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Journal articles on the topic 'Physics-informed Machine Learning'

Author: Grafiati

Published: 6 September 2023

Last updated: 1 March 2025

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1

Xypakis, Emmanouil, Valeria deTurris, Fabrizio Gala, Giancarlo Ruocco, and Marco Leonetti. "Physics-informed machine learning for microscopy." EPJ Web of Conferences 266 (2022): 04007. http://dx.doi.org/10.1051/epjconf/202226604007.

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We developed a physics-informed deep neural network architecture able to achieve signal to noise ratio improvements starting from low exposure noisy data. Our model is based on the nature of the photon detection process characterized by a Poisson probability distribution which we included in the training loss function. Our approach surpasses previous algorithms performance for microscopy data, moreover, the generality of the physical concepts employed here, makes it readily exportable to any imaging context.

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Pateras, Joseph, Pratip Rana, and Preetam Ghosh. "A Taxonomic Survey of Physics-Informed Machine Learning." Applied Sciences 13, no. 12 (June 7, 2023): 6892. http://dx.doi.org/10.3390/app13126892.

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Physics-informed machine learning (PIML) refers to the emerging area of extracting physically relevant solutions to complex multiscale modeling problems lacking sufficient quantity and veracity of data with learning models informed by physically relevant prior information. This work discusses the recent critical advancements in the PIML domain. Novel methods and applications of domain decomposition in physics-informed neural networks (PINNs) in particular are highlighted. Additionally, we explore recent works toward utilizing neural operator learning to intuit relationships in physics systems traditionally modeled by sets of complex governing equations and solved with expensive differentiation techniques. Finally, expansive applications of traditional physics-informed machine learning and potential limitations are discussed. In addition to summarizing recent work, we propose a novel taxonomic structure to catalog physics-informed machine learning based on how the physics-information is derived and injected into the machine learning process. The taxonomy assumes the explicit objectives of facilitating interdisciplinary collaboration in methodology, thereby promoting a wider characterization of what types of physics problems are served by the physics-informed learning machines and assisting in identifying suitable targets for future work. To summarize, the major twofold goal of this work is to summarize recent advancements and introduce a taxonomic catalog for applications of physics-informed machine learning.

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Karimpouli, Sadegh, and Pejman Tahmasebi. "Physics informed machine learning: Seismic wave equation." Geoscience Frontiers 11, no. 6 (November 2020): 1993–2001. http://dx.doi.org/10.1016/j.gsf.2020.07.007.

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Barmparis, G. D., and G. P. Tsironis. "Discovering nonlinear resonances through physics-informed machine learning." Journal of the Optical Society of America B 38, no. 9 (August 2, 2021): C120. http://dx.doi.org/10.1364/josab.430206.

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Pilania, G., K. J. McClellan, C. R. Stanek, and B. P. Uberuaga. "Physics-informed machine learning for inorganic scintillator discovery." Journal of Chemical Physics 148, no. 24 (June 28, 2018): 241729. http://dx.doi.org/10.1063/1.5025819.

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Lagomarsino-Oneto, Daniele, Giacomo Meanti, Nicolò Pagliana, Alessandro Verri, Andrea Mazzino, Lorenzo Rosasco, and Agnese Seminara. "Physics informed machine learning for wind speed prediction." Energy 268 (April 2023): 126628. http://dx.doi.org/10.1016/j.energy.2023.126628.

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Tóth, Máté, Adam Brown, Elizabeth Cross, Timothy Rogers, and Neil D. Sims. "Resource-efficient machining through physics-informed machine learning." Procedia CIRP 117 (2023): 347–52. http://dx.doi.org/10.1016/j.procir.2023.03.059.

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Kapoor, Taniya, Hongrui Wang, Alfredo Núñez, and Rolf Dollevoet. "Physics-informed machine learning for moving load problems." Journal of Physics: Conference Series 2647, no. 15 (June 1, 2024): 152003. http://dx.doi.org/10.1088/1742-6596/2647/15/152003.

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Abstract This paper presents a new approach to simulate forward and inverse problems of moving loads using physics-informed machine learning (PIML). Physics-informed neural networks (PINNs) utilize the underlying physics of moving load problems and aim to predict the deflection of beams and the magnitude of the loads. The mathematical representation of the moving load considered involves a Dirac delta function, to capture the effect of the load moving across the structure. Approximating the Dirac delta function with PINNs is challenging because of its instantaneous change of output at a single point, causing difficulty in the convergence of the loss function. We propose to approximate the Dirac delta function with a Gaussian function. The incorporated Gaussian function physical equations are used in the physics-informed neural architecture to simulate beam deflections and to predict the magnitude of the load. Numerical results show that PIML is an effective method for simulating the forward and inverse problems for the considered model of a moving load.

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Behtash, Mohammad, Sourav Das, Sina Navidi, Abhishek Sarkar, Pranav Shrotriya, and Chao Hu. "Physics-Informed Machine Learning for Battery Capacity Forecasting." ECS Meeting Abstracts MA2024-01, no. 2 (August 9, 2024): 210. http://dx.doi.org/10.1149/ma2024-012210mtgabs.

