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: Simulations of products during the design of the products can use solvers that are based on trained neural networks, and these solvers can provide results about the design of the product that can predict performance, failures, fatigue and other potential problems with the design. The neural network can include a generative neural network that is trained with a discretized version of a partial differential equation (PDE) that provides a model of the product in the simulation, and this discretized version acts as a discriminator that trains the neural network to provide solutions to the PDE.