The development of land, air, and sea vehicles with low drag and good stability has benefited greatly from the huge strides made in Computational Fluid Dynamics (CFD). Simulation of fluid flow over three-dimensional computer representations of a vehicle requires the solving of Navier-Stokes equations through many hundreds—and often thousands—of iterations. The result is an approximation of the flow field and pressure distribution that can be used to visualize the flow through streamlines and other techniques. The downside is the enormous amount of computing time that it takes—many hours or even days—to achieve a reasonably accurate and converged solution.
Now, Nobuyuki Umetani, formerly from Autodesk research (and now at the University of Tokyo), and Bernd Bickel, from the Institute of Science and Technology Austria (IST Austria), have devised a way to speed these simulations. They have developed a method using machine learning that “learns” to mode flow around three-dimensional objects, making streamlines and parameters like drag coefficient available in real time.
Using machine learning to help predict fluid flow came from discussions between Umetani and Bickel, long-time collaborators in CFD. "We both share the vision of making simulations faster," explained Bickel in an IST news release. "We want people to be able to design objects interactively, and therefore we work together to develop data-driven methods."
The new fluid flow simulation technique shows streamlines and pressure distribution on the vehicle surface (color-coded). On the left are some of the shapes used to train the program. On the right are the results of new vehicles simulated by the program. (Image source: Nobuyuki Umetani)
Machine Learning in Training
The technique the pair developed involves “training” the machine learning program on the converged CFD data for a variety of shapes and vehicle designs that are representative of typical vehicles. More than 800 vehicle shapes were used to train the program. Once the program has been trained, a process using Gaussian Process regression is utilized to infer the velocities and pressures for a new shape based on all of the previous vehicles and shapes. "With our machine learning tool, we are able to predict the flow in fractions of a second," said Nobuyuki Umetani in the IST release.
Machine learning has some restrictive requirements that had to be overcome in the development of this method. In machine learning, both the input and the output data need to be structured in a way that is consistent. This is relatively easy to accomplish with two-dimensional images, where a regular arrangement of pixels can represent the object. In three dimensions, however, the geometric objects define the shape. With a mesh of triangles, for example, the arrangement of the triangles can change if the shape changes, resulting in an inconsistency.
Umetani’s solution was to adapt polycubes to build a shape that could be used with machine learning. The polycube approach was originally developed to apply textures to objects in computer animations. The IST release described their use in this way: “A model starts with a small number of large cubes, which are then refined and split up in smaller ones following a well-defined procedure. If represented in this way, objects with similar shapes will have a similar data structure that machine learning methods can handle and compare.”
Aside from the huge time savings, the method described allows modifications and shape changes to be made in real time by interactively pulling and pushing the polycubes. The changes in drag coefficient, surface pressure distribution, and flow field streamlines are shown nearly instantly. As a result, the designer or stylist can immediately see the effect of their shape changes. This video shows the interactive capability of the new program.
A paper written by Umetani and Bickel and published in the journal ACM Transactions in Graphics also details the accuracy of the method. The results show similar errors (approximately 3.4% in drag coefficient) as do other CFD techniques, which is consistent with the error expected when various wind tunnels are compared to one another using similar conditions.
One reason for the high level of accuracy comes directly from machine learning. "When simulations are made in the classical way, the results for each tested shape are eventually thrown away after the computation. This means that every new computation starts from scratch. With machine learning, we make use of the data from previous calculations, and if we repeat a calculation, the accuracy increases,” explained Umetani.
Senior Editor Kevin Clemens has been writing about energy, automotive, and transportation topics for more than 30 years. He has masters degrees in Materials Engineering and Environmental Education and a doctorate degree in Mechanical Engineering, specializing in aerodynamics. He has set several world land speed records on electric motorcycles that he built in his workshop.
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