Dresden 2026 – wissenschaftliches Programm

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AKPIK: Arbeitskreis Physik, moderne Informationstechnologie und Künstliche Intelligenz

AKPIK 2: Machine Learning Prediction and Optimization Tasks

AKPIK 2.4: Vortrag

Dienstag, 10. März 2026, 10:15–10:30, BEY/0127

Modeling resonant soliton interactions in the Kadomtsev-Petviashvili equation using PINNs — •Gerald Kämmerer — Universität Duisburg

Resonant two-soliton interactions in the Kadomtsev-Petviashvili (KP) equation are modeled using Physics-Informed Neural Networks (PINNs). This framework directly solves the KP equation by incorporating the governing partial differential equation residuals into the loss function, specifically focusing on Y-shaped resonances and web-like patterns that occur under specific resonance conditions. Comparisons with known algebraic solutions show a good agreement in capturing characteristic interaction patterns. To accelerate the learning of complex dynamics, progressive training strategies and symmetry-informed network architectures are implemented, embedding the equation's inherent coordinate symmetries. The results demonstrate that PINNs can capture the rich dynamics of resonant soliton interactions, offering a framework for exploring parameter regimes beyond traditional numerical methods.

Keywords: PINNs; Kadomtsev-Petviashvili; PDE; Soliton