Manifold-Orthogonal Dual-spectrum Extrapolation for Parameterized Physics-Informed Neural Networks
National Center for Applied Mathematics, Tianjin University（天津大学应用数学中心）；School of Mechanical and Aerospace Engineering, Jilin University（吉林大学机械与 aerospace 工程学院）
Physics-informed neural networks (PINNs) have achieved notable success in modeling dynamical systems governed by partial differential equations (PDEs). To avoid computationally expensive retraining under new physical conditions, parameterized PINNs (P$^2$INNs) commonly adapt pre-trained operators using singular value decomposition (SVD) for out-of-distribution (OOD) regimes. However, SVD-based fine-tuning often suffers from rigid subspace locking and truncation of important high-frequency spectral modes, limiting its ability to capture complex physical transitions. While parameter-efficient fine-tuning (PEFT) methods appear to be promising alternatives, applying conventional adapters such as LoRA to P$^2$INNs introduces a severe Pareto trade-off, as additive updates increase parameter overhead and disrupt the structured physical manifolds inherent in operator representations. To address these limitations, we propose Manifold-Orthogonal Dual-spectrum Extrapolation (MODE), a lightweight micro-architecture designed for physics operator adaptation. MODE decomposes physical evolution into complementary mechanisms including principal-spectrum dense mixing that enables cross-modal energy transfer within frozen orthogonal bases, residual-spectrum awakening that activates high-frequency spectral components through a single trainable scalar, and affine Galilean unlocking that explicitly isolates spatial translation dynamics. Experiments on challenging PDE benchmarks including the 1D Convection--Diffusion--Reaction equation and the 2D Helmholtz equation demonstrate that MODE achieves strong out-of-distribution generalization while preserving the minimal parameter complexity of native SVD and outperforming existing PEFT-based baselines.
Yonsei University（延世大学）；Sandia National Laboratory（桑迪亚国家实验室）；Texas A&M University at Commerce（德克萨斯农工大学康莫斯分校）
We present a method for learning dynamics of complex physical processes described by time-dependent nonlinear partial differential equations (PDEs). Our particular interest lies in extrapolating solutions in time beyond the range of temporal domain used in training. Our choice for a baseline method is physics-informed neural network (PINN) [Raissi et al., J. Comput. Phys., 378:686--707, 2019] because the method parameterizes not only the solutions but also the equations that describe the dynamics of physical processes. We demonstrate that PINN performs poorly on extrapolation tasks in many ben…
Physics-informed neural networks (PINNs) as a means of discretizing partial differential equations (PDEs) are garnering much attention in the Computational Science and Engineering (CS&E) world. At least two challenges exist for PINNs at present: an understanding of accuracy and convergence characteristics with respect to tunable parameters and identification of optimization strategies that make PINNs as efficient as other computational science tools. The cost of PINNs training remains a major challenge of Physics-informed Machine Learning (PiML) - and, in fact, machine learning (ML) in general…
Many types of physics-informed neural network models have been proposed in recent years as approaches for learning solutions to differential equations. When a particular task requires solving a differential equation at multiple parameterizations, this requires either re-training the model, or expanding its representation capacity to include the parameterization -- both solution that increase its computational cost. We propose the HyperPINN, which uses hypernetworks to learn to generate neural networks that can solve a differential equation from a given parameterization. We demonstrate with exp…
Parameterized Physics-informed Neural Networks for Parameterized PDEs
Yonsei University（延世大学）；Arizona State University（亚利桑那州立大学）；LG CNS；Texas A&M University-Commerce（德州农工大学Commerce分校）；Oregon State University（俄勒冈州立大学）；KAIST（韩国科学技术院）
We present a Parametrization of the Physics Informed Neural Network (P-PINN) approach to tackle the problem of uncertainty quantification in reservoir engineering problems. We demonstrate the approach with the immiscible two phase flow displacement (Buckley-Leverett problem) in heterogeneous porous medium. The reservoir properties (porosity, permeability) are treated as random variables. The distribution of these properties can affect dynamic properties such as the fluids saturation, front propagation speed or breakthrough time. We explore and use to our advantage the ability of networks to in…
A Numerical Method for Coupling Parameterized Physics-Informed Neural Networks and FDM for Advanced Thermal-Hydraulic System Simulation
Division of Advanced Nuclear Engineering, Pohang University of Science and Technology（浦项科技大学先进核工程学部）；Mueunjae School of Undergraduate Studies, Pohang University of Science and Technology（浦项科技大学文在本科书院）；Department of Quantum System Engineering, Jeonbuk National University（全北国立大学量子系统工程系）
xLSTM-PINN: Memory-Gated Spectral Remodeling for Physics-Informed Learning
