The authors prove restricted strong convexity and smoothness for DeepONet and FNO losses, yielding gradient descent convergence guarantees that improve with network width.
This is the same setup as in (Wang et al., 2021a; Lu et al., 2021)
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Optimization for Neural Operators can Benefit from Width
The authors prove restricted strong convexity and smoothness for DeepONet and FNO losses, yielding gradient descent convergence guarantees that improve with network width.