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Building energy flexibility plays a critical role in demand-side management for reducing utility costs for building owners and sustainable, reliable, and smart grids. Realizing building energy flexibility in tropical regions requires solar photovoltaics and energy storage systems. However, quantifying the energy flexibility of buildings utilizing such technologies in tropical regions has yet to be explored, and a robust control sequence is needed for this scenario. Hence, this work presents a case study to evaluate the building energy flexibility controls and operations of a net-zero energy office building in Singapore. The case study utilizes a data-driven energy flexibility quantification workflow and employs a novel data-driven model predictive control (MPC) framework based on the physically consistent neural network (PCNN) model to optimize the building energy flexibility. To the best of our knowledge, this is the first instance that PCNN is applied to a mathematical MPC setting, and the stability of the system is formally proved. Three scenarios are evaluated and compared: the default regulated flat tariff, a real-time pricing mechanism, and an on-site battery energy storage system (BESS). Our findings indicate that incorporating real-time pricing into the MPC framework could be more beneficial to leverage building energy flexibility for control decisions than the flat-rate approach. Moreover, adding BESS to the on-site PV generation improved the building self-sufficiency and the PV self-consumption by 17% and 20%, respectively. This integration also addresses model mismatch issues within the MPC framework, thus ensuring a more reliable local energy supply. Future research can leverage the proposed PCNN-MPC framework for different data-driven energy flexibility quantification types.

Recent developments in acoustic signal processing have seen the integration of deep learning methodologies, alongside the continued prominence of classical wave expansion-based approaches, particularly in sound field reconstruction. Physics-informed neural networks (PINNs) have emerged as a novel framework, bridging the gap between data-driven and model-based techniques for addressing physical phenomena governed by partial differential equations. This paper introduces a PINN-based approach for the recovery of arbitrary volumetric acoustic fields. The network incorporates the wave equation to impose a regularization on signal reconstruction in the time domain. This methodology enables the network to learn the physical law of sound propagation and allows for the complete characterization of the sound field based on a limited set of observations. The proposed method's efficacy is validated through experiments involving speech signals in a real-world environment, considering varying numbers of available measurements. Moreover, a comparative analysis is undertaken against state-of-the-art frequency domain and time domain reconstruction methods from existing literature, highlighting the increased accuracy across the various measurement configurations. [ABSTRACT FROM AUTHOR]

The radiation impact on the thermal distribution of the radial fin with the temperature-dependent thermal conductivity is discussed in this paper. The basic governing heat equation of the radial fin is formulated with the assistance of the Fourier law of heat conduction. The dimensional heat equation of the radial fin is non-dimensionalised utilising appropriate dimensionless variables and this ordinary differential equation (ODE) is tackled by employing the physics-informed neural network (PINN) scheme. The thermal attributes of the radial fin are investigated for different parameters like convection–conduction parameter, radiation–conduction parameter and thermal conductivity parameter. The outcomes of the systematic assessments of these parameters are demonstrated with the support of graphs. The rise in the thermal conductivity variable promotes thermal variation in the fin. A decrease in radiative–conductive variable scales augments the temperature dispersal through the fin. Furthermore, PINN incorporates physics equations directly into its architecture, unlike standard numerical approaches, which frequently require extensive mathematical expertise for accuracy. This approach enables PINN to give precise findings even when working with minimal training data, saving substantial time and resources. [ABSTRACT FROM AUTHOR]

The exploitation of fatigue life prediction methods based on fatigue indicator parameters revealed the influence of the defect size, position, and morphology on the fatigue life and fatigue behavior of additively manufactured metals. Meanwhile, Data‐driven life prediction methods are time‐efficient but inexplainable. Current machine learning‐based fatigue life prediction methods call for not only the accuracy but also the interpretability and stability of prediction results. Thus, the fusion of physical methods and machine learning methods has been a prevailing research topic in fatigue life prediction. In this study, a novel physics‐informed neural network framework is proposed by integrating a fatigue indicator parameter based on defects into the physical constraints term of a loss function. This method outperforms conventional machine learning methods in high‐cycle and very high‐cycle regimes, exhibiting superior prediction performance and generalization ability. Furthermore, the prediction results can be explained from a physical standpoint, correlating with the applicability range of the introduced physical equation describing defect positions. Highlights: A novel machine learning framework integrating a fatigue index parameter is proposed.The physics‐informed neural network has the best fatigue life prediction results.The prediction can be partially interpreted by the introduced physical model. [ABSTRACT FROM AUTHOR]

