Physics-guided Neural Network Research Articles

High-efficiency Finite Element Model Updating of Bridge Structure using A Novel Physics-guided Neural Network

High-efficiency Finite Element Model Updating of Bridge Structure using A Novel Physics-guided Neural Network

Super-Resolving and Denoising 4D flow MRI of Neurofluids Using Physics-Guided Neural Networks.

To obtain high-resolution velocity fields of cerebrospinal fluid (CSF) and cerebral blood flow by applying a physics-guided neural network (div-mDCSRN-Flow) to 4D flow MRI. The div-mDCSRN-Flow network was developed to improve spatial resolution and denoise 4D flow MRI. The network was trained with patches of paired high-resolution and low-resolution synthetic 4D flow MRI data derived from computational fluid dynamic simulations of CSF flow within the cerebral ventricles of five healthy cases and five Alzheimer's disease cases. The loss function combined mean squared error with a binary cross-entropy term for segmentation and a divergence-based regularization term for the conservation of mass. Performance was assessed using synthetic 4D flow MRI in one healthy and one Alzheimer' disease cases, an in vitro study of healthy cerebral ventricles, and in vivo 4D flow imaging of CSF as well as flow in arterial and venous blood vessels. Comparison was performed to trilinear interpolation, divergence-free radial basis functions, divergence-free wavelets, 4DFlowNet, and our network without divergence constraints. The proposed network div-mDCSRN-Flow outperformed other methods in reconstructing high-resolution velocity fields from synthetic 4D flow MRI in healthy and AD cases. The div-mDCSRN-Flow network reduced error by 22.5% relative to linear interpolation for in vitro core voxels and by 49.5% in edge voxels. The results demonstrate generalizability of our 4D flow MRI super-resolution and denoising approach due to network training using flow patches and physics-based constraints. The mDCSRN-Flow network can facilitate MRI studies involving CSF flow measurements in cerebral ventricles and association of MRI-based flow metrics with cerebrovascular health.

Physics-guided federated learning as an enabler for digital twins

Digital twins bring the potential to increase the efficiency of assets, systems, and processes by building virtual replicas through real-time data and modeling. However, data are often confidential and distributed, high-fidelity models based on physical principles tend to be slow and require detailed knowledge about the asset design that may not be available, simplified models lack accuracy, and data-driven models are not interpretable and limited to their training space. We demonstrate the interplay of two enabling technologies, namely federated learning and hybrid analysis and modeling, to combine the strengths of physics-based and data-driven models on distributed data sets that are kept confidential by different stakeholders. Throughout the work, an ensemble of physics-guided neural networks is designed, optimized, and validated to infer the parameters of digital twin components. The physics-guided neural network is injected with output from a simplified physics-based model in intermediate layers for increased performance, and the injection layer is optimized through weight regularization. The model is then integrated into a simulation of the digital twin asset and validated there. It is shown that the model outperforms the simplified physics-based and the data-driven models both on component and on asset level. In the final step, the physics-guided neural network is trained using federated methods, which allows training on confidential data owned by different stakeholders without requiring the stakeholders to share their data. We show that federated hybrid models can – with the right training strategy – by design achieve results that are always identical and potentially superior to models trained on a central data set. The problem chosen for this demonstration is the prediction of airfoil lift and drag coefficients based on the airfoil shape and the angle of attack, which is a task crucial for simulating wind turbines. Using the physics-guided neural network, the estimation of the airfoil coefficients experiences a speedup of several orders of magnitude compared to the high-fidelity simulation, and integration into blade element momentum theory shows that the turbine thrust, torque, and mechanical power can be accurately calculated. The federated approach makes it possible to extend the training of the model to any number of distributed confidential data sets from both simulations and experiments to further increase the model’s accuracy.

Dynamic wake steering control for maximizing wind farm power based on a physics-guided neural network dynamic wake model

Wake effect is a significant factor contributing to power loss in wind farms. Studies have shown that wake steering control can mitigate this power loss. Currently, wind farm wake control strategies primarily utilize fixed yaw control due to limitations in the accuracy and efficiency of dynamic wake models. However, fixed yaw control fails to fully exploit the power improvement potential of wake steering control. Therefore, in this study, we first propose a dynamic wake model for wind farms based on the physics-guided neural network (PGNN) approach. This model can predict the dynamic wake flow field within wind farms in real time using instantaneous inflow wind speed and turbine operational states. Then, by employing the PGNN dynamic wake model as the predictive model, a wind farm dynamic wake control strategy based on the model predictive control method is proposed. To quantify the advantages of the proposed control strategy, both fixed yaw control and dynamic yaw control are tested on a wind farm with a 3 × 2 layout. Results from large eddy simulations demonstrate that the proposed dynamic wake control strategy increases the power output of the wind farm by 11.51% compared to a 6.56% increase achieved with fixed yaw control.