Nanophotonics and Biophotonics Key Laboratory of Jilin Province, School of Physics, Changchun University of Science and Technology（吉林省纳米光子与生物光子重点实验室，物理学院，长春理工大学）
A Coupled Physics-Informed Neural Network for Greenhouse Climate State Reconstruction and Parameter Identification under Sparse Sensor Measurements
Centro de Modelamiento Matemático (CMM), University of Chile（智利大学数学建模中心）；College of Science, King Khalid University（哈立德国王大学理学院）；Presidency University（总统大学）
PIDT: Physics-Informed Digital Twin for Optical Fiber Parameter Estimation
Dept. of Electrical Engineering, Chalmers Univ. of Technology, Sweden（电气工程系，瑞典查尔姆斯理工大学）；Dept. of Microtechnology and Nanoscience, Chalmers Univ. of Technology, Sweden（微电子与纳米科技系，瑞典查尔姆斯理工大学）
National Innovation Institute of Defense Technology, Chinese Academy of Military Science（中国人民解放军军事科学院国防科技创新研究院）
Physics-informed neural networks (PINNs) have been widely used to solve various scientific computing problems. However, large training costs limit PINNs for some real-time applications. Although some works have been proposed to improve the training efficiency of PINNs, few consider the influence of initialization. To this end, we propose a New Reptile initialization based Physics-Informed Neural Network (NRPINN). The original Reptile algorithm is a meta-learning initialization method based on labeled data. PINNs can be trained with less labeled data or even without any labeled data by adding p…
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）
FO-PINNs: A First-Order formulation for Physics Informed Neural Networks
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；NVIDIA（英伟达）；University of California Davis（加州大学戴维斯分校）；Illinois Institute of Technology（伊利诺伊理工学院）
The objective of this paper is to investigate the ability of physics-informed neural networks to learn the magnetic field response as a function of design parameters in the context of a two-dimensional (2-D) magnetostatic problem. Our approach is as follows. First, we present a functional whose minimization is equivalent to solving parametric magnetostatic problems. Subsequently, we use a deep neural network (DNN) to represent the magnetic field as a function of space and parameters that describe geometric features and operating points. We train the DNN by minimizing the physics-informed funct…
KAIST（韩国科学技术院）；HITS incorporation（HITS 公司）；KI for Artificial Intelligence, KAIST（韩国科学技术院人工智能研究院）
Recently, deep neural network (DNN)-based drug-target interaction (DTI) models were highlighted for their high accuracy with affordable computational costs. Yet, the models' insufficient generalization remains a challenging problem in the practice of in-silico drug discovery. We propose two key strategies to enhance generalization in the DTI model. The first is to predict the atom-atom pairwise interactions via physics-informed equations parameterized with neural networks and provides the total binding affinity of a protein-ligand complex as their sum. We further improved the model generalizat…
Quantum-classical physics-informed Kolmogorov-Arnold networks for PDEs
School of Petroleum Engineering, Yangtze University（扬州大学石油工程学院）；School of Computer Science, Yangtze University（扬州大学计算机科学学院）；State Key Laboratory of Low Carbon Catalysis and Carbon Dioxide Utilization (Yangtze University)（扬州大学低碳催化与二氧化碳利用国家重点实验室）；Western Research Institute, Yangtze University（扬州大学西部研究院）
The University of Arizona（亚利桑那大学）；Massachusetts Institute of Technology（麻省理工学院）
This study presents a novel unsupervised convolutional Neural Network (NN) architecture with nonlocal interactions for solving Partial Differential Equations (PDEs). The nonlocal Peridynamic Differential Operator (PDDO) is employed as a convolutional filter for evaluating derivatives the field variable. The NN captures the time-dynamics in smaller latent space through encoder-decoder layers with a Convolutional Long-short Term Memory (ConvLSTM) layer between them. The ConvLSTM architecture is modified by employing a novel activation function to improve the predictive capability of the learning…
University of Calgary（卡尔加里大学）；Carleton University（卡尔顿大学）
In this work, we present a deep neural network architecture that can efficiently approximate classical elasto-plastic constitutive relations. The network is enriched with crucial physics aspects of classical elasto-plasticity, including additive decomposition of strains into elastic and plastic parts, and nonlinear incremental elasticity. This leads to a Physics-Informed Neural Network (PINN) surrogate model named here as Elasto-Plastic Neural Network (EPNN). Detailed analyses show that embedding these physics into the architecture of the neural network facilitates a more efficient training of…
Massachusetts Institute of Technology（麻省理工学院）；Dalian University of Technology（大连理工大学）；Centre Internacional de Mètodes Numèrics en Enginyeria（国际工程数值方法中心）
Inverse design arises in a variety of areas in engineering such as acoustic, mechanics, thermal/electronic transport, electromagnetism, and optics. Topology optimization is a major form of inverse design, where we optimize a designed geometry to achieve targeted properties and the geometry is parameterized by a density function. This optimization is challenging, because it has a very high dimensionality and is usually constrained by partial differential equations (PDEs) and additional inequalities. Here, we propose a new deep learning method -- physics-informed neural networks with hard constr…
