Modeling distributed dynamical systems governed by hyperbolic partial differential equations (PDEs) remains challenging due to discontinuities and shocks that hinder the convergence of traditional physics-informed neural networks (PINNs). The recently proposed vanishing stacked residual PINN (VSR-PINN) embeds a vanishing-viscosity mechanism within stacked residual refinements to enable a smooth transition from the parabolic to hyperbolic regime. This paper integrates three curriculum-learning methods as primal-dual (PD) optimization, causality progression, and adaptive sampling into the VSR-PINN. The PD strategy balances physics and data losses, the causality scheme unlocks deeper stacks by respecting temporal and gradient evolution, and adaptive sampling targets high residuals. Numerical experiments on traffic reconstruction confirm that enforcing causality systematically reduces the median point-wise MSE and its variability across runs, yielding improvements of nearly one order of magnitude over non-causal training in both the baseline and PD variants.
Long-term simulation of physical and mechanical behaviors using curriculum-transfer-learning based physics-informed neural networks
College of Mechanics and Engineering Science, Hohai University（河海大学力学与工程科学学院）；China Three Gorges Corporation（中国长江三峡集团有限公司）；Cairo University（开罗大学）；Leibniz Universität Hannover（汉诺威莱布尼茨大学）
Hybrid Quantum-Classical PINNs for Scientific Computing: A Multi-GPU Open-Source Framework
Faculty of Mechanical Engineering, Technion Israel Institute of Technology, Haifa, Israel（技术学院机械工程系，以色列技术学院，海法，以色列）；Andrew and Erna Viterbi Faculty of Electrical & Computer Engineering, Technion Israel Institute of Technology, Haifa, Israel（安德鲁和伊尔纳·维特比电气与计算机工程学院，技术学院，海法，以色列）；Helen Diller Quantum Center, Technion Israel Institute of Technology, Haifa, Israel（海伦·迪尔量子中心，技术学院，海法，以色列）；Faculty of Electrical and Computer Engineering, Cornell University, Ithaca, NY, USA（电气与计算机工程学院，康奈尔大学，纽约州伊萨克，美国）
Characterizing possible failure modes in physics-informed neural networks
Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；University of California, Berkeley（加州大学伯克利分校）；University of Utah（犹他大学）；International Computer Science Institute（国际计算机科学研究所）
Physics-Informed Neural Networks for Predicting Hydrogen Sorption in Geological Formations: Thermodynamically Constrained Deep Learning Integrating Classical Adsorption Theory
University of Oslo（奥斯陆大学）；SINTEF Industry（挪威科技工业研究院）；China University of Petroleum, Beijing（中国石油大学（北京））
Resolving gradient pathology in physics-informed epidemiological models
Disease-informed Modeling, Methods & Systems (DIMMS) Lab, Department of Mathematics and Statistics, York University, Toronto, Canada（疾病导向建模、方法与系统实验室，数学与统计学系，约克大学，多伦多，加拿大）
Physics-Informed Neural Networks for Methane Sorption: Cross-Gas Transfer Learning, Ensemble Collapse Under Physics Constraints, and Monte Carlo Dropout Uncertainty Quantification
Environmental Geosciences, Department of Geosciences, University of Oslo（奥斯陆大学环境地质学系）；National Key Laboratory of Petroleum Resources and Engineering, China University of Petroleum (Beijing)（中国石油大学（北京）石油资源与工程国家级重点实验室）；College of Geosciences, China University of Petroleum (Beijing)（中国石油大学（北京）地质学院）；State Key Laboratory of Coal Mine Disaster Prevention and Control, China University of Mining and Technology（中国矿业大学煤矿灾害防治控制国家重点实验室）；The Lyell Centre, Heriot-Watt University（赫瑞斯泰大学利尔中心）；Subsurface Energy Transition and Innovation Centre, Heriot-Watt University（赫瑞斯泰大学地下能源转型与创新中心）