Physics-Guided Inverse Regression for Crop Quality Assessment

AbstractWe present an innovative approach leveraging Physics-Guided Neural Networks (PGNNs) for enhancing agricultural quality assessments. Central to our methodology is the application of physics-guided inverse regression, a technique that significantly improves the model’s ability to precisely predict quality metrics of crops. This approach directly addresses the challenges of scalability, speed, and practicality that traditional assessment methods face. By integrating physical principles, notably Fick’s second law of diffusion, into neural network architectures, our developed PGNN model achieves a notable advancement in enhancing both the interpretability and accuracy of assessments. Empirical validation conducted on cucumbers and mushrooms demonstrates the superior capability of our model in outperforming conventional computer vision techniques in postharvest quality evaluation. This underscores our contribution as a scalable and efficient solution to the pressing demands of global food supply challenges.

Prediction of oil pipeline process operating parameters based on mechanism and data mining

Abstract Precisely forecasting the operational characteristics of oil pipelines is essential for developing rational design, production, and operation strategies, as well as reducing energy consumption and saving energy. Due to significant disparities in the computation outcomes of conventional mechanism models and the inadequate performance of machine learning models when handling limited sample data, their conclusions likewise lack tangible significance. In this study, a novel physics-guided neural network (PGNN) model, which integrates mechanisms with machine learning models, is introduced. The proposed model incorporates essential physical intermediate factors that impact the temperature and pressure of oil pipelines as artificial neurons within the loss function. Additionally, an adaptive moment estimate approach is employed to optimize the parameters of the model. Through a comparative analysis of various models' predictive capabilities on an oil pipeline, it was shown that PGNN has the highest level of accuracy in forecasting pipeline temperature and pressure. Furthermore, PGNN demonstrates the ability to generate satisfactory prediction outcomes even with a limited sample size. Simultaneously, the predictive outcomes of PGNN exhibit a stronger correlation with variables that have a direct impact on temperature and pressure.

Physics-guided deep learning-based inversion for airborne electromagnetic data

SUMMARY The Earth's subsurface structure provides critical insights into sustainable resource management and geologic evolution. The airborne electromagnetic (AEM) method is an efficient data acquisition technique and can be used to image the underground resistivity structure with high spatial resolution. However, inversion of the increasingly huge volume of AEM data poses a heavy computational burden. In this study, we develop a hybrid deep learning-based approach by using the physics-guided neural network (PGNN) which incorporates the governing physical laws into the loss function to solve the AEM inverse problem. The PGNN integrates the strength of data-driven method for representation learning with electromagnetic laws and allows for the underlying physical constraints to be strictly satisfied. We validate the effectiveness of our approach using both synthetic and field datasets. Compared with the classic Gauss–Newton method, our PGNN inversion system shows strong robustness against multiple noise sources and reduces the risk of being trapped in local extrema. Moreover, the PGNN-inverted results are physically more consistent with the AEM observations compared to the purely data-driven approach. Application to the field AEM data from Northern Australia demonstrates that the PGNN-based inversion framework effectively estimates the subsurface electrical properties with considerable lateral continuity and significantly higher efficiency, completing the inversion of more than 2734000 AEM soundings taking only minutes on a common PC. Our proposed PGNN-based method shows great promise for large-scale underground resistivity imaging, and the well-identified subsurface resistivity structure can effectively improve our understanding of resource distributions and geological hazards.

Development of a semi-empirical physical model for transient NOx emissions prediction from a high-speed diesel engine

With emissions regulations becoming increasingly restrictive and the advent of real driving emissions limits, control of engine-out NOx emissions remains an important research topic for diesel engines. Progress in experimental engine development and computational modelling has led to the generation of a large amount of high-fidelity emissions and in-cylinder data, making it attractive to use data-driven emissions prediction and control models. While pure data-driven methods have shown robustness in NOx prediction during steady-state engine operation, deficiencies are found under transient operation and at engine conditions far outside the training range. Therefore, physics-based, mean value models that capture cyclic-level changes in in-cylinder thermo-chemical properties appear as an attractive option for transient NOx emissions modelling. Previous experimental studies have highlighted the existence of a very strong correlation between peak cylinder pressure and cyclic NOx emissions. In this study, a cyclic peak pressure-based semi-empirical NOx prediction model is developed. The model is calibrated using high-speed NO and NO2 emissions measurements during transient engine operation and then tested under different transient operating conditions. The transient performance of the physical model is compared to that of a previously developed data-driven (artificial neural network) model, and is found to be superior, with a better dynamic response and low (<10%) errors. The results shown in this study are encouraging for the use of such models as virtual sensors for real-time emissions monitoring and as complimentary models for future physics-guided neural network development.

