Using SASQuaTCh for Time-Series Prediction of Spatiotemporal Systems

In the classical machine learning literature, it has been shown that transformer neural networks have state-of-the-art performance at learning to predict complex dynamical systems including spatiotemporal systems such as weather systems, fluid flow, and heat flow. A recent quantum transformer circuit called SASQuaTCh was developed based on the principle of kernel-based self-attention and applied to classification problems. We extend this approach to a hybrid graph-learning problem where the spatiotemporal system is represented as a graph, a classical graph neural network learns an efficient latent space vector, and SASQuaTCh is used to predict the next latent vector from a sequence of latent vectors, which is used through a classical decoder to produce a prediction of the PDE at the next time-instant. SASQuaTCh benefits from a logarithmic qubit complexity with respect to the latent space vector, and a linear parameter growth with respect to the number of qubits, yielding a hardware and parameter efficient quantum circuit. We demonstrate the PDE time-series prediction task in simulation and on IBM QPUs using computational fluid dynamics data of a lid-driven cavity generated from OpenFOAM using the Reynolds averaged Navier Stokes (RANS) equations.