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DoMINO: A Decomposable Multi-scale Iterative Neural Operator for Modeling Large Scale Engineering Simulations
Rishikesh Ranade, Mohammad Amin Nabian, Kaustubh Tangsali, Alexey Kamenev, Oliver Hennigh, Ram Cherukuri, Sanjay Choudhry
TL;DR
Large-scale engineering simulations are costly, while existing ML surrogates can struggle with mesh size, geometry representation, accuracy, and generalization. DoMINO addresses these challenges with a multi-scale iterative neural operator that uses point-cloud geometry and local representations to predict flow fields. On automotive aerodynamics data, it captures surface and volume fields and generalizes across test samples and mesh or point-cloud configurations.
Problem
Existing ML surrogates struggle to scale to very large simulations and may lose accuracy or generalization across geometry and point-cloud configurations.
Method
DoMINO uses point-cloud geometry, multi-scale iterative representations, and local geometry encodings to predict solutions at discrete computational points.
Results
The experiments show accurate surface and volume flow-field predictions, engineering-metric modeling, out-of-distribution generalization, and scaling to large meshes and point clouds.
Takeaways & Limitations
DoMINO provides a demonstrated surrogate-modeling approach for large-scale automotive aerodynamics without requiring mesh generation during inference.
Takeaways & Limitations
The model currently relies on fixed-resolution latent spaces, and some bounding-box behavior is not clearly understood.
Abstract
from arXiv · showhide
Numerical simulations play a critical role in design and development of engineering products and processes. Traditional computational methods, such as CFD, can provide accurate predictions but are computationally expensive, particularly for complex geometries. Several machine learning (ML) models have been proposed in the literature to significantly reduce computation time while maintaining acceptable accuracy. However, ML models often face limitations in terms of accuracy and scalability and depend on significant mesh downsampling, which can negatively affect prediction accuracy and generalization. In this work, we propose a novel ML model architecture, DoMINO (Decomposable Multi-scale Iterative Neural Operator) developed in NVIDIA Modulus to address the various challenges of machine learning based surrogate modeling of engineering simulations. DoMINO is a point cloudbased ML model that uses local geometric information to predict flow fields on discrete points. The DoMINO model is validated for the automotive aerodynamics use case using the DrivAerML dataset. Through our experiments we demonstrate the scalability, performance, accuracy and generalization of our model to both in-distribution and out-of-distribution testing samples. Moreover, the results are analyzed using a range of engineering specific metrics important for validating numerical simulations.
1. Introduction
Engineering simulations require a trade-off between accuracy and computational cost, while existing ML surrogates struggle with large meshes, geometry representation, and distribution shifts. DoMINO is proposed as a scalable, accurate, and generalizable point-cloud surrogate, demonstrated on automotive aerodynamics.
- Traditional numerical simulation cost grows with mesh size, motivating methods that improve computational efficiency without sacrificing accuracy.Meshing and solving become more expensive as element counts increase.
- Existing ML methods often cannot scale to simulations with hundreds of millions or billions of elements while retaining accuracy and generalizability.Large-scale methods may fail to represent geometry efficiently or capture long-range interactions.
- ML models trained on simulation meshes can lose accuracy and generalization when evaluated on uniform point clouds or meshes.
- DoMINO is introduced as a decomposable, multi-scale, iterative neural operator for scalable, accurate, and generalizable surrogate modeling.The architecture is demonstrated for external automotive aerodynamics, where large meshes and fine geometric features make scalability and representation especially challenging.
- Using DrivAerML, the study evaluates surface and volume flow fields, engineering metrics, design trends, and drag comparisons on remaining samples after training.The dataset contains high-fidelity simulations on large meshes and substantial geometric variation.
2. DoMINO Model Overview
DoMINO encodes point-cloud geometry globally and extracts local, multi-scale representations around sampled computational stencils. Separate aggregation networks then predict solution variables from local geometry and point features.
- 2. DoMINO Model Overview: DoMINO transforms a geometry point cloud into a structured global encoding, then uses local encodings to predict PDE solutions at sampled computational points.The global representation captures geometry features across the domain, while local representations focus prediction on nearby information.
- 2.1. Global geometry representation: A multi-resolution iterative strategy propagates geometry information through the computational domain to learn short- and long-range dependencies.
- 2.3. Aggregation network: Surface and volume solution variables use separate aggregation networks while sharing the global geometry representation.
- 2.1. Global geometry representation: Point convolutions project surface-point features onto structured grids, while additional multi-scale kernels and CNN blocks propagate geometry features into the computational domain.The geometry network uses bounding boxes for the surface and computational domain.