Federated Learning and Unlearning as Enablers of Wind Turbine Digital Twins

Real-time capable models are paramount for the successful adaptation of digital twin technology into industries such as wind energy, but high-fidelity physics-based models cannot achieve the required speed, while data-driven and hybrid methods require large amounts of training data which is typically confidential. In this work, the combination of federated learning with hybrid modeling is proposed to train fast and reliable models across multiple confidential data sets owned by different stakeholders. The approach is demonstrated on physics-guided neural networks to estimate the lift and drag of wind turbine airfoils. A scenario is devised where multiple confidential data subsets are confined to different client devices. It is shown that the physics-guided neural networks can be trained through federated learning across those devices and data subsets and that the resulting models can recover and even surpass the accuracy of a model that is trained conventionally by merging the data subsets on a single device. The presented approach is highly scalable and can be easily adapted to many other applications. This work also discusses federated unlearning methods, which allow data owners to remove all traces of a data subset used in training if they decide to revoke their contribution.

Physics-guided neural network for grinding temperature prediction

Creep-feed grinding is a high-efficiency, high-precision grinding process widely used in the manufacturing of aviation engines. However, the workpiece burn and other quality issues caused by high processing temperature limit the yield of grinding. Therefore, the accurate model of grinding temperature has become the key to improving processing efficiency and quality. Different from the traditional physical or data-driven models, this paper attempts to combine both perspectives based on Physics-Guided Neural Networks (PGNN) to accurately predict grinding temperature with a small number of experiments. At the level of data acquisition, real grinding experiment data was obtained and a data augmentation method had been proposed. At the level of neural network structure, optimisation processes were implemented to enhance prediction performance, and a physics-guided loss function was inserted to guide network training. The experiment results shows that PGNN had better prediction accuracy than the physical model, while also mitigating the limitations of data-driven models on small sample sets. PGNN also performed better with noisy data and predictions out of the training data range, this reveals the benefits of PGNN for small sample problems in processing scenarios.

A micromechanical scheme with nonlinear concentration functions by physics-guided neural network

The mechanical behavior of heterogeneous materials has been reported to be significantly influenced by the nonlinear properties of both the matrix and interface. However, the micromechanical homogenization methods for predicting the effective properties are challenged in nonlinear problems due to the difficulties in solving the analytical form of the concentration tensors. In this study, we develop a nonlinear micromechanical scheme for heterogeneous materials with complex interfacial behaviors, where the key component, namely nonlinear concentration functions, is determined by the devised physics-guided neural network. In particular, the nonlinear Mori–Tanaka method (NMT) implemented within this new micromechanical scheme yields accurate solutions to axisymmetric nonlinear homogenization problems considering the effects of finite deformation, loading conditions, volume fraction, etc. Furthermore, the NMT is equivalent to the linear Mori–Tanaka method in the condition of the small deformation. Notably, this neural-network-based micromechanical scheme shows good generalization for different types of nonlinear interfaces, while the corresponding approach for generating training data via the finite element method (FEM) is cost-effective. This theoretical framework introduces a novel approach to nonlinear physical modeling, namely, not by the direct regression from the dataset but by deeply embedding neural networks in physical laws.

Enhancing accuracy of surface wind sensors in wind tunnel Testing: A Physics-Guided neural network calibration approach

Irwin’s surface wind sensor is widely used in wind tunnel testing for urban and environmental aerodynamics studies. However, the conventional physics-based calibration of this sensor could result in reduced measurement accuracy in regions with low flow velocities and high turbulence intensity. To address this issue, this study proposes a novel physics-guided neural network (PGNN) calibration approach, which couples a physics-based calibration model, derived from extended Taylor series expansions of measured wind speed, with an adaptive, data-driven general regression neural network. Sensors are calibrated within the turbulent boundary layer of an empty flat plate, considering both mean and standard deviation of wind velocity measured by high-accuracy thermal anemometry. The accuracy of calibrated sensors is then assessed using a 1:400 benchmark urban model. Experimental results show significant improvement in measurement accuracy, reducing mean absolute percentage error for wind speed standard deviation from 92.3 % with the current model to 9.8 % using PGNN.

