Shock-centered scaling of DSMC fields in micro-nozzles reveals low-rank density structure, enabling DeepONet surrogates with mean errors reduced to 4.51% on hardest test cases.
$\phi-$DeepONet: A Discontinuity Capturing Neural Operator
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abstract
We present $\phi-$DeepONet, a physics-informed neural operator designed to learn mappings between function spaces that may contain discontinuities or exhibit non-smooth behavior. Classical neural operators are based on the universal approximation theorem which assumes that both the operator and the functions it acts on are continuous. However, many scientific and engineering problems involve naturally discontinuous input fields as well as strong and weak discontinuities in the output fields caused by material interfaces. In $\phi$-DeepONet, discontinuities in the input are handled using multiple branch networks, while discontinuities in the output are learned through a nonlinear latent embedding of the interface. This embedding is constructed from a {\it one-hot} representation of the domain decomposition that is combined with the spatial coordinates in a modified trunk network. The outputs of the branch and trunk networks are then combined through a dot product to produce the final solution, which is trained using a physics- and interface-informed loss function. We evaluate $\phi$-DeepONet on several one- and two-dimensional benchmark problems and demonstrate that it delivers accurate and stable predictions even in the presence of strong interface-driven discontinuities.
years
2026 2representative citing papers
Cut-DeepONet uses a lifting strategy and an auxiliary network to predict discontinuity locations, enabling a neural operator to learn smooth components in partitioned regions and outperforming prior methods on benchmark PDEs with fewer parameters even on low-resolution data.
citing papers explorer
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Shock-Centered Low-Rank Structure and Neural-Operator Representation of Rarefied Micro-Nozzle Flows
Shock-centered scaling of DSMC fields in micro-nozzles reveals low-rank density structure, enabling DeepONet surrogates with mean errors reduced to 4.51% on hardest test cases.
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Smooth Piecewise Cutting for Neural Operator to Handle Discontinuities and Sharp Transitions
Cut-DeepONet uses a lifting strategy and an auxiliary network to predict discontinuity locations, enabling a neural operator to learn smooth components in partitioned regions and outperforming prior methods on benchmark PDEs with fewer parameters even on low-resolution data.