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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…
math.NA2025
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…