Efficient probabilistic prediction of seismic responses is crucial for assessing the seismic-resistant capability of long-span continuous girder high-speed railway bridges. Thus, a Bayesian physics-informed neural network (BPINN) is adopted to rapidly and effectively predict the probabilistic seismic responses of such bridges. The BPINN model combines deep learning and physics to improve the accuracy and consistency of predictions, while also quantifying the uncertainties using Bayesian inference methods. Various seismic excitations, including pulse, far-field and near-field types, are employed to probabilistically predict the seismic responses of the top of bridge pier. Evaluation metrics, including mean squared error and prediction interval coverage probability, are used to assess the deterministic and probabilistic estimates of BPINN. Results demonstrate that BPINN performs better in deterministic results for far-/near-field ground motions compared to pulse-like earthquakes, with most cases exhibiting a close approximation to the 95% confidence interval. The flexibility and adaptability of BPINN in handling different types of ground motions can provide valuable insights for assessing the seismic performance of such structures. [ABSTRACT FROM AUTHOR]

Cement hydration kinetics, characterized by heat generation in early-age concrete, poses a modeling challenge. This work proposes a physics-informed neural network (PINN) named PINN-CHK designed for cement hydration kinetics, to predict early-age temperature rises in cement paste. PINN-CHK leverages data-driven solutions to craft a high-fidelity prediction model, encompassing material properties and maturity functions in cement hydration. Trained on heated cement paste data, it simultaneously fits experimental results and underlying physics, yielding a mesh-free simulation. Incorporating governing partial differential equations (PDEs), and initial and boundary conditions into its loss function, PINN-CHK architecture undergoes rigorous benchmark testing, demonstrating unparalleled predictive accuracy compared to conventional deep-learning methods. It excels in predicting complete temperature fields during spatial–temporal cement hydration, achieving a remarkable relative L2 error as low as 0.00341. PINN-CHK achieves exceptional convergence and accuracy with only 5% of the training data, ushering in a new era in this crucial field. This innovative approach bridges the gap between theory and practice, offering an attractive alternative to conventional finite element solvers for enhanced comprehension of cement hydration kinetics and concrete maturity and strength development in cement-based materials. [ABSTRACT FROM AUTHOR]

The history of variational calculus dates back to the late 17th century when Johann Bernoulli presented his famous problem concerning the brachistochrone curve. Since then, variational calculus has developed intensively as many problems in physics and engineering are described by equations from this branch of mathematical analysis. This paper presents two non-classical, distinct methods for solving such problems. The first method is based on the differential transform method (DTM), which seeks an analytical solution in the form of a certain functional series. The second method, on the other hand, is based on the physics-informed neural network (PINN), where artificial intelligence in the form of a neural network is used to solve the differential equation. In addition to describing both methods, this paper also presents numerical examples along with a comparison of the obtained results.Comparingthe two methods, DTM produced marginally more accurate results than PINNs. While PINNs exhibited slightly higher errors, their performance remained commendable. The key strengths of neural networks are their adaptability and ease of implementation. Both approaches discussed in the article are effective for addressing the examined problems. [ABSTRACT FROM AUTHOR]

Investigating blood flow in the cardiovascular system is crucial for assessing cardiovascular health. Computational approaches offer some noninvasive alternatives to measure blood flow dynamics. Numerical simulations based on traditional methods such as finite-element and other numerical discretizations have been extensively studied and have yielded excellent results. However, adapting these methods to real-life simulations remains a complex task. In this paper, we propose a method that offers flexibility and can efficiently handle real-life simulations. We suggest utilizing the physics-informed neural network to solve the Navier--Stokes equation in a deformable domain, specifically addressing the simulation of blood flow in elastic vessels. Our approach models blood flow using an incompressible, viscous Navier--Stokes equation in an arbitrary Lagrangian--Eulerian form. The mechanical model for the vessel wall structure is formulated by an equation of Newton's second law of momentum and linear elasticity to the force exerted by the fluid flow. Our method is a mesh-free approach that eliminates the need for discretization and meshing of the computational domain. This makes it highly efficient in solving simulations involving complex geometries. Additionally, with the availability of well-developed open-source machine learning framework packages and parallel modules, our method can easily be accelerated through GPU computing and parallel computing. To evaluate our approach, we conducted experiments on regular cylinder vessels as well as vessels with plaque on their walls. We compared our results to a solution calculated by finite element methods using a dense grid and small time steps, which we considered as the ground truth solution. We report the relative error and the time consumed to solve the problem, highlighting the advantages of our method. [ABSTRACT FROM AUTHOR]

