4 papers · 1 filter
Stability and Bifurcation Analysis of Nonlinear PDEs via Random Projection-based PINNs: A Krylov-Arnoldi Approach
Gianluca Fabiani, Michail E. Kavousanakis, Constantinos Siettos +1
We address a numerical framework for the stability and bifurcation analysis of nonlinear partial differential equations (PDEs) in which the solution is sought in the function space…
HEATNETs: Explainable Random Feature Neural Networks for High-Dimensional Parabolic PDEs
Kyriakos Georgiou, Gianluca Fabiani, Constantinos Siettos +1
We deal with the solution of the forward problem for high-dimensional parabolic PDEs with random feature (projection) neural networks (RFNNs). We first prove that there exists a si…
Linear Stability Analysis of Physics-Informed Random Projection Neural Networks for ODEs
Gianluca Fabiani, Erik Bollt, Constantinos Siettos +1
We present a linear stability analysis of physics-informed random projection neural networks (PI-RPNNs), for the numerical solution of {the initial value problem (IVP)} of (stiff)…
On the accuracy of interpolation based on single-layer artificial neural networks with a focus on defeating the Runge phenomenon
Ferdinando Auricchio, Maria Roberta Belardo, Gianluca Fabiani +2
In the present paper, we consider one-hidden layer ANNs with a feedforward architecture, also referred to as shallow or two-layer networks, so that the structure is determined by t…