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arXiv AI By Ha Dang, Sebastian Schmidt, Juergen Hesser

Smooth Piecewise Cutting for Neural Operator to Handle Discontinuities and Sharp Transitions

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The paper introduces Cut-DeepONet, a two‑stage training framework that explicitly models discontinuities in partial differential equations by partitioning the domain into smooth subregions and representing discontinuities as boundaries in a higher‑dimensional space. This lifting strategy aligns the operator learning task with neural network inductive biases, allowing the model to avoid directly approximating discontinuities. Experiments on benchmark PDEs demonstrate that Cut‑DeepONet outperforms state‑of‑the‑art methods, even with low‑resolution data, while using fewer trainable parameters.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv AI.

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