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Batteries, recognized as effective energy storage solutions, are considered the main facilitators of the world-wide transition towards clean and renewable energy sources. Among different types of batteries, lithium-ion (Li-ion) variants offer higher energy densities and relatively longer life spans when compared to other types. Nonetheless, a primary concern with these batteries is their lifetime. Batteries undergo various degradation mechanisms under storage and use, significantly impacting their lifespan. To this end, it is crucial to predict the degradation and lifetime of Li-ion batteries under given conditions. Researchers use three main methodologies to perform battery health diagnostics and to predict the lifetime of batteries. One approach revolves around using mechanistic, first-principle electrochemical models, also known as physics-based models. If equipped with proper thermodynamic theories, such models can show promising capabilities; however, holistic degradation prediction with these models is still challenging due to the computational complexities and the multitude of parameters that need to be fine-tuned in this approach. The other common strategy is to use empirical models to predict battery degradation. These models generally entail fewer parameters to be identified and are computationally less intensive to solve. Nonetheless, empirical models can suffer from the accuracy point-of-view as they are constrained to predict degradation trends introduced by certain degradation modes. Another common technique in battery life prediction is to utilize purely data-driven methods, such as machine learning (ML) algorithms, which also have shown promising results in the literature on rapid health predictions. However, these methods require large volumes of experimental data for training and testing ML models to ensure accuracy. In addition, data-driven methods are likely to extrapolate poorly to conditions beyond their training data and are indifferent towards the underlying degradation mechanisms. Recently, physics-informed machine learning (PI-ML) methods have garnered significant attention. They integrate physics-based or empirical models (developed based on physics) with a data-driven approach and allow one to train ML models on a smaller set of experimental data. To the best of the authors’ knowledge, the performance comparison between first-principle and empirical models when integrated within PI-ML remains unclear. Therefore, in this work, we aim to compare these two models when applied to prognostics (capacity forecasting and remaining useful life prediction) of a set of Li-ion batteries. To perform this study, we generate aging data for 40 Li-ion coin cells cycled under randomized conditions. Each cell undergoes a three-step charging stage followed by a two-step discharge stage. After obtaining the aging data, we will develop two PI-ML models, one equipped with a physics-based model and another with a set of empirical models. Both PI-ML models in this work will follow the sequential integration approach, where the training data for the final PI-ML model come from both experimental and computational data, the latter of which are obtained from the physics-based or empirical models. The parameters for the physics-based and empirical models are identified from another set of experimental data. Finally, the PI-ML models will be tested with experimental data obtained at different cycling conditions. The data flow for the sequential architecture of PI-ML is shown in the attached figure. This comparative study will help identify the performance of physics-based and empirical models when integrated into PI-ML. The main performance metric considered in this work is each model’s ability to extrapolate beyond the experimental training data set, hence aiding the final PI-ML model in generalizing to conditions not covered by its experimental training data set. Figure 1

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Mandl, Luis, Somdatta Goswami, Lena Lambers, and Tim Ricken. "Separable physics-informed DeepONet: Breaking the curse of dimensionality in physics-informed machine learning." Computer Methods in Applied Mechanics and Engineering 434 (February 2025): 117586. http://dx.doi.org/10.1016/j.cma.2024.117586.

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Lympany, Shane V., Matthew F. Calton, Mylan R. Cook, Kent L. Gee, and Mark K. Transtrum. "Mapping ambient sound levels using physics-informed machine learning." Journal of the Acoustical Society of America 152, no. 4 (October 2022): A48—A49. http://dx.doi.org/10.1121/10.0015498.

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Mapping the spatial and temporal distribution of ambient sound levels is critical for understanding the impacts of natural sounds and noise pollution on humans and the environment. Previously, ambient sound levels have been predicted using either machine learning or physics-based modeling. Machine learning models have been trained on acoustical measurements at geospatially diverse locations to predict ambient sound levels across the world based on geospatial features. However, machine learning requires a large number of acoustical measurements to predict ambient sound levels at high spatial and temporal resolution. Physics-based models have been applied to predict transportation noise at high spatial and temporal resolution on regional scales, but these predictions do not include other anthropogenic, biological, or geophysical sound sources. In this work, physics-based predictions of transportation noise are combined with machine learning models to predict ambient sound levels at high spatial and temporal resolution across the conterminous United States. The physics-based predictions of transportation noise are incorporated into the machine learning models as a geospatial feature. The result is a physics-informed machine learning model that predicts ambient sound levels at high spatial and temporal resolution across the United States. [Work funded by an Army SBIR]

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Lee, Jonghwan. "Physics-informed machine learning model for bias temperature instability." AIP Advances 11, no. 2 (February 1, 2021): 025111. http://dx.doi.org/10.1063/5.0040100.

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Mondal, B., T. Mukherjee, and T. DebRoy. "Crack free metal printing using physics informed machine learning." Acta Materialia 226 (March 2022): 117612. http://dx.doi.org/10.1016/j.actamat.2021.117612.

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Howland, Michael F., and John O. Dabiri. "Wind Farm Modeling with Interpretable Physics-Informed Machine Learning." Energies 12, no. 14 (July 16, 2019): 2716. http://dx.doi.org/10.3390/en12142716.