A Novel Physics-Guided Neural Network for Predicting Fatigue Life of Materials

A physics-guided neural network (PGNN) is proposed to predict the fatigue life of materials. In order to reduce the complexity of fatigue life prediction and reduce the data required for network training, the PGNN only predicts the fatigue performance parameters under a specific loading environment, and calculates the fatigue life by substituting the load into the fatigue performance parameters. The advantage of this is that the network does not need to evaluate the effect of numerical changes in the load on fatigue life. The load only needs to participate in the error verification, which reduces the dimension of the function that the neural network needs to approximate. The performance of the PGNN is verified using published data. Due to the reduction in the complexity of the problem, the PGNN can use fewer training samples to obtain more accurate fatigue life prediction results and has a certain extrapolation ability for the changes in trained loading environment parameters. The prediction process of the PGNN for fatigue life is not completely a black box, and the prediction results are helpful for scholars to further study the fatigue phenomenon.

Interpretable chiller fault diagnosis based on physics-guided neural networks

Chillers are critical for building system energy efficiency and occupant comfort. Various methods have been developed for diagnosing chiller faults, with deep learning being a common choice due to its strong end-to-end learning capability. But in the absence of physical knowledge, deep learning models cannot provide a diagnosis outcome in accordance with the mechanisms behind faults, resulting in models lacking interpretability. In this regard, this paper proposes an interpretable chiller fault diagnosis method based on physics-guided neural networks. Through a comprehensive analysis of the chiller’s working process and fault evolution, a key physical indicator related to the condenser fouling fault is derived. Then a corresponding physical inconsistency loss function is developed to construct a condenser fouling fault-oriented diagnostic model. The proposed method has been demonstrated to be effective in reducing physical inconsistency while retaining diagnostic performance. The proposed method is conducive to applying the neural network approach in real operational scenarios and can serve as a reference for future research.

A physics-guided machine learning framework for real-time dynamic wake prediction of wind turbines

Efficient and accurate prediction of the wind turbine dynamic wake is crucial for active wake control and load assessment in wind farms. This paper proposes a real-time dynamic wake prediction model for wind turbines based on a physics-guided neural network. The model can predict the instantaneous dynamic wake field under various operating conditions using only the inflow wind speed as input. The model utilizes Taylor's frozen-flow hypothesis and a steady-state wake model to convert instantaneous inflow wind speed and turbine parameters into neural network input features. A deep convolutional neural network then maps these features to desired wake field snapshots, enabling dynamic wake predictions for wind turbines. To train the model, we generated approximately 255 000 instantaneous flow field snapshots of single-turbine wakes using the large eddy simulation, covering different thrust coefficients and yaw angles. The model was trained using the supervised learning method and verified on the test set. The results indicate that the model can effectively predict the dynamic wake characteristics, including the dynamic wake meandering and the wake deflection of the yawed turbines. The model can also assess both the instantaneous wake velocity and the instantaneous wake center of a wind turbine. At a thrust coefficient of 0.75, the root mean square error for the predicted instantaneous wake velocity is around 6.53%, while the Pearson correlation coefficient for the predicted instantaneous wake center can reach 0.624. Furthermore, once the model is trained, its prediction accuracy does not decrease with the increase in the time span.

Regression transients modeling of solid rocket motor burning surfaces with physics-guided neural network

Monitoring the burning surface regression in ground static ignition tests is crucial for predicting the internal ballistic performance of solid rocket motors (SRMs). A previously proposed ultra-sparse computed tomography imaging method provides a possibility for real-time monitoring. However, sample shortages of SRMs highlights the need for monitoring accuracy, especially given the high cost associated with the design and development of SRM systems. Therefore, constructing datasets via regression simulations to compensate for SRM sample shortages is critical. To address this issue, we recommend adopting the level-set method to dynamically track the burning surface by solving partial differential equations (PDEs). The computational cost of numerical solution is prohibitive for scientific applications involving large-scale spatiotemporal domains. The physics-informed neural network (PINN) and neural operator have been used to accelerate the solution of PDE, showing satisfactory prediction performance and high computational efficiency. We designed a physics-guided network, named LS-PhyNet, that couples the potential physical mechanisms of burning surface regression into the deep learning framework. The proposed method is capable of encoding well-established traditional numerical discretization methods into the network architecture to leverage prior knowledge of underlying physics, thus providing the model with enhanced expressive power and interpretability. Experimental results prove that LS-PhyNet can better reproduce the burning surfaces obtained by numerical solution with only small data regimes, providing a new paradigm for real-time monitoring of burning surface regression transients during static ignition tests.

