Cellular Sheaf Neural Operators for Structure-Preserving Surrogate Modeling of Constrained PDEs
arXiv:2606.00937v1 Announce Type: new Abstract: Neural operators provide fast surrogate models for PDE simulations, but standard architectures often treat geometry and discretization as secondary to field data. Physical states are usually represented as grid-channel stacks, even when different quantities naturally belong on vertices, edges, faces, cells, boundaries, or interfaces and must satisfy compatibility constraints. We propose Cellular Sheaf Neural Operators, a discretization-aware framework for structure-preserving neural PDE surrogates. The method represents PDE states on oriented cel
The increasing complexity of PDE simulations and the drive for more efficient, physically consistent AI models necessitate advancements in neural operator architectures.
This development addresses a critical limitation of current neural operators by enabling structure-preserving surrogate modeling, leading to more accurate and reliable AI in scientific computing.
Neural PDE surrogates can now better incorporate fundamental physical and geometric constraints, leading to improved fidelity and broader applicability in complex systems.
- · Scientific computing researchers
- · Engineering simulation developers
- · AI model developers for scientific applications
- · Traditional PDE solvers (in specific applications)
- · AI models lacking geometric and physical awareness
More accurate and faster AI surrogates for complex PDE simulations become available.
Accelerated design and optimization cycles in fields like materials science, plasma physics, and climate modeling due to improved simulation speed and accuracy.
Enhanced AI-driven discovery of novel materials, energy solutions, and climate mitigation strategies through high-fidelity, physically informed models.
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Read at arXiv cs.LG