Abstract: Partial differential equations used to simulate physical systems can be solved, in one embodiment, by a solver that has been trained with a set of generative neural networks that operated at different resolutions in a solution space of a domain that defines the physical space of the physical system. The solver can operate in a latent vector space which encodes solutions to the PDE in latent vectors in the latent vector space. The variables of the PDE can be partially decoupled in the latent vector space while the solver operates. The domain can be divided into subdomains that are classified based on their positions in the domain.

Abstract: A method and apparatus for determining spatial characteristics of three-dimensional objects is described. In an exemplary embodiment, the device receives a point cloud representation of a three-dimensional surface structure of a plurality of objects. The device may further generate a set of bins to represent the three-dimensional surface structure based on the point cloud representation, each bin corresponding to a spatial occupancy related to the point cloud representation, each bin including a respective type indicating a spatial relationship of the surface structures and a corresponding spatial occupancy of the bin. In addition, the device may encode the set of bins using a convolutional neural network. The device may further determine a classification for the spatial characteristic of the surface structures based on the convolutional neural network with the encoded set of bins.

Abstract: Partial differential equations used to simulate physical systems can be solved, in one embodiment, by a solver that has been trained with a set of generative neural networks that operated at different resolutions in a solution space of a domain that defines the physical space of the physical system. The solver can operate in a latent vector space which encodes solutions to the PDE in latent vectors in the latent vector space. The variables of the PDE can be partially decoupled in the latent vector space while the solver operates. The domain can be divided into subdomains that are classified based on their positions in the domain.