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Turbulent wakes trailing utility-scale wind turbines reduce the power production and efficiency of downstream turbines. Thorough understanding and modeling of these wakes is required to optimally design wind farms as well as control and predict their power production. While low-order, physics-based wake models are useful for qualitative physical understanding, they generally are unable to accurately predict the power production of utility-scale wind farms due to a large number of simplifying assumptions and neglected physics. In this study, we propose a suite of physics-informed statistical models to accurately predict the power production of arbitrary wind farm layouts. These models are trained and tested using five years of historical one-minute averaged operational data from the Summerview wind farm in Alberta, Canada. The trained models reduce the prediction error compared both to a physics-based wake model and a standard two-layer neural network. The trained parameters of the statistical models are visualized and interpreted in the context of the flow physics of turbulent wind turbine wakes.

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Tartakovsky, A. M., D. A. Barajas-Solano, and Q. He. "Physics-informed machine learning with conditional Karhunen-Loève expansions." Journal of Computational Physics 426 (February 2021): 109904. http://dx.doi.org/10.1016/j.jcp.2020.109904.

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Hsu, Abigail, Baolian Cheng, and Paul A. Bradley. "Analysis of NIF scaling using physics informed machine learning." Physics of Plasmas 27, no. 1 (January 2020): 012703. http://dx.doi.org/10.1063/1.5130585.

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17

Karpov, Platon I., Chengkun Huang, Iskandar Sitdikov, Chris L. Fryer, Stan Woosley, and Ghanshyam Pilania. "Physics-informed Machine Learning for Modeling Turbulence in Supernovae." Astrophysical Journal 940, no. 1 (November 1, 2022): 26. http://dx.doi.org/10.3847/1538-4357/ac88cc.

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Abstract Turbulence plays an important role in astrophysical phenomena, including core-collapse supernovae (CCSNe), but current simulations must rely on subgrid models, since direct numerical simulation is too expensive. Unfortunately, existing subgrid models are not sufficiently accurate. Recently, machine learning (ML) has shown an impressive predictive capability for calculating turbulence closure. We have developed a physics-informed convolutional neural network to preserve the realizability condition of the Reynolds stress that is necessary for accurate turbulent pressure prediction. The applicability of the ML subgrid model is tested here for magnetohydrodynamic turbulence in both the stationary and dynamic regimes. Our future goal is to utilize this ML methodology (available on GitHub) in the CCSN framework to investigate the effects of accurately modeled turbulence on the explosion of these stars.

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Lang, Xiao, Da Wu, and Wengang Mao. "Physics-informed machine learning models for ship speed prediction." Expert Systems with Applications 238 (March 2024): 121877. http://dx.doi.org/10.1016/j.eswa.2023.121877.

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19

Piccialli, Francesco, Maizar Raissi, Felipe A. C. Viana, Giancarlo Fortino, Huimin Lu, and Amir Hussain. "Guest Editorial: Special Issue on Physics-Informed Machine Learning." IEEE Transactions on Artificial Intelligence 5, no. 3 (March 2024): 964–66. http://dx.doi.org/10.1109/tai.2023.3342563.

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20

Kapoor, Taniya, Abhishek Chandra, Daniel M. Tartakovsky, Hongrui Wang, Alfredo Nunez, and Rolf Dollevoet. "Neural Oscillators for Generalization of Physics-Informed Machine Learning." Proceedings of the AAAI Conference on Artificial Intelligence 38, no. 12 (March 24, 2024): 13059–67. http://dx.doi.org/10.1609/aaai.v38i12.29204.

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A primary challenge of physics-informed machine learning (PIML) is its generalization beyond the training domain, especially when dealing with complex physical problems represented by partial differential equations (PDEs). This paper aims to enhance the generalization capabilities of PIML, facilitating practical, real-world applications where accurate predictions in unexplored regions are crucial. We leverage the inherent causality and temporal sequential characteristics of PDE solutions to fuse PIML models with recurrent neural architectures based on systems of ordinary differential equations, referred to as neural oscillators. Through effectively capturing long-time dependencies and mitigating the exploding and vanishing gradient problem, neural oscillators foster improved generalization in PIML tasks. Extensive experimentation involving time-dependent nonlinear PDEs and biharmonic beam equations demonstrates the efficacy of the proposed approach. Incorporating neural oscillators outperforms existing state-of-the-art methods on benchmark problems across various metrics. Consequently, the proposed method improves the generalization capabilities of PIML, providing accurate solutions for extrapolation and prediction beyond the training data.

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Marian, Max, and Stephan Tremmel. "Physics-Informed Machine Learning—An Emerging Trend in Tribology." Lubricants 11, no. 11 (October 30, 2023): 463. http://dx.doi.org/10.3390/lubricants11110463.

