6 papers
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…
Barycentric model aggregation in the Wasserstein space of distributions and a variational approach to consistency
Emmanouil Androulakis, Georgios I. Papayiannis, Athanasios N. Yannacopoulos
We study the problem of model aggregation within the Wasserstein space for probability measures on the real line. Given a fixed finite collection of candidate probability models, w…
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…
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…
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)…