20 citations · 59 across the 22 of their papers we have counts for
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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…
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…
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…