System and method for combining differentiable partial differential equation solvers and graph neural networks for fluid flow prediction

A computer-implemented method, comprising:

• receiving a coarse mesh input that includes a first set of nodes, wherein the coarse mesh input is input to a computational fluid dynamics solver with physical parameters to obtain a coarse mesh solution;
• receiving a fine mesh input that is of a second set of nodes, wherein the second set of nodes includes more nodes than the first set of nodes;
• concatenating the fine mesh input with the physical parameters and run the concatenation through a graph convolution layer to obtain a fine mesh hidden layer;
• upsampling the coarse mesh solution to obtain a coarse mesh upsample including a same number of nodes as the second set of nodes;
• and
• outputting a prediction in response to at least the coarse mesh upsample.

A system, comprising:

• a processor programmed to:
• receive a coarse mesh input that includes a first set of nodes, wherein the coarse mesh input is input to a computational fluid dynamics solver with physical parameters to obtain a coarse mesh solution;
• receive a fine mesh input that is of a second set of nodes, wherein the second set of nodes includes more nodes than the first set of nodes;
• upsample the coarse mesh solution to obtain a coarse mesh upsample including a same number of nodes as the second set of nodes;
• output a prediction in response to the fine mesh input and the coarse mesh upsample.