Multi-scale Geometry Transformer Enables Accurate Drag/Lift Prediction in CAE Simulations

The challenge of accurately simulating complex physical phenomena, such as airflow around vehicles, demands increasingly sophisticated computational methods. Corey Adams, Rishikesh Ranade, and Ram Cherukuri, alongside Sanjay Choudhry from NVIDIA Corporation, present GeoTransolver, a new approach to operator learning that significantly improves the accuracy and efficiency of these simulations. This innovative system employs a multi-scale geometry-aware physics attention transformer, effectively linking physical laws with the complex shapes of real-world objects. By persistently anchoring computations to domain structure and operating regimes, GeoTransolver delivers superior performance on challenging aerodynamic datasets, demonstrating improved robustness and data efficiency compared to existing methods and paving the way for high-fidelity surrogate modeling across complex, irregular domains.

Geometric Transformers Learn Partial Differential Equations

This research introduces Geometry-Informed Neural Operator Transformers (GNOT), a novel architecture combining Neural Operators (NOs) and Transformers for learning and predicting solutions to Partial Differential Equations (PDEs). The key innovation lies in incorporating geometric information into the transformer architecture by leveraging Graph Neural Networks to encode domain geometry and employing geometry-aware attention mechanisms. This approach improves prediction accuracy and captures underlying physics more effectively. The work builds upon existing research in Neural Operators, including Fourier Neural Operators and Graph Neural Operators, and extends the application of Transformers to scientific computing.

It also draws from Physics-Informed Machine Learning techniques like Physics-Informed Neural Networks. Benchmarking on standardized datasets, such as those used in automotive aerodynamics, demonstrates improved performance compared to existing methods. The field of operator learning is rapidly evolving, with a growing emphasis on combining different machine learning techniques and incorporating geometric information into models. Benchmarking on standardized datasets is essential for evaluating algorithm performance, and the combination of neural operators and transformers holds great promise for solving complex PDEs and advancing scientific computing.

Geometry-Aware Transformers for Physics Simulation

Scientists developed GeoTransolver, a new transformer architecture for computational analysis that addresses limitations in handling complex geometries and varying physical conditions. This system replaces standard attention mechanisms with Geometry-Aware Latent Embeddings (GALE), coupling physics-aware self-attention with cross-attention to a shared geometric context. This context, derived from multi-scale analysis, persistently anchors computations to the domain structure and operating conditions throughout the simulation. The team engineered a method for pre-computing multi-scale features and appending them to local inputs, alongside the shared context, before the initial transformer block. This ensures consistent geometric and physical awareness throughout the computation. Tested on benchmarks including DrivAerML and Luminary SHIFT models, GeoTransolver demonstrates improved accuracy and robustness compared to existing methods.

Geometry-Aware Transformers for Engineering Simulations

Scientists developed GeoTransolver, a new transformer architecture for computer-aided engineering, significantly advancing surrogate modeling for complex physical simulations. The work introduces Geometry-Aware Latent Embedding (GALE) attention, pairing physics-aware self-attention with cross-attention to multi-scale geometric neighborhoods and global context. This innovative approach directly addresses challenges in modeling physics, such as handling irregular geometries and limited data availability. Experiments demonstrate that GeoTransolver achieves improved accuracy, data efficiency, and robustness across datasets including DrivAerML, Luminary SHIFT-SUV, and Luminary SHIFT-Wing. The team benchmarked GeoTransolver against state-of-the-art architectures, consistently demonstrating superior performance. A key element of the design is a geometry-context projection strategy, mapping geometric and global features into physical state spaces and injecting them into every transformer block, which reduces representation drift and enhances stability.

Geometry-Aware Transformers Improve Simulation Accuracy

GeoTransolver, a new transformer architecture for computational engineering, successfully integrates geometry into the learning process, enhancing the accuracy and robustness of simulations. The team achieved this by replacing standard attention mechanisms with Geometry-Aware Latent Embeddings (GALE), coupling physics-aware self-attention with cross-attention to a shared geometric context. This context, derived from multi-scale analysis, persistently anchors computations to the domain structure and operating conditions throughout the simulation. Extensive benchmarking on datasets including DrivAerML, SHIFT-SUV, and SHIFT-Wing demonstrates that GeoTransolver consistently matches or exceeds the performance of existing state-of-the-art methods. The model exhibits improved resilience to changes in geometry and operating conditions while maintaining efficient data usage. The GeoTransolver architecture and associated software are openly available, facilitating broader access and collaboration within the research community.