Adaptive-Growth Randomized Neural Networks for Level-Set Computation of Multivalued Nonlinear First-Order PDEs with Hyperbolic Characteristics
This paper proposes an Adaptive-Growth Randomized Neural Network (AG-RaNN) method for computing multivalued solutions of nonlinear first-order PDEs with hyperbolic characteristics, including quasilinear hyperbolic balance laws and Hamilton--Jacobi equations. Such solutions arise in geometric optics, seismic waves, semiclassical limit of quantum dynamics and high frequency limit of linear waves, and differ markedly from the viscosity or entropic solutions. The main computational challenges lie in that the solutions are no longer functions, and become union of multiple branches, after the formation of singularities. Level-set formulations offer a systematic alternative by embedding the nonl...
| Authors | Haoning Dang, Shi Jin, Fei Wang |
|---|---|
| Primary category | math.NA |
| Published | 1 March 2026 |
| Last updated at source | 1 March 2026 |
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