arXiv:2607. 07637v1 Announce Type: new Abstract: This work presents a novel approach for adapting neural network architecture along the depth based on a posteriori error estimation.
By C G Krishnanunni, Thomas Scott, Tan Bui-Thanh
arXiv:2601. 07397v2 Announce Type: replace-cross Abstract: In this work, we propose a novel layerwise adaptive construction method for neural network architectures.
By Michael Hinterm\"uller, Michael Hinze, Denis Korolev
arXiv:2605. 09075v2 Announce Type: replace-cross Abstract: Although the Laplace approximation offers a simple route to uncertainty quantification in deep neural networks, its reliance on inverting large Hessian matrices has motivated a range of computationally feasible low-dimensional or sparse approximations.
By Swarnali Raha, Kshitij Khare, Rohit K Patra
arXiv:2505. 15497v3 Announce Type: replace Abstract: Neural networks hold great potential to act as approximate models of nonlinear dynamical systems, with the resulting neural approximations enabling verification and control of such systems.
By Frederik Baymler Mathiesen, Nikolaus Vertovec, Francesco Fabiano, Luca Laurenti, Alessandro Abate
arXiv:2604. 20219v2 Announce Type: replace Abstract: Depth is widely viewed as a central contributor to the success of deep neural networks, whereas standard neural network approximation theory typically provides guarantees only for the final output and leaves the role of intermediate layers largely unclear.
By Shijun Zhang, Zuowei Shen, Yuesheng Xu
arXiv:2608. 06428v1 Announce Type: new Abstract: Deep Operator Networks (DeepONets; arXiv:1910.
By Khemraj Shukla, George Em Karniadakis