研究人员开发了新颖的物理信息神经网络（PINNs）来解决复杂的微分方程。一种方法，伪微分增强PINNs，利用傅里叶变换实现更快、更有效的训练，提高保真度并处理分数阶导数。另一种方法，元逆PINNs，将逆向建模重新表述为元学习问题，以提高高维常微分方程的样本效率和泛化能力，并在药代动力学模型中取得了成功。 AI
影响 PINNs的这些进展可以通过对复杂动力学系统进行更准确、更有效的建模来加速科学发现。
排序理由 该集群包含多篇arXiv论文，详细介绍了物理信息神经网络的新研究和方法。
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arXiv:2605.05217v1 Announce Type: new Abstract: We propose a self-supervised physics-informed neural network (PINN) framework that adaptively balances physics-based and data-driven supervision for scientific machine learning under data scarcity. Unlike prior PINNs that rely on fi…
arXiv:2506.13950v2 Announce Type: replace-cross Abstract: We propose a hybrid physics-informed machine learning framework to approximate invariant manifolds (IMs) of discrete-time dynamical systems driven by exogenous autonomous dynamics (exosystems). Such systems appear in appli…
arXiv:2408.01914v4 Announce Type: replace-cross Abstract: Several forms for constructing novel physics-informed neural-networks (PINN) for the solution of partial-differential-algebraic equations based on derivative operator splitting are proposed, using the nonlinear Kirchhoff r…
arXiv:2605.03511v1 Announce Type: new Abstract: Solving inverse problems in dynamical systems governed by high-dimensional coupled ordinary differential equations (ODEs) is a ubiquitous challenge in scientific machine learning. In many real-world applications, researchers seek to…
arXiv:2602.14663v2 Announce Type: replace Abstract: We present pseudo-differential enhanced physics-informed neural networks (PINNs), an extension of gradient enhancement but in Fourier space. Gradient enhancement of PINNs dictates that the PDE residual is taken to a higher diffe…
Solving inverse problems in dynamical systems governed by high-dimensional coupled ordinary differential equations (ODEs) is a ubiquitous challenge in scientific machine learning. In many real-world applications, researchers seek to uncover unknown parameters or model unknown dyn…