Neural Monte Carlo rendering of finite-time Lyapunov exponent fields

The finite-time Lyapunov exponent (FTLE) is widely used for understanding the Lagrangian behavior of unsteady flow fields. The FTLE field contains many important fine-level structures (e.g., Lagrangian coherent structures). These structures are often thin in depth, requiring Monte Carlo rendering for unbiased visualization. However, Monte Carlo rendering requires hundreds of billions of samples for a high-resolution FTLE visualization, which may cost up to hundreds of hours for rendering a single frame on a multi-core CPU. In this paper, we propose a neural representation of the flow map and FTLE field to reduce the cost of expensive FTLE computation. We demonstrate that a simple multi-layer perceptron (MLP)-based network can accelerate the FTLE computation by up to hundreds of times, and speed up the rendering by tens of times, while producing satisfactory rendering results. We also study the impact of the network size, the amount of training, and the predicted property, which may serve as guidance for selecting appropriate network structures.