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: 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 specification for a semi-conductor chip is received. The specification specifies a set of photomasks associated with a metal layer of the semi-conductor chip. Multiple portions of an area of the metal layer are identified. A respective image is generated for each portion of the area based on the photomasks. A respective drawn density of metal wires for each portion of the area is calculated. A trained machine learning model is invoked to predict a respective silicon density of metal wires for each respective portion of the area based on an image and a drawn density for the respective portion of the area. A silicon density for the area of the metal layer is calculated based on a combination of predicted silicon densities for the multiple portions of the area. The combination is based on an average value of the predicted silicon densities for the multiple portions of the area.

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.