Physics-informed neural operator for parametric phase-field modelling of interfacial degradation and microstructural evolution
Tongji University, College of Civil Engineering（同济大学，土木工程学院）；Tongji University, State Key Laboratory of Disaster Reduction in Civil Engineering（同济大学，灾害防治工程重点实验室）
Pacific Northwest National Laboratory（太平洋西北国家实验室）；University of Washington（华盛顿大学）；Pennsylvania State University（宾夕法尼亚州立大学）
Fundamental diagrams describe the relationship between speed, flow, and density for some roadway (or set of roadway) configuration(s). These diagrams typically do not reflect, however, information on how speed-flow relationships change as a function of exogenous variables such as curb configuration, weather or other exogenous, contextual information. In this paper we present a machine learning methodology that respects known engineering constraints and physical laws of roadway flux - those that are captured in fundamental diagrams - and show how this can be used to introduce contextual informa…
Variational Quantum Physics-Informed Neural Networks for Hydrological PDE-Constrained Learning with Inherent Uncertainty Quantification
Faculty of Computer Science and Multimedia, Lincoln University College, Petaling Jaya, Selangor, Malaysia（计算机科学与多媒体学院，林肯大学学院，Petaling Jaya，Selangor，马来西亚）
Hamburg University of Technology（汉堡工业大学）；Stanford University（斯坦福大学）；Brown University（布朗大学）
Understanding real-world dynamical phenomena remains a challenging task. Across various scientific disciplines, machine learning has advanced as the go-to technology to analyze nonlinear dynamical systems, identify patterns in big data, and make decision around them. Neural networks are now consistently used as universal function approximators for data with underlying mechanisms that are incompletely understood or exceedingly complex. However, neural networks alone ignore the fundamental laws of physics and often fail to make plausible predictions. Here we integrate data, physics, and uncertai…
Accelerating physics-informed neural networks for full waveform inversion using a hybrid quantum-classical finite-basis architecture
Department of Geophysics, Colorado School of Mines（地质学系，科罗拉多矿业学院）；Department of Energy Science and Engineering, Stanford University（能源科学与工程系，斯坦福大学）；Department of Petroleum Engineering, Colorado School of Mines（石油工程系，科罗拉多矿业学院）
The placement of temperature sensitive and safety-critical components is crucial in the automotive industry. It is therefore inevitable, even at the design stage of new vehicles that these components are assessed for potential safety issues. However, with increasing number of design proposals, risk assessment quickly becomes expensive. We therefore present a parameterized surrogate model for the prediction of three-dimensional flow fields in aerothermal vehicle simulations. The proposed physics-informed neural network (PINN) design is aimed at learning families of flow solutions according to a…
Grad-Shafranov equilibria via data-free physics informed neural networks
Institute for Research in Electronics and Applied Physics, University of Maryland（马里兰大学电子与应用物理研究所）；Courant Institute, New York University（纽约大学柯朗数学科学研究所）；Princeton University（普林斯顿大学）；Rensselaer Polytechnic Institute（伦斯勒理工学院）
Lane Department of Computer Science and Electrical Engineering, West Virginia University（计算机科学与电气工程系，西弗吉尼亚大学）
Despite the relentless progress of deep learning models in analyzing the system conditions under cyber-physical events, their abilities are limited in the power system domain due to data availability issues, cost of data acquisition, and lack of interpretation and extrapolation for the data beyond the training windows. In addition, the integration of distributed energy resources (DERs) such as wind and solar generations increases the complexities and nonlinear nature of power systems. Therefore, an interpretable and reliable methodology is of utmost need to increase the confidence of power sys…
Investment professionals rely on extrapolating company revenue into the future (i.e. revenue forecast) to approximate the valuation of scaleups (private companies in a high-growth stage) and inform their investment decision. This task is manual and empirical, leaving the forecast quality heavily dependent on the investment professionals' experiences and insights. Furthermore, financial data on scaleups is typically proprietary, costly and scarce, ruling out the wide adoption of data-driven approaches. To this end, we propose a simulation-informed revenue extrapolation (SiRE) algorithm that gen…
Yale Center for Medical Informatics（耶鲁医学信息学中心）；VA Connecticut Healthcare System（康涅狄格州退伍军人医疗系统）
We study the generalization of over-parameterized deep networks (for image classification) in relation to the convex hull of their training sets. Despite their great success, generalization of deep networks is considered a mystery. These models have orders of magnitude more parameters than their training samples, and they can achieve perfect accuracy on their training sets, even when training images are randomly labeled, or the contents of images are replaced with random noise. The training loss function of these models has infinite number of near zero minimizers, where only a small subset of …
