We develop a convergent scheme to train neural networks involving analytic activation functions based on gradient flows. Convergence properties are guaranteed by Lojasiewicz theory.
arXiv:2607. 13574v1 Announce Type: cross Abstract: We develop a convergent scheme to train neural networks involving analytic activation functions based on gradient flows.
arXiv:2601. 07397v2 Announce Type: replace-cross Abstract: In this work, we propose a novel layerwise adaptive construction method for neural network architectures.
arXiv:2607. 24726v1 Announce Type: new Abstract: The Deep Galerkin Method (DGM) and Physics Informed Neural Networks (PINNs) have become widely-used methods for solving partial differential equations (PDEs) in the rapidly growing field of scientific machine learning.
arXiv:2402. 00152v5 Announce Type: replace Abstract: Constructing the architecture of a neural network is a challenging pursuit for the machine learning community, and the dilemma of whether to go deeper or wider remains a persistent question.
arXiv:2507. 14177v2 Announce Type: replace-cross Abstract: This paper aims to understand the training solution, which is obtained by the back-propagation algorithm, of two-layer neural networks whose hidden layer is composed of the units with smooth activation functions, including the usual sigmoid type most commonly used before the advent of ReLUs.
arXiv:2505. 12430v2 Announce Type: replace Abstract: Recently, innovative adaptations of the Ritz method incorporating deep learning have been developed, known as the Deep Ritz Method.
arXiv:2607. 10200v1 Announce Type: new Abstract: The Neural Tangent Kernel (NTK) is one powerful tool for analyzing the training dynamics of neural networks in the over-parameterized regime.
arXiv:2606. 12337v1 Announce Type: cross Abstract: Inverse problems governed by partial differential equations (PDEs) are central to computational mechanics and are commonly solved by adjoint-based optimization, while physics-informed neural networks (PINNs) have emerged as a flexible alternative.
arXiv:2608. 14733v1 Announce Type: cross Abstract: Building on the foundation of single-hidden-layer neural networks, Fourier Feature Networks (FENs) are proposed, which incorporate Fourier features using $\cos$, $\sin$, or a combination of both.
arXiv:2510. 09685v2 Announce Type: replace-cross Abstract: Deep learning has become a pivotal technology in fields such as computer vision, scientific computing, and dynamical systems, significantly advancing these disciplines.
arXiv:2606. 19895v1 Announce Type: cross Abstract: The matrices arising from large scale $N$-body problems can be efficiently represented using hierarchical matrices, whose key idea is that the admissible off-diagonal sub-matrices can be well approximated by low-rank matrices across a hierarchy of matrix partitions.
arXiv:2508. 21571v2 Announce Type: replace Abstract: Physics informed neural networks (PINNs) represent a very popular class of neural solvers for partial differential equations.