimensional model of generative adversarial learning (GAL), to learn the invariant distribution of a sufficiently chaotic dynamical system from a single deterministically evolving time series of its states or measurements thereof, and give explicit rates for the convergence to the solution in terms of the Jensen-Shannon divergence.