- 2.1. Global geometry representation: The radius of influence controls whether point convolutions capture finer geometric details or propagate information over larger distances.DoMINO combines multiple kernel sizes to represent both local features and long-range geometry interactions.
- 2.3. Aggregation network: For each sampled point, neighboring points form a computational stencil whose coordinates, SDF, and normals are combined with local geometry features to predict solution values.The aggregation network predicts stencil-point solutions and averages them with inverse-distance weighting; separate instances are used for each solution variable.
3. Experiments details
The experiments apply DoMINO to predict aerodynamic volume and surface fields from car geometry using the high-fidelity DrivAerML dataset. Training uses sampled simulation points, mixed-precision optimization, and a large set of morphed vehicle geometries.
- 3.1. Problem setup: DoMINO predicts volume velocity, pressure, and turbulent viscosity alongside surface pressure and wall-shear stress from an STL car geometry.Sampled-point coordinates, signed distance values, domain-center normals, and surface normals provide aggregation-network inputs.
- 3.1. Problem setup: The setup evaluates DoMINO on surface and volume fields, using sampled points where ground-truth simulation values are available for training losses.
- 3.2. Dataset: DrivAerML contains high-fidelity volume and surface data for 500 geometrically morphed DrivAer Notchback variants.The dataset includes surface pressure and wall-shear-stress data and corresponding volume data from hybrid RANS/LES simulations.
- 3.3. Training: The model is trained with Adam for 500 epochs using a reduce-on-plateau schedule that lowers the learning rate from 1e−3 to 1e−6.Training uses float-16 precision with Automatic Mixed Precision.
4. Results and analysis
DoMINO is evaluated on in-distribution and out-of-distribution automotive aerodynamics samples using surface and volume field errors, contour comparisons, and drag-force trends. The model captures surface and volumetric flow behavior reasonably accurately, while showing unexplained edge artifacts in the bounding-box contours.
- Surface quantities: Area-weighted relative errors are lower for all surface solution variables, while Y- and Z-wall-shear-stress errors are comparatively worse because their magnitudes are small.The errors are averaged over the test cases for pressure and wall-shear-stress fields on the car surface.
- Surface quantities: Surface pressure and wall-shear-stress contours are captured reasonably well across test designs, including the windshield, side mirrors, and underbody.Figure 6 compares simulated contours, DoMINO predictions, and their errors.
- Surface quantities: R2 = 0.96 for both surface-mesh and 10-million-point-cloud drag-force calculations, indicating a reasonable match between simulated and DoMINO-predicted drag forces.Design trends are captured well, although smaller directional changes between successive designs show oscillatory behavior in predictions.
- Volume quantities: Volume predictions capture flow dynamics reasonably accurately in the wake, underbody, and near the hood, including sparse turbulent-viscosity fields downstream of the car.Figure 8 presents pressure, velocity-magnitude, and turbulent-viscosity comparisons on X-Y and X-Z planes.
- Volume quantities: Contour artifacts appear near the bounding-box edges, but they do not affect important regions near the car; their cause remains unclear.This behavior is identified as requiring further investigation.
5. Conclusion
DoMINO is designed for scalable, accurate, and generalizable large-scale simulation modeling through point-cloud inputs, multi-scale propagation, local encodings, and stencil-based prediction. Experiments on automotive aerodynamics show accurate field and engineering-metric predictions, including out-of-distribution samples and large meshes, while future work targets oscillatory predictions and richer resolution or physics constraints.
- 5. Conclusion: DoMINO operates directly on point-cloud geometries, avoiding mesh generation during inference and supporting flexible use across sampled representations.Dynamic ball-query kernels encode geometry, while batched evaluation supports large computational domains and meshes.
- 5. Conclusion: Multi-scale kernels propagate geometry information iteratively to model both short- and long-range interactions efficiently.The architecture combines global geometry representations with local encodings and dynamically constructed stencils around prediction points.
- 5. Conclusion: Local stencil processing captures neighborhood information needed to predict solutions accurately at sampled points.A basis-function neural network processes local stencil points and aggregates them to calculate the solution.
- 5. Conclusion: DoMINO accurately captures surface and volume flow fields, drag-force regression, and design trends while generalizing to out-of-distribution samples and varying mesh or point-cloud configurations.The experiments also demonstrate scaling to large meshes and point clouds with real-time inference.
- 5. Conclusion: Future work targets oscillatory predictions, fixed-point convergence, multi-resolution latent spaces, PDE-based training constraints, transient problems, and broader engineering applications.The proposed extensions are intended to improve accuracy, performance, geometric detail, and long-range interactions.