Machine learning three-dimensional fluid flows for interactive aerodynamic design

1. A computer-implemented method for simulating a three-dimensional fluid flow, the method comprising:

parameterizing a first representation of a design object to compute a first polycube representation;

computing a first distortion grid based on the first polycube representation;

computing, via a first neural network, a surface pressure model based on the first polycube representation;

computing, via a second neural network, a velocity field model based on the first polycube representation and the first distortion grid; and

generating a visualization of the surface pressure model and the velocity field model for display on a display device.

2. The method of claim 1 , wherein parameterizing the first representation comprises:

generating a bounding box that surrounds the first polycube representation;

determining that a cube lies within the bounding box and is internal to the first polycube representation; and

classifying the cube as an input cube.

3. The method of claim 1 , wherein parameterizing the first representation comprises:

generating a bounding box that surrounds the first polycube representation;

determining that a cube lies within the bounding box and is external to the first polycube representation; and

classifying the cube as an exterior cube.

4. The method of claim 1 , wherein the first distortion grid includes a first plurality of grid points, parameterizing the first representation comprises computing a first valence value for a first grid point included in the first plurality of grid points, and the first valence value represents a number of faces of the first polycube representation that intersect with the first grid point.

5. The method of claim 4 , wherein parameterizing the first representation further comprises:

subdividing the first distortion grid to include a second plurality of grid points;

determining that a second grid point included in the second plurality of grid points lies on a surface of the design object; and

classifying the second grid point as a surface subdivision point.

6. The method of claim 4 , wherein parameterizing the first representation further comprises:

subdividing the first distortion grid to include a second plurality of grid points;

determining that a second grid point included in the second plurality of grid points lies exterior to the design object; and

classifying the second grid point as an exterior subdivision point.

7. A non-transitory computer-readable storage medium including instructions that, when executed by a processor, cause the processor to simulate a three-dimensional fluid flow by performing the steps of:

parameterizing a first representation of a design object to compute a first polycube representation;

computing a first distortion grid based on the first polycube representation;

computing, via a neural network, a velocity field model and a surface pressure model based on the first polycube representation and the first distortion grid; and

generating a visualization of the surface pressure model and the velocity field model for display on a display device.

8. The non-transitory computer-readable storage medium of claim 7 , wherein the first distortion grid includes a first plurality of grid points, parameterizing the first representation comprises computing a first valence value for a first grid point included in the first plurality of grid points, and the first valence value represents a number of faces of the first polycube representation that intersect with the first grid point.

9. The non-transitory computer-readable storage medium of claim 7 , wherein parameterizing the first representation further comprises determining that the first valence value is an odd number; and classifying the first grid point as a corner point.

10. The non-transitory computer-readable storage medium of claim 9 , wherein parameterizing the first representation further comprises determining that the first grid point does not lie on any surface of the design object, and moving a location of the first grid point in a first normal direction until the first grid point lies on a surface of the design object.

11. The non-transitory computer-readable storage medium of claim 10 , wherein parameterizing the first representation further comprises:

classifying a second point included in the first plurality of grid points as a surface point;

determining that the second grid point does not lie on any surface of the design object; and

moving a location of the second grid point until the second grid point lies on the surface of the design object based a ratio of a first distance between the second grid point and the first grid point and a second distance between the second grid point and a third grid point.

12. The non-transitory computer-readable storage medium of claim 9 , wherein parameterizing the first representation further comprises:

classifying a second grid point included the first plurality of grid points as an exterior point; and

moving a location of the second grid point as a linear function of a location of the first grid point.

13. The non-transitory computer-readable storage medium of claim 7 , wherein parameterizing the first representation further comprises determining that the first valence value is a non-zero even number, and classifying the first grid point as a surface point.

14. The non-transitory computer-readable storage medium of claim 7 , wherein parameterizing the first representation further comprises determining that the first valence value is zero, and classifying the first grid point as an exterior point.

15. The non-transitory computer-readable storage medium of claim 7 , further comprising generating a visualization of the surface pressure model and the velocity field model for display on a display device.

16. A computing device, comprising:

a memory that includes a parameterization application and a machine learning application; and

a processor that is coupled to the memory,

wherein, when the processor executes the parameterization application, the processor is configured to:

parameterize a first representation of a design object to compute a first polycube representation; and

compute a first distortion grid based on the first polycube representation, and

wherein, when the processor executes the machine learning application, the processor is configured to:

compute a surface pressure model based on the first polycube representation; and

compute a velocity field model based on the first polycube representation and the first distortion grid.

17. The computing device of claim 16 , wherein the machine learning application comprises a neural network that includes a linear regressor for computing a linear component of the surface pressure model and a nonlinear regressor for computing a nonlinear component of the surface pressure model.

18. The computing device of claim 16 , wherein the machine learning application comprises a neural network that includes a linear regressor for computing a linear component of the velocity field model and a nonlinear regressor for computing a nonlinear component of the velocity field model.

19. The computing device of claim 18 , wherein:

the nonlinear regressor includes a plurality of hidden layers;

a first hidden layer included in the plurality of hidden layers comprises a first number of neurons that include a first set of weights related to the nonlinear component;

a second hidden layer included in the plurality of hidden layers comprises a second number of neurons that include a second set of weights related to the nonlinear component; and

the first number of neurons is an integral multiple of the second number of neurons.

20. The computing device of claim 18 , wherein computing the velocity field model and the surface pressure model comprises:

receiving a first parameter set associated with the design object; and

converting the first parameter set to a second parameter set associated with the design object;

wherein a number of parameters included in the second parameter set is less than a number of parameters included in the first parameter set to reduce a number of neurons included in the neural network.