Geometry-Informed Neural Operator for Large-Scale 3D PDEs
Zongyi Li Nikola Borislavov Kovachki Chris Choy Boyi Li Jean Kossaifi Shourya Prakash Otta Mohammad Amin Nabian Maximilian Stadler Christian Hundt Kamyar Azizzadenesheli Anima Anandkumar
We propose the geometry-informed neural operator (GINO), a highly efficient
approach to learning the solution operator of large-scale partial differential
equations with varying geometries. GINO uses a signed distance function and
point-cloud representations of the input shape and neural operators based on
graph and Fourier architectures to learn the solution operator. The graph
neural operator handles irregular grids and transforms them into and from
regular latent grids on which Fourier neural operator can be efficiently
applied. GINO is discretization-convergent, meaning the trained model can be
applied to arbitrary discretization of the continuous domain and it converges
to the continuum operator as the discretization is refined. To empirically
validate the performance of our method on large-scale simulation, we generate
the industry-standard aerodynamics dataset of 3D vehicle geometries with
Reynolds numbers as high as five million. For this large-scale 3D fluid
simulation, numerical methods are expensive to compute surface pressure. We
successfully trained GINO to predict the pressure on car surfaces using only
five hundred data points. The cost-accuracy experiments show a $26,000 \times$
speed-up compared to optimized GPU-based computational fluid dynamics (CFD)
simulators on computing the drag coefficient. When tested on new combinations
of geometries and boundary conditions (inlet velocities), GINO obtains a
one-fourth reduction in error rate compared to deep neural network approaches.