HOSSNet: An efficient physics-guided neural network for simulating micro-crack propagation

The Hybrid Optimization Software Suite (HOSS), which combines the finite-discrete element method (FDEM), is an advanced approach for simulating high-fidelity fracture and fragmentation processes. However, the application of pure HOSS simulation is computationally expensive. Meanwhile, machine learning methods, which have shown tremendous success in various scientific problems, are increasingly being considered as promising alternatives to physics-based models in scientific domains. Thus, the objective of this work is to develop a new data-driven methodology to accurately reconstruct micro-crack fractures in both spatial and temporal fields. We leverage physical constraints to regularize the fracture propagation in long-term reconstructions. Additionally, we introduce perceptual loss and several machine learning optimization approaches to further enhance the reconstruction performance of fracture data. We demonstrate the effectiveness of the proposed method through both extrapolation and interpolation experiments. The results confirm that the proposed method can reconstruct high-fidelity fracture data across space and time in terms of pixel-wise reconstruction error and structural similarity. Visual comparisons also yield promising results in long-term reconstruction.

Reconstructing Turbulent Flows Using Spatio-temporal Physical Dynamics

Accurate simulation of turbulent flows is of crucial importance in many branches of science and engineering. Direct numerical simulation (DNS) provides the highest fidelity means of capturing all intricate physics of turbulent transport. However, the method is computationally expensive because of the wide range of turbulence scales that must be accounted for in such simulations. Large eddy simulation (LES) provides an alternative. In such simulations, the large scales of the flow are resolved, and the effects of small scales are modelled. Reconstruction of the DNS field from the low-resolution LES is needed for a wide variety of applications. Thus the construction of super-resolution methodologies that can provide this reconstruction has become an area of active research. In this work, a new physics-guided neural network is developed for such a reconstruction. The method leverages the partial differential equation that underlies the flow dynamics in the design of spatio-temporal model architecture. A degradation-based refinement method is also developed to enforce physical constraints and to further reduce the accumulated reconstruction errors over long periods. Detailed DNS data on two turbulent flow configurations are used to assess the performance of the model.

Physics-Guided Neural Network for Load Margin Assessment of Power Systems

The power system load margin is an important index used in power system operation centers. Traditional load margin calculation involves solving a set of differential-algebraic equations where not all information is always available. Data-driven methods such as Neural Networks (NNs) have been proposed but present poor performance and lack of generalization, especially in cases other than the operating history of power systems. In this article, we propose a Physics-Guided Neural Network (PGNN) to calculate the load margin of power systems. The PGNN is regularized by an auxiliary process that aims to reconstruct the power flow equations at the stability threshold that defines the load margin. In the PGNN training stage, there are two error functions that must be minimized, one related to the empirical knowledge of the system and the other related to the physical knowledge of the system associated with the guarantee of power flow. Case studies are presented for two test power systems, IEEE 68-bus system and Brazilian interconnected power system, considering a set of operating conditions, signal noise and outliers. The results show the superior performance of PGNN over traditional NNs.

Physics-Guided State-Space Model Augmentation Using Weighted Regularized Neural Networks

Physics-guided neural networks (PGNN) is an effective tool that combines the benefits of data-driven modeling with the interpretability and generalization of underlying physical information. However, for a classical PGNN, the penalization of the physics-guided part is at the output level, which leads to a conservative result as systems with highly similar state-transition functions, i.e. only slight differences in parameters, can have significantly different time-series outputs. Furthermore, the classical PGNN cost function regularizes the model estimate over the entire state space with a constant trade-of hyperparameter. In this paper, we introduce a novel model augmentation strategy for nonlinear state-space model identification based on PGNN, using a weighted function regularization (W-PGNN). The proposed approach can efficiently augment the prior physics-based state-space models based on measurement data. A new weighted regularization term is added to the cost function to penalize the difference between the state and output function of the baseline physics-based and final identified model. This ensures the estimated model follows the baseline physics model functions in regions where the data has low information content, while placing greater trust in the data when a high informativity is present. The effectiveness of the proposed strategy over the current PGNN method is demonstrated on a benchmark example.