English(EN)The limits of exactness: On the failure of automatic differentiation in physics-informed machine learning
新研究探讨物理信息神经网络和算子 · 追踪10个来源
作者PulseAugur 编辑部·[11 个来源]·
多篇研究论文探讨了物理信息神经网络（PINNs）和神经网络算子的进展。一项研究调查了机器学习模型中改进的分数是否能直接转化为翼型周围流动模拟的更好物理精度。另一篇论文质疑了PINNs对自动微分的依赖，认为数值精度不能保证物理保真度。其他研究引入了新颖的架构和训练方法，例如用于界面对流的无数据算子、使用嘈杂的蒙特卡洛估计进行粒子输运训练，以及用于改善物理信息训练中条件化的预处理损失。还提出了因果积分项和梯度手术等技术，以增强PINNs在复杂演化方程和多任务优化问题上的性能和可扩展性。
AI
arXiv:2610.00415v1 Announce Type: new Abstract: Machine-learning surrogates accelerate physical simulation, but lower prediction error need not coincide with lower error in physically relevant flow statistics. We examine this question for flow around a NACA4418 airfoil using pair…
arXiv:2609.33078v2 Announce Type: replace Abstract: Automatic differentiation (AD) lets neural networks compute derivatives of governing equations to machine precision, and this precision has made it the computational backbone of physics-informed machine learning. Yet exactness i…
arXiv cs.LG
TIER_1English(EN)·Muhammad Akbar Khan·
arXiv:2609.38195v1 Announce Type: new Abstract: Operators for interfacial problems are trained on reference solutions produced by the solver they are intended to replace. This work develops a data-free physics-informed neural operator for level-set interface advection, in which t…
arXiv cs.AI
TIER_1English(EN)·Yubo Cao, Xi Deng, Mengqi Xia, Vignesh Gopakumar, Ander Gray, Anima Anandkumar·
arXiv:2609.40090v1 Announce Type: new Abstract: Particle transport under multiple scattering is central to radiative transfer and plasma physics, yet high-fidelity Monte Carlo (MC) simulations must trace prohibitively many particles. Learning-based surrogates can amortize this co…
arXiv cs.LG
TIER_1English(EN)·Alexandre Caboussat, Anna Peruso·
arXiv:2501.10162v3 Announce Type: replace-cross Abstract: Optimal transportation of raw material from suppliers to customers is an issue arising in logistics that is addressed here with a continuous model relying on optimal transport theory. A physics informed neural network meth…
arXiv cs.LG
TIER_1English(EN)·Carlo Marcati, Christoph Schwab·
arXiv:2112.08125v3 Announce Type: replace-cross Abstract: We construct and analyze approximation rates of deep operator networks (ONets) between infinite-dimensional spaces that emulate with an exponential rate of convergence the coefficient-to-solution map of elliptic second-ord…
arXiv cs.AI
TIER_1English(EN)·Huiwen Zhang, Feng Ye, Chu Ma·
arXiv:2609.38023v1 Announce Type: new Abstract: Physics-Informed Neural Networks (PINNs) embed governing equations into deep learning, but enforce them only through loss residuals, leaving highly oscillatory wave behavior to be discovered by optimization. As a result, methods tha…
arXiv cs.LG
TIER_1English(EN)·Shizheng Wen, Siddhartha Mishra, Marius Zeinhofer·
arXiv:2609.36216v1 Announce Type: new Abstract: Neural operators are typically trained in a supervised fashion, which requires a dataset to be generated with a classical solver. Training them physics-informed, i.e., purely from the governing equations, removes this large offline …
arXiv cs.LG
TIER_1English(EN)·Xiaodong Feng, Ziyu Sun, Tao Tang, Xiaoliang Wan, Tao Zhou·
arXiv:2609.36615v1 Announce Type: cross Abstract: Physics-informed neural networks (PINNs) solve partial differential equations (PDEs) by incorporating governing physical laws into the training loss. For evolution equations, however, their conventional pointwise space--time repre…
arXiv cs.LG
TIER_1English(EN)·Thomas Borsani, Giuseppe Di Fatta·
arXiv:2609.30966v1 Announce Type: new Abstract: Physics-Informed Neural Networks (PINNs) are trained by optimising a composite objective that combines data fitting with physics-based constraints, typically resulting in a highly imbalanced multi-task optimisation problem. Under th…
We introduce Distance-Residual Physics-Informed Neural Networks (DR-PINNs), a physics-informed learning framework for approximating solutions of ordinary and partial differential inclusions (DIs), governing laws in which a differential operator is constrained to lie in a set-valu…
