arXiv:2606.14597v1 Announce Type: new Abstract: Transformer-based neural operators have shown remarkable performance for approximating solution operators of partial differential equations on complex geometries. However, existing approaches implicitly assume a fixed domain size, which limits their ability to generalize at inference. In this work, we investigate domain extension, namely zero-shot inference on spatial domains that are significantly larger than those encountered during training. We argue that this setting fundamentally requires spatial locality and translation equivariance. We pro
The continuous advancements in transformer architectures are leading to explorations of their limits and generalization capabilities in complex scientific computing domains like PDE solving.
Improving zero-shot generalization for neural operators in larger domains can significantly reduce dependency on extensive retraining for new problem sizes, accelerating scientific discovery and engineering R&D.
The ability to generalize AI models across different problem scales without re-training fundamentally alters development cycles and deployment costs in AI-driven simulation and design.
- · AI research labs
- · Engineering simulation software providers
- · Industries relying on complex PDE solvers (e.g., aerospace, pharmaceuticals)
- · Cloud computing providers
- · Traditional fixed-grid simulation software companies
More robust and scalable AI models for scientific and engineering applications.
Reduced computational costs and time for designing and optimizing complex systems.
Accelerated discovery of new materials, drugs, and other innovations through more efficient simulation and prediction.
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Read at arXiv cs.LG