AI RESEARCH
Fredholm Neural Networks for inverse problems in elliptic PDEs
arXiv CS.LG
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ArXi:2507.06038v4 Announce Type: replace-cross 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 elliptic partial differential equations. The proposed scheme consists of a custom-designed deep neural network (DNN) in which the number of layers, weights, biases and hyperparameters are computed in an explainable manner based on a fixed-point scheme, and we. therefore. refer to this as the Potential Fredholm Neural Network.