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Physics-informed machine learning (PIML) has gained significant attention in various scientific fields and is now emerging in the area of tribology. By integrating physics-based knowledge into machine learning models, PIML offers a powerful tool for understanding and optimizing phenomena related to friction, wear, and lubrication. Traditional machine learning approaches often rely solely on data-driven techniques, lacking the incorporation of fundamental physics. However, PIML approaches, for example, Physics-Informed Neural Networks (PINNs), leverage the known physical laws and equations to guide the learning process, leading to more accurate, interpretable and transferable models. PIML can be applied to various tribological tasks, such as the prediction of lubrication conditions in hydrodynamic contacts or the prediction of wear or damages in tribo-technical systems. This review primarily aims to introduce and highlight some of the recent advances of employing PIML in tribological research, thus providing a foundation and inspiration for researchers and R&D engineers in the search of artificial intelligence (AI) and machine learning (ML) approaches and strategies for their respective problems and challenges. Furthermore, we consider this review to be of interest for data scientists and AI/ML experts seeking potential areas of applications for their novel and cutting-edge approaches and methods.

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Osorio, Julian D., Mario De Florio, Rob Hovsapian, Chrys Chryssostomidis, and George Em Karniadakis. "Physics-Informed machine learning for solar-thermal power systems." Energy Conversion and Management 327 (March 2025): 119542. https://doi.org/10.1016/j.enconman.2025.119542.

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23

De Ryck, Tim, and Siddhartha Mishra. "Numerical analysis of physics-informed neural networks and related models in physics-informed machine learning." Acta Numerica 33 (July 2024): 633–713. http://dx.doi.org/10.1017/s0962492923000089.

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Physics-informed neural networks (PINNs) and their variants have been very popular in recent years as algorithms for the numerical simulation of both forward and inverse problems for partial differential equations. This article aims to provide a comprehensive review of currently available results on the numerical analysis of PINNs and related models that constitute the backbone of physics-informed machine learning. We provide a unified framework in which analysis of the various components of the error incurred by PINNs in approximating PDEs can be effectively carried out. We present a detailed review of available results on approximation, generalization and training errors and their behaviour with respect to the type of the PDE and the dimension of the underlying domain. In particular, we elucidate the role of the regularity of the solutions and their stability to perturbations in the error analysis. Numerical results are also presented to illustrate the theory. We identify training errors as a key bottleneck which can adversely affect the overall performance of various models in physics-informed machine learning.

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Carpenter, Chris. "Physics-Informed Deep-Learning Models Improve Forecast Scalability, Reliability." Journal of Petroleum Technology 76, no. 10 (October 1, 2024): 90–93. http://dx.doi.org/10.2118/1024-0090-jpt.

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_ This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper URTeC 4042557, “Physics-Informed Deep-Learning Models for Improving Shale and Tight Forecast Scalability and Reliability,” by Kainan Wang, SPE, Lichi Deng, and Yuzhe Cai, SPE, Chevron, et al. The paper has not been peer reviewed. _ In the complete paper, the authors present a workflow that combines probabilistic modeling and deep-learning models trained on an ensemble of physics models to improve scalability and reliability for shale and tight reservoir forecasting. Their approach is applied to synthetic cases and many wells in the Permian Basin. Through hindsight studies, these models have been demonstrated to generate realistic and diverse production curves, capture the physics of unconventional flow, quantify well-production-outlook uncertainty, and help interpretation of subsurface uncertainty. Introduction In the realm of unconventional asset development, scalable forecasting is a key component in forecast reliability. In recent years, data-driven machine-learning models and workflows have emerged as potent tools for predicting well performance, particularly in scenarios where wells share similar reservoir properties, completion designs, and operational conditions. A novel approach known as physics-informed machine learning (PIML) has gained prominence. These models leverage the strengths of machine learning while honoring the constraints imposed by physical laws. By incorporating observational, inductive, or learning bias, they bridge the gap between empirical data and fundamental physics. In this paper, the authors showcase the application of a PIML system tailored specifically for unconventional reservoirs. Their methodology involves the selection of an appropriate physics modeling framework, coupled with the development of multiple machine-learning models that augment the limited field data set. Data Acquisition and Generation Bottomhole pressure (BHP) data are key to reliable forecasting because they reflect constraints to well production. Downhole pressure gauges can provide measurements of BHP accurately, but these measurements are not always available. Numerical models can be used to correlate surface measurements to BHP with some accuracy, taking into consideration the well configuration and fluid properties, yet it is too time-consuming to develop such models for many wells in relation to the speed needed for unconventional reservoir development. An in-house machine-learning model was developed for BHP calculation to further augment the data set of gauge measurements and numerical modeling. Through a workflow that chooses the wells with higher-fidelity data as a training set, and careful calibration and iterations between incrementally adding wells of high-fidelity data to reduce uncertainty, the trained machine- learning model is able to predict BHP accurately for many more wells. Another type of engineering data important for reliable well-performance analysis and forecasting is reservoir-fluid description. In this study, the authors leveraged an internally developed pressure/volume/temperature (PVT) machine-learning model trained on proprietary PVT data, which was also shown to provide reliable predictions to key PVT properties such as saturation pressure, formation volume factor, and viscosity from limited inputs at the reservoir and separator level. These PVT models not only enhance scalability of any downstream forecasting models but also play a crucial role in physics-informed uncertainty analysis for these models.

