Researchers are developing novel neural network architectures to solve complex partial differential equations (PDEs) and model dynamical systems. These include structure-oriented randomized neural networks (SO-RaNN) for ion transport, informed neural controlled differential equations (INDEQS) for time-series forecasting with known graph structures, and starter-iterator neural operators (SINO) for high-fidelity PDE solutions. Additionally, orthogonal regularization (OrthoReg) is proposed to improve hybrid symbolic-neural models by preventing overlap between components, while other work explores conservation laws in modern neural architectures and a dynamical systems perspective for analyzing neural networks.
AI
IMPACT
These advancements could lead to more accurate and efficient modeling of complex physical systems, accelerating scientific discovery and engineering applications.
RANK_REASON
Multiple arXiv papers introducing new research methodologies in neural networks for scientific computing.
arXiv:2606.19368v1 Announce Type: cross Abstract: In this work we investigate the role of neural architectures as implicit functional priors in control problems governed by ordinary differential equations. Rather than focusing on highly complex problems, our objective is to inves…
arXiv:2604.06001v2 Announce Type: replace-cross Abstract: Efficiently solving the Fokker-Planck equation (FPE) is central to analyzing complex parameterized stochastic systems. However, current numerical methods lack parallel computation capabilities across varying conditions, se…
arXiv:2606.19912v1 Announce Type: cross Abstract: We develop a structure-oriented randomized neural network framework, termed SO-RaNN, for the Poisson-Nernst-Planck (PNP) system and the Poisson-Nernst-Planck-Navier-Stokes (PNP-NS) system. The decoupled linearized subproblems are …
We develop a structure-oriented randomized neural network framework, termed SO-RaNN, for the Poisson-Nernst-Planck (PNP) system and the Poisson-Nernst-Planck-Navier-Stokes (PNP-NS) system. The decoupled linearized subproblems are solved iteratively by randomized neural networks i…
arXiv:2606.19145v1 Announce Type: cross Abstract: Dynamical systems are fundamental to modeling the natural world, yet modeling them involves a persistent trade-off: manually prescribed mechanistic models are interpretable by design but often overly simplistic and misspecified; i…
arXiv:2606.18305v1 Announce Type: cross Abstract: Operator learning is an emerging interdisciplinary field that integrates machine learning with scientific computing. By mapping infinite-dimensional function spaces, this approach provides an efficient surrogate modeling framework…
arXiv cs.LG
TIER_1English(EN)·Michael Detzel, Gabriel Nobis, Kristiyan Blagov, Juri Schubert, Jackie Ma, Wojciech Samek·
arXiv:2606.19138v1 Announce Type: new Abstract: Neural Controlled Differential Equations (NCDE) provide a powerful continuous-time framework for forecasting time series, but standard graph-based extensions typically learn spatial structure purely from data, even in settings where…
Dynamical systems are fundamental to modeling the natural world, yet modeling them involves a persistent trade-off: manually prescribed mechanistic models are interpretable by design but often overly simplistic and misspecified; in contrast, flexible data-driven neural methods la…
arXiv cs.LG
TIER_1English(EN)·Dennis Chemnitz, Maximilian Engel, Christian Kuehn, Sara-Viola Kuntz·
arXiv:2507.05164v2 Announce Type: replace-cross Abstract: In this chapter, we utilize dynamical systems to analyze several aspects of machine learning algorithms. As an expository contribution we demonstrate how to re-formulate a wide variety of challenges from deep neural networ…
arXiv:2503.05598v2 Announce Type: replace-cross Abstract: This review examines neural operator architectures for learning solution operators of parametric partial differential equations (PDEs), with an emphasis on conceptual clarity and practical implementation. The work analyzes…
arXiv cs.AI
TIER_1English(EN)·Viet-Hoang Tran, Vinh Khanh Bui, Tan Lai Ngoc, Nam Nguyen, Tuan Dam, Tan M. Nguyen·
arXiv:2606.17816v1 Announce Type: cross Abstract: Understanding gradient descent dynamics is key to explaining the success of over-parameterized models, where implicit bias manifests through conservation laws in gradient flow. While such laws are well understood for linear and Re…
Understanding gradient descent dynamics is key to explaining the success of over-parameterized models, where implicit bias manifests through conservation laws in gradient flow. While such laws are well understood for linear and ReLU networks, they remain largely unexplored for mo…
arXiv cs.AI
TIER_1English(EN)·Reza T Batley, Andrew Kichline, Sourav Saha·
arXiv:2606.14934v1 Announce Type: cross Abstract: This work introduces the Separable Neural Architecture (SNA), a function representational class combining neural approximation with tensor decomposition. The SNA decouples localized coordinate functions (atoms) from global interac…
Neural Controlled Differential Equations (NCDE) provide a powerful continuous-time framework for forecasting time series, but standard graph-based extensions typically learn spatial structure purely from data, even in settings where a directed graph structure is known a priori. W…
