Case Studies

Abstract

This chapter describes a work involving the Lagrangian simulation of fluids using convolutional networks and another work whose goal is the generation of new numerical frames in higher resolution from simulations in lower spatial resolution. The former is an adaptation of the CNN architecture to obtain a convolutional neural network capable of processing Smoothed Particle Hydrodynamics (SPH) data. The network input is composed of dynamic particle positions and velocities together with static particles that model the boundary of the fluid domain. The convolutional neural network output is a displacement array that must be used to update the positions and velocities of the fluid particles. The other focused approach is motivated by the success of generative adversarial networks (GANs) for data generation. The approach can be trained in 2D and 3D data produced using traditional solvers of the Navier–Stokes equations simulated using grid-based numerical methods. It is implemented through CNNs, using residual networks. The methodology includes a data augmentation step implemented through invariance properties (symmetry groups) of the Navier–Stokes equations. The chapter includes simulations generated with both techniques besides comparisons with numerical (ground-truth) results.