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Tetali, Harsha Vardhan, and Joel Harley. "A physics-informed machine learning based dispersion curve estimation for non-homogeneous media." Journal of the Acoustical Society of America 152, no. 4 (October 2022): A239. http://dx.doi.org/10.1121/10.0016136.

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Modern machine learning has been on the rise in many scientific domains, such as acoustics. Many scientific problems face challenges with limited data, which prevent the use of the many powerful machine learning strategies. In response, the physics of wave-propagation can be exploited to reduce the amount of data necessary and improve performance of machine learning techniques. Based on this need, we present a physics-informed machine learning framework, known as wave-informed regression, to extract dispersion curves from a guided wave wavefield data from non-homogeneous media. Wave-informed regression blends matrix factorization with known wave-physics by borrowing results from optimization theory. We briefly derive the algorithm and discuss a signal processing-based interpretability aspect of it, which aids in extracting dispersion curves for non-homogenous media. We show our results on a non-homogeneous media, where the dispersion curves change as a function of space. We demonstrate our ability to use wave-informed regression to extract spatially local dispersion curves.

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Kutz, J. Nathan, and Steven L. Brunton. "Parsimony as the ultimate regularizer for physics-informed machine learning." Nonlinear Dynamics 107, no. 3 (January 20, 2022): 1801–17. http://dx.doi.org/10.1007/s11071-021-07118-3.

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Corson, Gregory, Jaydeep Karandikar, and Tony Schmitz. "Physics-informed Bayesian machine learning case study: Integral blade rotors." Journal of Manufacturing Processes 85 (January 2023): 503–14. http://dx.doi.org/10.1016/j.jmapro.2022.12.004.

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Sharma, Pushan, Wai Tong Chung, Bassem Akoush, and Matthias Ihme. "A Review of Physics-Informed Machine Learning in Fluid Mechanics." Energies 16, no. 5 (February 28, 2023): 2343. http://dx.doi.org/10.3390/en16052343.

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Physics-informed machine-learning (PIML) enables the integration of domain knowledge with machine learning (ML) algorithms, which results in higher data efficiency and more stable predictions. This provides opportunities for augmenting—and even replacing—high-fidelity numerical simulations of complex turbulent flows, which are often expensive due to the requirement of high temporal and spatial resolution. In this review, we (i) provide an introduction and historical perspective of ML methods, in particular neural networks (NN), (ii) examine existing PIML applications to fluid mechanics problems, especially in complex high Reynolds number flows, (iii) demonstrate the utility of PIML techniques through a case study, and (iv) discuss the challenges and opportunities of developing PIML for fluid mechanics.

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Zeng, Shi, and Dechang Pi. "Milling Surface Roughness Prediction Based on Physics-Informed Machine Learning." Sensors 23, no. 10 (May 22, 2023): 4969. http://dx.doi.org/10.3390/s23104969.

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Surface roughness is a key indicator of the quality of mechanical products, which can precisely portray the fatigue strength, wear resistance, surface hardness and other properties of the products. The convergence of current machine-learning-based surface roughness prediction methods to local minima may lead to poor model generalization or results that violate existing physical laws. Therefore, this paper combined physical knowledge with deep learning to propose a physics-informed deep learning method (PIDL) for milling surface roughness predictions under the constraints of physical laws. This method introduced physical knowledge in the input phase and training phase of deep learning. Data augmentation was performed on the limited experimental data by constructing surface roughness mechanism models with tolerable accuracy prior to training. In the training, a physically guided loss function was constructed to guide the training process of the model with physical knowledge. Considering the excellent feature extraction capability of convolutional neural networks (CNNs) and gated recurrent units (GRUs) in the spatial and temporal scales, a CNN–GRU model was adopted as the main model for milling surface roughness predictions. Meanwhile, a bi-directional gated recurrent unit and a multi-headed self-attentive mechanism were introduced to enhance data correlation. In this paper, surface roughness prediction experiments were conducted on the open-source datasets S45C and GAMHE 5.0. In comparison with the results of state-of-the-art methods, the proposed model has the highest prediction accuracy on both datasets, and the mean absolute percentage error on the test set was reduced by 3.029% on average compared to the best comparison method. Physical-model-guided machine learning prediction methods may be a future pathway for machine learning evolution.

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Meguerdijian, Saro, Rajesh J. Pawar, Bailian Chen, Carl W. Gable, Terry A. Miller, and Birendra Jha. "Physics-informed machine learning for fault-leakage reduced-order modeling." International Journal of Greenhouse Gas Control 125 (May 2023): 103873. http://dx.doi.org/10.1016/j.ijggc.2023.103873.

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Soyarslan, Celal, and Marc Pradas. "Physics-informed machine learning in asymptotic homogenization of elliptic equations." Computer Methods in Applied Mechanics and Engineering 427 (July 2024): 117043. http://dx.doi.org/10.1016/j.cma.2024.117043.

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32

Antonion, Klapa, Xiao Wang, Maziar Raissi, and Laurn Joshie. "Machine Learning Through Physics–Informed Neural Networks: Progress and Challenges." Academic Journal of Science and Technology 9, no. 1 (January 20, 2024): 46–49. http://dx.doi.org/10.54097/b1d21816.

