Architecture--Optimization Co-Design for Physics-Informed Neural Networks via Layer-wise Coordinate Adaptation and Gradient Conflict Resolution
College of Applied Mathematics（应用数学学院）；Chengdu University of Information Technology（成都信息科技大學）；College of Mathematics（数学学院）；Sichuan University（四川大学）；School of Sciences（科学学院）
Pancheng Niu, Jun Guo, Qiaolin He, Yongming Chen, Yanchao Shi
Physics-informed neural networks (PINNs) can be limited by coordinate representations and conflicting gradients from heterogeneous physical constraints. We propose Architecture--Conflict-Resolved PINN (ACR-PINN), combining Layer-wise Dynamic Adaptation (LDA) and Gradient-Conflict-Resolved PINN (GCR-PINN). LDA constructs layer-specific coordinate features and fuses two encoding branches through input-conditioned, feature-wise gates. GCR-PINN treats PDE, initial-condition, and boundary-condition losses as separate tasks and conditionally projects negatively aligned gradients before aggregation, without changing the physical loss formulation. Across seven benchmark problems, ACR-PINN achieves the lowest observed mean across all metrics among four core architecture--optimizer combinations, reducing mean relative $L_2$ error by approximately 56--97\% relative to Std-PINN and improving on the better single-component variant. Capacity-controlled comparisons and gate interventions indicate that these gains reflect the learned coordinate-fusion pathway rather than parameter count alone. Gradient diagnostics suggest that LDA can improve task-gradient compatibility and reduce the correction required by GCR-PINN, with effects depending on the problem and update rule. Comparisons with representative PINN baselines and tests over sampling and temporal-horizon changes support the observed accuracy gains within the studied settings, while equal-time experiments reveal an accuracy--cost trade-off from the richer LDA representation.
Per-Loss Adapters for Gradient Conflict in Physics-Informed Neural Networks
The University of Tokyo, Japan（东京大学）；Axiom Research Group（Axiom研究组）；Department of Applied Mathematics and Computational Science, NM-AIST, Tanzania（应用数学与计算科学系，NM-AIST，坦桑尼亚）；African Institute for Mathematical Sciences (AIMS), Research and Innovation Centre, Rwanda（非洲数学科学研究所（AIMS），研究与创新中心，卢旺达）
Physics-Informed Neural Network Digital Twin for Dynamic Tray-Wise Modeling of Distillation Columns under Transient Operating Conditions
Department of Chemical Engineering, Veer Surendra Sai University of Technology（维杰·苏雷纳·赛大学化学工程系）；Department of Computer Science & Engineering, Veer Surendra Sai University of Technology（维杰·苏雷纳·赛大学计算机科学与工程系）
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）
Gradient Alignment in Physics-informed Neural Networks: A Second-Order Optimization Perspective
Institution for Foundation of Data Science, Yale University（数据科学基础研究所，耶鲁大学）；Penn Institute for Computational Science, University of Pennsylvania（宾夕法尼亚大学计算科学研究所）；Department of Mathematics, City University of Hong Kong（香港城市大学数学系）；Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania（宾夕法尼亚大学机械工程与应用力学系）
Physics-informed deep operator network for traffic state estimation
The Key Laboratory of Road and Traffic Engineering, Ministry of Education, Tongji University, Shanghai 201804, China（交通工程重点实验室，教育部，同济大学，上海201804，中国）；College of Transportation Engineering, Tongji University, Shanghai 201804, China（交通工程学院，同济大学，上海201804，中国）
On the training of physics-informed neural operators for solving parametric partial differential equations
College of Civil Engineering, Tongji University（同济大学土木工程学院）；Department of Engineering Science, University of Oxford（牛津大学工程科学系）；Institute for Foundations of Data Science, Yale University（耶鲁大学数据科学基础研究所）
