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Research questionHow can DeepONet-style neural operators represent sharp moving discontinuities in shock-dominated, low-viscosity PDEs?Sharp moving discontinuities and slowly decaying solution spectra make finite-dimensional separable representations difficult to use for shock-dominated and low-viscosity PDEs. The challenge concerns how function observations and query locations are represented and combined.
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Latest papersRecent research connected to this question, newest first.Feature Interaction Modeling for Neural OperatorsThe source studies DeepONet-style operators and introduces feature construction and interaction changes intended to improve this setting. Evidence comes from multiple PDE benchmarks comparing the proposed operator with vanilla DeepONet and Shift-DeepONet.research paper · Sep 2, 2026
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