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Physics-Informed Neural Networks (PINNs) represent a groundbreaking approach wherein neural networks (NNs) integrate model equations, such as Partial Differential Equations (PDEs), within their architecture. This innovation has become instrumental in solving diverse problem sets including PDEs, fractional equations, integral-differential equations, and stochastic PDEs. It's a versatile multi-task learning framework that tasks NNs with fitting observed data while simultaneously minimizing PDE residuals. This paper delves into the landscape of PINNs, aiming to delineate their inherent strengths and weaknesses. Beyond exploring the fundamental characteristics of these networks, this review endeavors to encompass a wider spectrum of collocation-based physics-informed neural networks, extending beyond the core PINN model. Variants like physics-constrained neural networks (PCNN), variational hp-VPINN, and conservative PINN (CPINN) constitute pivotal aspects of this exploration. The study accentuates a predominant focus in research on tailoring PINNs through diverse strategies: adapting activation functions, refining gradient optimization techniques, innovating neural network structures, and enhancing loss function architectures. Despite the extensive applicability demonstrated by PINNs, surpassing classical numerical methods like Finite Element Method (FEM) in certain contexts, the review highlights ongoing opportunities for advancement. Notably, there are persisting theoretical challenges that demand resolution, ensuring the continued evolution and refinement of this revolutionary approach.

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Omar, Sara Ibrahim, Chen Keasar, Ariel J. Ben-Sasson, and Eldad Haber. "Protein Design Using Physics Informed Neural Networks." Biomolecules 13, no. 3 (March 1, 2023): 457. http://dx.doi.org/10.3390/biom13030457.

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The inverse protein folding problem, also known as protein sequence design, seeks to predict an amino acid sequence that folds into a specific structure and performs a specific function. Recent advancements in machine learning techniques have been successful in generating functional sequences, outperforming previous energy function-based methods. However, these machine learning methods are limited in their interoperability and robustness, especially when designing proteins that must function under non-ambient conditions, such as high temperature, extreme pH, or in various ionic solvents. To address this issue, we propose a new Physics-Informed Neural Networks (PINNs)-based protein sequence design approach. Our approach combines all-atom molecular dynamics simulations, a PINNs MD surrogate model, and a relaxation of binary programming to solve the protein design task while optimizing both energy and the structural stability of proteins. We demonstrate the effectiveness of our design framework in designing proteins that can function under non-ambient conditions.

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Kong, Lingju, Ryan Z. Shi, and Min Wang. "A physics-informed neural network model for social media user growth." Applied Computing and Intelligence 4, no. 2 (2024): 195–208. http://dx.doi.org/10.3934/aci.2024012.

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<p>In this paper, a physics-informed neural network model is proposed to predict the growth of online social network users. The number of online social network users is modeled by a stochastic process and the associated Kolmogorov forward equation is derived. Then, a physics-informed neural network model is built based on the Kolmogorov forward equation and trained using real-world data. By combining mathematical modeling with machine learning, our approach provides a practical and interpretable methodology that harnesses the strengths of both physical laws and advancements in machine learning, while minimizing the opacity in machine learning models.</p>

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Manzoor, Tayyab, Hailong Pei, Zhongqi Sun, and Zihuan Cheng. "Model Predictive Control Technique for Ducted Fan Aerial Vehicles Using Physics-Informed Machine Learning." Drones 7, no. 1 (December 21, 2022): 4. http://dx.doi.org/10.3390/drones7010004.

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This paper proposes a model predictive control (MPC) approach for ducted fan aerial robots using physics-informed machine learning (ML), where the task is to fully exploit the capabilities of the predictive control design with an accurate dynamic model by means of a hybrid modeling technique. For this purpose, an indigenously developed ducted fan miniature aerial vehicle with adequate flying capabilities is used. The physics-informed dynamical model is derived offline by considering the forces and moments acting on the platform. On the basis of the physics-informed model, a data-driven ML approach called adaptive sparse identification of nonlinear dynamics is utilized for model identification, estimation, and correction online. Thereafter, an MPC-based optimization problem is computed by updating the physics-informed states with the physics-informed ML model at each step, yielding an effective control performance. Closed-loop stability and recursive feasibility are ensured under sufficient conditions. Finally, a simulation study is conducted to concisely corroborate the efficacy of the presented framework.

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Hooshyar, Saman, and Arash Elahi. "Sequencing Initial Conditions in Physics-Informed Neural Networks." Journal of Chemistry and Environment 3, no. 1 (March 26, 2024): 98–108. http://dx.doi.org/10.56946/jce.v3i1.345.

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The scientific machine learning (SciML) field has introduced a new class of models called physics-informed neural networks (PINNs). These models incorporate domain-specific knowledge as soft constraints on a loss function and use machine learning techniques to train the model. Although PINN models have shown promising results for simple problems, they are prone to failure when moderate level of complexities are added to the problems. We demonstrate that the existing baseline models, in particular PINN and evolutionary sampling (Evo), are unable to capture the solution to differential equations with convection, reaction, and diffusion operators when the imposed initial condition is non-trivial. We then propose a promising solution to address these types of failure modes. This approach involves coupling Curriculum learning with the baseline models, where the network first trains on PDEs with simple initial conditions and is progressively exposed to more complex initial conditions. Our results show that we can reduce the error by 1 – 2 orders of magnitude with our proposed method compared to regular PINN and Evo.