Enhancing training of physics-informed neural networks using domain-decomposition based preconditioning strategies
Division of Applied Mathematics, Brown University（布朗大学应用数学系）；Euler Institute, Università della Svizzera italiana（瑞士意大利语区大学欧拉研究所）；UniDistance, Switzerland（瑞士远程大学）
Division of Big Data Science, Korea University（高丽大学大数据科学系）；Department of Mathematics, North Carolina State University（北卡罗来纳州立大学数学系）；Center for Applied Scientific Computing, Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室应用科学计算中心）
Finite basis physics-informed neural networks with hard constraints for viscous fluid flow in highly perforated domains
Korea Advanced Institute of Science and Technology（韩国科学技术院）；Weierstrass-Institute for Applied Analysis and Stochastics（魏尔斯特拉斯应用分析与随机学研究所）；Leibniz-Institut für Verbundwerkstoffe GmbH（莱布尼茨复合材料有限公司研究所）
Lagged backward-compatible physics-informed neural networks for unsaturated soil consolidation analysis
George Mason University（乔治梅森大学）；National Institute of Natural Hazards, Ministry of Emergency Management（应急管理部国家自然灾害防治研究院）；Northwest Institute of Eco-Environment and Resources, Chinese Academy of Sciences（中国科学院西北生态环境资源研究院）；École Nationale des Ponts et Chaussées（巴黎路桥学院）；Hebei University of Engineering（河北工程大学）；Zhejiang University of Technology（浙江工业大学）
Inverse-Dirichlet Weighting Enables Reliable Training of Physics Informed Neural Networks
Technische Universität Dresden（德累斯顿工业大学）；Max Planck Institute of Molecular Cell Biology and Genetics（马克斯·普朗克分子细胞生物学与遗传学研究所）；Center for Systems Biology Dresden（德累斯顿系统生物学中心）；Flatiron Institute（弗拉蒂伦研究所）；Helmholtz Zentrum München（亥姆霍兹慕尼黑中心）；Center for Scalable Data Analytics and Artificial Intelligence ScaDS.AI（可扩展数据分析与人工智能中心（ScaDS.AI））；Helmholtz-Zentrum Dresden-Rossendorf（亥姆霍兹德累斯顿罗森多夫研究中心）；Center for Advanced Systems Understanding (CASUS)（高级系统理解中心（CASUS））
PINN-Cast: Exploring the Role of Continuous-Depth NODE in Transformers and Physics Informed Loss as Soft Physical Constraints in Short-term Weather Forecasting
Towards Layer-Wise Personalized Federated Learning: Adaptive Layer Disentanglement via Conflicting Gradients
Pusan National University（釜山国立大学）；Hanoi University of Technology（河内工业大学）；University of Sydney（悉尼大学）；Trinity College of Dublin（都柏林圣三一学院）；Zhejiang University（浙江大学）
Weight-Informed Self-Explaining Clustering for Mixed-Type Tabular Data
School of Computing, National University of Singapore（新加坡国立大学计算机学院）；School of Intelligence Science and Engineering, Harbin Institute of Technology (Shenzhen)（哈尔滨工业大学（深圳）智能科学与工程学院）
An anatomically-informed 3D CNN for brain aneurysm classification with weak labels
Lausanne University Hospital and University of Lausanne（洛桑大学医院和洛桑大学）；Center for Biomedical Imaging（生物医学成像中心）；Ecole Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）
Electrical Engineering and Computer Science, University of California, Merced, CA 95343, USA（电气工程与计算机科学系，加州大学默塞德分校）；Department of Applied Mathematics, University of California, Merced, CA 95343, USA（应用数学系，加州大学默塞德分校）；Department of Innovation and Research, North Carolina State University, Raleigh, NC, USA（创新与研究系，北卡罗来纳州立大学）；Automation (MESA) Lab, Department of Mechanical Engineering, School of Engineering, University of California, Merced, CA 95343, USA（自动化（MESA）实验室，机械工程系，工程学院，加州大学默塞德分校）
Entropy-Informed Weighting Channel Normalizing Flow for Deep Generative Models
School of Mathematics, South China University of Technology, Guangzhou, China（华南理工大学数学学院）；Shenzhen International Graduate School, Tsinghua University, Shenzhen, China（清华大学深圳国际研究生院）；School of Electronic and Information Engineering, South China University of Technology, Guangzhou, China（华南理工大学电子信息学院）；Department of Electrical Engineering, Columbia University, New York, NY USA（哥伦比亚大学电气工程系）
