102 citations · 132 across the 8 of their papers we have counts for
13 papers
Learning Contractive Integral Operators with Fredholm Integral Neural Operators
Kyriakos C. Georgiou, Constantinos Siettos, Athanasios N. Yannacopoulos
We generalize the framework of Fredholm Neural Networks, to learn non-expansive integral operators arising in Fredholm Integral Equations (FIEs) of the second kind in arbitrary dim…
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…
Fredholm Neural Networks for inverse problems in elliptic PDEs
Kyriakos C. Georgiou, Constantinos Siettos, Athanasios N. Yannacopoulos
Building on our previous work on Fredholm Neural Networks (Fredholm NNs/ FNNs) for solving integral equations, we extend the framework to inverse problems for linear and nonlinear…
Fredholm Neural Networks
Kyriakos Georgiou, Constantinos Siettos, Athanasios N. Yannacopoulos
Within the family of explainable machine-learning, we present Fredholm neural networks (Fredholm NNs): deep neural networks (DNNs) architectures motivated by fixed-point iteration…
Probability of Default modelling with Lévy-driven Ornstein-Uhlenbeck processes and applications in credit risk under the IFRS 9
Kyriakos Georgiou, Athanasios N. Yannacopoulos
In this paper we develop a framework for estimating Probability of Default (PD) based on stochastic models governing an appropriate asset value processes. In particular, we build u…
Security-Hardening Software Libraries with Ada and SPARK -- A TCP Stack Use Case
Kyriakos Georgiou, Guillaume Cluzel, Paul Butcher +1
This white paper demonstrates how the assurance, reliability, and security of an existing professional-grade, open-source embedded TCP/IP stack implementation written in the C prog…