A Data-Free Physics-Informed Neural Operator for Level-Set Interface Advection
Operators for interfacial problems are trained on reference solutions produced by the solver they are intended to replace. This work develops a data-free physics-informed neural operator for level-set interface advection, in which the interface is the equation's unknown and the operator maps an initial interface to the full spatiotemporal trajectory under a prescribed flow. Training uses only the transport residual and a geometric constraint; no reference solution enters the objective at any point. A spacetime Fourier backbone emits the entire trajectory in one pass, and the initial condition is imposed by construction rather than by penalty, which removes the competition between the anch...
| Authors | Muhammad Akbar Khan |
|---|---|
| Primary category | cs.LG |
| Published | 18 September 2026 |
| Last updated at source | 18 September 2026 |
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