Stability and Bifurcation Analysis of Nonlinear PDEs via Random Projection-based PINNs: A Krylov-Arnoldi Approach
We present a numerical framework for the stability and bifurcation analysis of nonlinear partial differential equations (PDEs) in which the solutions are sought in the function space spanned by physics-informed random projection neural networks (PI-RPNNs), and discretized via a collocation approach. These are shallow, single-hidden-layer networks with randomly sampled and fixed a priori hidden-layer weights; only the linear output layer weights are optimized, reducing training to a single least-squares solve. This linear output structure enables the explicit generalized eigenvalue formulation governing the linear stability of stationary solutions, separating the physical domain interior d...
| Authors | Gianluca Fabiani, Michail E. Kavousanakis, Constantinos Siettos et al. |
|---|---|
| Primary category | math.NA |
| Published | 23 March 2026 |
| Last updated at source | 20 September 2026 |
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