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About this paper
Yuan Guo, Hanshu Chen, Qiang Xi, Timon Rabczuk, Zhuojia Fu
KernelOnet replaces DeepONet’s learned spatial basis with explicit kernels that reflect PDE physics. Its physics-informed variant uses an analytic fundamental solution, while its hybrid variant adds a learned correction for nonlinear effects. At ε = 4, the hybrid error is 2.75 × 10⁻³ versus 2.08 × 10⁻² without correction; this supports an advantage in that tested setting, not universally.
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