arXiv:2605.30112v1 Announce Type: new Abstract: Cross-Reynolds generalisation in neural PDE solvers remains poorly characterised. On the canonical forced 2D Navier-Stokes benchmark, a trained Fourier Neural Operator reaches 46.68% relative L2 error under a 10x Reynolds-number shift, yet zero-forward-model retrieval baselines already improve to 41-42%. This suggests representation geometry as a major organising variable among the tested methods. We test this hypothesis through ConvAE-Relay, which matches states in a source-trained convolutional autoencoder latent space and borrows dynamics from
Ongoing research in AI and scientific computing is continuously pushing the boundaries of neural network generalization for complex physical systems, making this a natural progression.
Improved generalization of neural PDE solvers across varying conditions like Reynolds numbers is crucial for more robust and reliable AI applications in engineering and scientific discovery.
The focus is shifting towards understanding and leveraging representation geometry to achieve better out-of-distribution generalization in neural PDE models, potentially moving beyond brute-force data scaling.
- · AI/ML researchers
- · Engineering R&D
- · Scientific computing
- · Fluid dynamics simulation
- · Traditional numerical methods (in specific applications)
- · Black-box AI models lacking interpretability
More accurate and efficient AI-driven simulations for complex physical phenomena, reducing computational cost and time.
Accelerated design cycles and discovery pipelines in fields like aerospace, climate modeling, and material science.
The development of truly general-purpose AI models capable of understanding and predicting diverse physical processes with minimal retraining.
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Read at arXiv cs.LG