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LAGRANGIAN FLUID SIMULATION WITH CONTINUOUS CONVOLUTIONS
2022-08-11 06:15:00 【zhSunw】
LAGRANGIAN FLUID SIMULATION WITH CONTINUOUS CONVOLUTIONS
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
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