WITH CONTINUOUS CONVOLUTIONS)

motivation: Predicting particles affected by the environment through the networkcase offsets for a more realistic simulation.

CONTINUOUS CONVOLUTIONS

Traditional convolution definition

Unstructured Particle Set Convolution Definition

Use the mapping Λ(r) of a unit sphere to map the relative position within the sphere to the convolution kernel offset:

N(x, R) is a set of points within a radius R of the center of the x point, a ensures smooth response of convolution in different particle neighborhoods:

ψ is a scalar function for normalization. Since the change of particle density is an important feature of the simulated fluid, it is set to 1:

The convolution has been packaged into the open3d library:

LEARNING FLUID MECHANICS WITH CONVOLUTIONAL NETWORKS

Calculate motion state under fixed force:
optionalAs a dynamic particle feature, Boundary static particle feature.
Use network convolution to predict the offset of each particle's environmental impact at the current timestep:

Update initial state for next timestep:

NETWORK ARCHITECTURE

Loss design:

emphasize loss with few adjacent particles

Experiments