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Navidi, Sina, Adam Thelen, Tingkai Li, and Chao Hu. "A Comparative Study on Physics-Informed Machine Learning for Battery Degradation Diagnostics." ECS Meeting Abstracts MA2023-01, no. 4 (August 28, 2023): 848. http://dx.doi.org/10.1149/ma2023-014848mtgabs.

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Quantifying the extent of degradation in lithium-ion battery cells using non-destructive approaches can provide valuable insights into the cell’s state of health and remaining useful life. However, physics-based degradation diagnostic methods typically require collecting long-term aging data and are computationally expensive to deploy locally on a device. This work investigates combining physics-based modeling and machine learning to retain high diagnostic accuracy while mitigating the need to collect long-term degradation data. To transfer knowledge from a physics-based model to a machine learning model, we develop two new approaches: co-kriging and physics-informed neural networks. We aim to effectively diagnose cell health in the late aging stage without needing long-term degradation data. Using a small set of early-life experimental data collected from an aging experiment, we train a co-kriging machine learning model to learn the difference between the experimental data and a set of simulation data generated from a physics-based half-cell model. Additionally, we train a neural network model using a physics-informed loss function with a new term that penalizes discrepancies between neural network model prediction and physics-based model prediction. The trained models can then be used to diagnose cell capacity and three primary component-level degradation modes at a future time. The proposed methods and two existing physics-informed machine learning methods named data augmentation and delta learning are comprehensively evaluated using data from a long-term (4+ years) cycle aging experiment of 24 implantable-grade Li-ion cells cycled under two different temperatures and C-rates. Cross-validated results show that the proposed physics-informed machine learning models can significantly improve the estimation accuracy of cell capacity and three primary degradation modes compared to a purely data-driven approach. Furthermore, this work comprehensively analyzes the trends of the degradation modes and provides insight into the long-term performance of high-quality implantable-grade lithium-ion cells.

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Li, Zhenyu. "A Review of Physics-Informed Neural Networks." Applied and Computational Engineering 133, no. 1 (January 24, 2025): 165–73. https://doi.org/10.54254/2755-2721/2025.20636.

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This article presents Physics-Informed Neural Networks (PINNs), which integrate physical laws into neural network training to model complex systems governed by partial differential equations (PDEs). PINNs enhance data efficiency, allowing for accurate predictions with less training data, and have applications in fields such as biomedical engineering, geophysics, and material science. Despite their advantages, PINNs face challenges like learning high-frequency components and computational overhead. Proposed solutions include causality constraints and improved boundary condition handling. A numerical experiment demonstrates the effectiveness of PINNs in solving the one-dimensional heat conduction equation, showcasing enhanced model stability and accuracy. Overall, PINNs represent a significant advancement in merging machine learning with physics.

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Kashinath, K., M. Mustafa, A. Albert, J.-L. Wu, C. Jiang, S. Esmaeilzadeh, K. Azizzadenesheli, et al. "Physics-informed machine learning: case studies for weather and climate modelling." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 379, no. 2194 (February 15, 2021): 20200093. http://dx.doi.org/10.1098/rsta.2020.0093.

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Machine learning (ML) provides novel and powerful ways of accurately and efficiently recognizing complex patterns, emulating nonlinear dynamics, and predicting the spatio-temporal evolution of weather and climate processes. Off-the-shelf ML models, however, do not necessarily obey the fundamental governing laws of physical systems, nor do they generalize well to scenarios on which they have not been trained. We survey systematic approaches to incorporating physics and domain knowledge into ML models and distill these approaches into broad categories. Through 10 case studies, we show how these approaches have been used successfully for emulating, downscaling, and forecasting weather and climate processes. The accomplishments of these studies include greater physical consistency, reduced training time, improved data efficiency, and better generalization. Finally, we synthesize the lessons learned and identify scientific, diagnostic, computational, and resource challenges for developing truly robust and reliable physics-informed ML models for weather and climate processes.This article is part of the theme issue ‘Machine learning for weather and climate modelling’.

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Wenzel, Sören, Elena Slomski-Vetter, and Tobias Melz. "Optimizing System Reliability in Additive Manufacturing Using Physics-Informed Machine Learning." Machines 10, no. 7 (June 29, 2022): 525. http://dx.doi.org/10.3390/machines10070525.

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Fused filament fabrication (FFF), an additive manufacturing process, is an emerging technology with issues in the uncertainty of mechanical properties and quality of printed parts. The consideration of all main and interaction effects when changing print parameters is not efficiently feasible, due to existing stochastic dependencies. To address this issue, a machine learning method is developed to increase reliability by optimizing input parameters and predicting system responses. A structure of artificial neural networks (ANN) is proposed that predicts a system response based on input parameters and observations of the system and similar systems. In this way, significant input parameters for a reliable system can be determined. The ANN structure is part of physics-informed machine learning and is pretrained with domain knowledge (DK) to require fewer observations for full training. This includes theoretical knowledge of idealized systems and measured data. New predictions for a system response can be made without retraining but by using further observations from the predicted system. Therefore, the predictions are available in real time, which is a precondition for the use in industrial environments. Finally, the application of the developed method to print bed adhesion in FFF and the increase in system reliability are discussed and evaluated.

