Physics-Informed Neural Networks (PINNs) have emerged as a powerful framework for solving partial differential equations (PDEs) by embedding physical laws directly into the loss function. However, as a fundamental optimization issue, internal covariate shift (ICS) hinders the stable and effective training of PINNs by disrupting feature distributions and limiting model expressiveness. Unlike standard deep learning tasks, conventional remedies for ICS -- such as Batch Normalization and Layer Normalization -- are not directly applicable to PINNs, as they distort the physical consistency required for reliable PDE solutions. To address this issue, we propose Mask-PINNs, a novel architecture that introduces a learnable mask function to regulate feature distributions while preserving the underlying physical constraints of PINNs. We provide a theoretical analysis showing that the mask suppresses the expansion of feature representations through a carefully designed modulation mechanism. Empirically, we validate the method on multiple PDE benchmarks -- including convection, wave propagation, and Helmholtz equations -- across diverse activation functions. Our results show consistent improvements in prediction accuracy, convergence stability, and robustness. Furthermore, we demonstrate that Mask-PINNs enable the effective use of wider networks, overcoming a key limitation in existing PINN frameworks.
Improved physics-informed neural network in mitigating gradient related failures
College of Applied Mathematics, Chengdu University of Information Technology（成都信息工程大学应用数学学院）；College of Mathematics, Sichuan University（四川大学数学学院）；School of Sciences, Southwest Petroleum University（西南石油大学理学院）
Mitigating Gradient Pathology in PINNs through Aligned Constraint
Department of Information Science and Engineering, KTH Royal Institute of Technology, Stockholm, Sweden（信息科学与工程系，皇家理工学院，斯德哥尔摩，瑞典）；School of Advanced Manufacturing and Robotics, Peking University, Beijing, China（先进制造与机器人学院，北京大学，北京，中国）；School of Advanced Technology, Xi’an Jiaotong-Liverpool University, Suzhou, China（先进技术学院，西安交通大学利物浦大学，苏州，中国）；Department of AI, School of Engineering, Westlake University, Hangzhou, China（人工智能系，工程学院，西湖大学，杭州，中国）
Institute of Automation, Chinese Academy of Sciences（中国科学院自动化研究所）；University of Chinese Academy of Sciences（中国科学院大学）
Domain generalization (DG) aims to learn a model on several source domains, hoping that the model can generalize well to unseen target domains. The distribution shift between domains contains the covariate shift and conditional shift, both of which the model must be able to handle for better generalizability. In this paper, a novel DG method is proposed to deal with the distribution shift via Visual Alignment and Uncertainty-guided belief Ensemble (VAUE). Specifically, for the covariate shift, a visual alignment module is designed to align the distribution of image style to a common empirical …
Physics-informed deep learning for infectious disease forecasting
School of Chemical, Materials, and Biomedical Engineering, University of Georgia（化学、材料与生物医学工程学院，佐治亚大学）；Odum School of Ecology and Center for the Ecology of Infectious Diseases, University of Georgia（生态学院与传染病生态研究中心，佐治亚大学）；School of Environmental, Civil Agricultural and Mechanical Engineering, College of Engineering, University of Georgia（环境、土木农业与机械工程学院，工程学院，佐治亚大学）；Department of Epidemiology & Biostatistics, University of Georgia（流行病学与生物统计学系，佐治亚大学）；Department of Infectious Diseases, College of Veterinary Medicine, University of Georgia（传染病系，兽医学学院，佐治亚大学）；Center for Influenza Disease and Emergence Research, University of Georgia（流感疾病与新兴病研究中心，佐治亚大学）
Mitigating covariate shift in non-colocated data with learned parameter priors
Institute of Business Administration Karachi（卡拉奇工商管理学院）；Habib University Karachi（卡拉奇哈比卜大学）；National University of Computer and Emergings Sciences, Karachi（卡拉奇国立计算机与新兴科学大学）
This paper studies offline Imitation Learning (IL) where an agent learns to imitate an expert demonstrator without additional online environment interactions. Instead, the learner is presented with a static offline dataset of state-action-next state transition triples from a potentially less proficient behavior policy. We introduce Model-based IL from Offline data (MILO): an algorithmic framework that utilizes the static dataset to solve the offline IL problem efficiently both in theory and in practice. In theory, even if the behavior policy is highly sub-optimal compared to the expert, we sho…
Towards regularized learning from functional data with covariate shift
Institute for Machine Learning（机器学习研究所）；Johannes Kepler University（约翰·凯撒大学）；Medical University of Innsbruck（因斯布鲁克医学院）；Austrian Academy of Sciences（奥地利科学院）；Indian Institute of Technology Delhi（德里印度理工学院）
Early Detection of Misinformation for Infodemic Management: A Domain Adaptation Approach
Lerner College of Business and Economics, University of Delaware（德克萨斯大学德尔韦大学商学院与经济学学院）；School of Information Management & Engineering, Shanghai University of Finance and Economics（上海财经大学信息管理与工程学院）
Institute for Cognitive Science（认知科学研究所）；Osnabrück University（奥斯纳布吕克大学）
The most widely used activation functions in current deep feed-forward neural networks are rectified linear units (ReLU), and many alternatives have been successfully applied, as well. However, none of the alternatives have managed to consistently outperform the rest and there is no unified theory connecting properties of the task and network with properties of activation functions for most efficient training. A possible solution is to have the network learn its preferred activation functions. In this work, we introduce Adaptive Blending Units (ABUs), a trainable linear combination of a set of…
Physics-Informed Heterogeneous Graph Neural Networks for DC Blocker Placement
Argonne National Laboratory（阿贡国家实验室）；Oak Ridge National Laboratory（橡树岭国家实验室）；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）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）
