arXiv:2606.03260v1 Announce Type: new Abstract: Deep learning surrogates for 3D Partial Differential Equations (PDEs) often fail to generalize across geometric transformations because they depend heavily on specific coordinate systems. While equivariant networks offer a solution, they typically rely on local operations in the spatial domain, making the global receptive field, which is essential for PDE dynamics, computationally expensive. Conversely, Fourier Neural Operators (FNOs) efficiently capture global interactions, yet establishing 3D equivariance within them remains impractical due to
The continuous drive for more efficient and robust deep learning models for scientific computing necessitates addressing current architectural limitations, particularly in handling complex 3D physics.
Improving the generalization and computational efficiency of AI surrogates for 3D Partial Differential Equations accelerates scientific discovery and engineering design across numerous fields.
The proposed EqGINO framework offers a method to combine the strengths of equivariant networks and Fourier Neural Operators, potentially overcoming current limitations in applying deep learning to complex 3D physical simulations.
- · Scientific computing researchers
- · Engineering design firms
- · AI model developers
- · Materials science
- · Traditional numerical simulation methods (in niche applications)
More accurate and faster simulations will become feasible for a range of 3D physical problems.
Accelerated design cycles for new materials, drugs, and complex systems could lead to faster innovation.
Reduced computational costs for research and development could lower barriers to entry for certain industries, fostering new competition.
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Read at arXiv cs.LG