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Fang, Dehong, and Jifu Tan. "Immersed boundary-physics informed machine learning approach for fluid–solid coupling." Ocean Engineering 263 (November 2022): 112360. http://dx.doi.org/10.1016/j.oceaneng.2022.112360.

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Raymond, Samuel J., David Collins, and John Willams. "Designing acoustofluidic devices using a simplified physics-informed machine learning approach." Journal of the Acoustical Society of America 151, no. 4 (April 2022): A254. http://dx.doi.org/10.1121/10.0011237.

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The safe positioning of particles within an acoustofluidic device is critical in biomedical and biological applications. Relating the design of acoustofluidic device walls and the internal acoustic field is a complex, nonlinear problem. The field of Physics-Informed Machine Learning (PIML) offers a number of potential approaches to simplify the design of these devices. One such PIML approach is learning from synthetic data. With large scientific data sets with rich spatial-temporal data and high-performance computing providing large amounts of data to be inferred and interpreted, the task of PIML is to ensure that these predictions and inferences are enforced by, and conform to the limits imposed by physical laws. The tools employed in PIML can include large, deep neural networks, Bayesian modeling, and deep reinforcement learning with sophisticated simulations of the environment. In this work, we show a simplified version of PIML using a combination of a small fully connected neural network and a 2D meshfree simulator of acoustic devices to predict the boundary shape for an acoustically actuated device. We will discuss the real-world results and applications, as well as the current limitations of this approach and the path ahead to scale and include more complexity for more applications and designs.

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Chen, Wenqian, Qian Wang, Jan S. Hesthaven, and Chuhua Zhang. "Physics-informed machine learning for reduced-order modeling of nonlinear problems." Journal of Computational Physics 446 (December 2021): 110666. http://dx.doi.org/10.1016/j.jcp.2021.110666.

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Miller, Scott T., John F. Lindner, Anshul Choudhary, Sudeshna Sinha, and William L. Ditto. "The scaling of physics-informed machine learning with data and dimensions." Chaos, Solitons & Fractals: X 5 (March 2020): 100046. http://dx.doi.org/10.1016/j.csfx.2020.100046.

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Srinivasan, Shriram, Eric Cawi, Jeffrey Hyman, Dave Osthus, Aric Hagberg, Hari Viswanathan, and Gowri Srinivasan. "Physics-informed machine learning for backbone identification in discrete fracture networks." Computational Geosciences 24, no. 3 (May 17, 2020): 1429–44. http://dx.doi.org/10.1007/s10596-020-09962-5.

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Zhang, Xinlei, Jinlong Wu, Olivier Coutier-Delgosha, and Heng Xiao. "Recent progress in augmenting turbulence models with physics-informed machine learning." Journal of Hydrodynamics 31, no. 6 (December 2019): 1153–58. http://dx.doi.org/10.1007/s42241-019-0089-y.

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Xie, Chiyu, Shuyi Du, Jiulong Wang, Junming Lao, and Hongqing Song. "Intelligent modeling with physics-informed machine learning for petroleum engineering problems." Advances in Geo-Energy Research 8, no. 2 (March 12, 2023): 71–75. http://dx.doi.org/10.46690/ager.2023.05.01.

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Li, Shijiang, Shaojie Wang, Xiu Chen, Gongxi Zhou, Binyun Wu, and Liang Hou. "Application of physics-informed machine learning for excavator working resistance modeling." Mechanical Systems and Signal Processing 209 (March 2024): 111117. http://dx.doi.org/10.1016/j.ymssp.2024.111117.

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Yan, Bicheng, Manojkumar Gudala, Hussein Hoteit, Shuyu Sun, Wendong Wang, and Liangliang Jiang. "Physics-informed machine learning for noniterative optimization in geothermal energy recovery." Applied Energy 365 (July 2024): 123179. http://dx.doi.org/10.1016/j.apenergy.2024.123179.

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Kuo, T., S. Manikkan, I. Bilionis, X. Liu, and P. Karava. "Physics-informed machine learning framework to model buildings from incomplete information." Journal of Physics: Conference Series 2600, no. 7 (November 1, 2023): 072013. http://dx.doi.org/10.1088/1742-6596/2600/7/072013.

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Abstract This paper introduces a physics-informed machine learning framework that leverages statistical methods to seamlessly integrate diverse sources of information, enabling the automated generation of building energy models for specific target buildings. The proposed framework comprises five modules: building survey, building asset database, building information schema, multi-class classification, and physics-based energy model. To illustrate the framework’s effectiveness, we present a case study involving a building with two possible baselines. The results demonstrate that our developed framework successfully generates comprehensive building energy models even when faced with incomplete, effectively capturing baseline scenarios.

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