In order to offer guidelines for physics-informed neural network (PINN) implementation, this study presents a comprehensive review of PINN, an emerging field at the intersection of deep learning and computational physics. PINN offers a novel approach to solve physics problems by leveraging the flexibility and scalability of neural networks, even with small or no data. First, a general description of different physics problem types and target tasks addressable with PINN was provided. A generic PINN architecture was described in detail using a component-wise approach, with components ranging from collocation points to optimization methods. Then, we surveyed studies that sought to improve upon each of these components. To offer practical insights, we highlighted studies that focused on key issues of PINN implementation and showcased three practical applications. Lastly, a summary and potential research directions were provided to offer guidelines for reliable and customized PINN implementations. [ABSTRACT FROM AUTHOR]

This research adopts emerging machine learning techniques to tackle the soil–structure interaction analysis problems of laterally loaded piles through physics-informed neural networks (PINNs), which employs prior physical information in the form of partial differential equations during the model training, eliminating the tremendous data requirement in the traditional data-driven machine learning methods. The formulations to describe the problem are discussed, and the corresponding governing equations are derived. A PINN framework, including neural networks architecture and loss functions, is developed for the machine learning-based solution and elaborated with details. The corresponding model training process is presented, based on which the surrogate model construction and back analysis implementation are introduced to demonstrate the effectiveness and flexibility of the proposed method. This method has been demonstrated for its accuracy via several examples with benchmark solutions from the existing well-developed methods. Finally, a case study of the uncertainty evaluation of a laterally loaded pile is conducted to illustrate its high computational efficiency and advantages in potential engineering applications. [ABSTRACT FROM AUTHOR]

This study briefly describes the concept of guided training of deep neural networks (DNNs) to learn physically reasonable solutions. The proposed method does not need the gradients of the physical equations, although the conventional physics-informed models need the gradients. DNNs are widely used to predict phenomena in physics and mechanics. One of the issues with DNNs is that their output does not always satisfy physical equations. One approach to consider with physical equations is adding a residual of the equations into the loss function; this is called physics-informed neural network (PINN). One feature of PINNs is that the physical equations and corresponding residuals must be implemented as part of a neural network model. In addition, the residual does not always converge to a small value. The proposed model is a physics-guided generative adversarial network (PG-GAN) that uses a GAN architecture, in which physical equations are used to judge whether the neural network's output is consistent with physics. The proposed method was applied to a simple problem to assess its potential usability. [ABSTRACT FROM AUTHOR]

Recently, the physics-informed neural network (PINN) has attracted much attention in solving partial differential equations (PDEs). The success is due to the strong generalization ability of the neural network (NN), which is supported by the universal approximation theorem, and its mesh-free implementation. In this paper, we propose a multi-head NN enriched PINN (MultiPINN) for solving differential equations. The trial function is built based on the radial basis function (RBF)-interpolation, which makes NN training parameters partially interpre. The loss function is constructed by embedding the physics information of differential equations and boundary conditions. Then the parameters in MultiPINN are trained using the ADAM optimizer. A significant feature of MultiPINN is that it combines the traditional RBF interpolation method with machine learning (ML) techniques. The ML technique is employed to learn the basis feature enrichment that provides global information. The multi-head mechanism is used so that each node has multiple bases, which can improve the accuracy of the MultiPINN solution. Two ordinary differential equations and three partial differential equations, i.e. the convection equation, the Burgers equation, and the Poisson equation, are used in the numerical experiments. The experimental outcomes demonstrate that MultiPINN produces solutions consistent with both analytical solutions and solutions obtained through traditional numerical methods. Additionally, MultiPINN shows robustness and adaptability over the other NN-based methods in the implementations. [ABSTRACT FROM AUTHOR]

This paper presents a novel framework aimed at quantifying uncertainties associated with the 3D reconstruction of smoke from2Dimages. This approach reconstructs color and density fields from2Dimages usingNeural Radiance Field (NeRF) and improves image quality using frequency regularization. The NeRF model is obtained via joint training ofmultiple artificial neural networks, whereby the expectation and standard deviation of density fields and RGB values can be evaluated for each pixel. In addition, customized physics-informed neural network (PINN) with residual blocks and two-layer activation functions are utilized to input the density fields of the NeRF into Navier- Stokes equations and convection-diffusion equations to reconstruct the velocity field. The velocity uncertainties are also evaluated through ensemble learning. The effectiveness of the proposed algorithm is demonstrated through numerical examples. The presentmethod is an important step towards downstream tasks such as reliability analysis and robust optimization in engineering design. [ABSTRACT FROM AUTHOR]

With the increase in the number of power electronic devices in power systems, various techniques for assessing their stability have emerged. Among these techniques, impedance model-based stability analysis techniques have been widely used. However, conducting such analyses across multiple operating points requires abundant impedance measurement data from power electronic devices. In this paper, we propose a method for constructing impedance models of equipment with fewer impedance measurement data in voltage-source converter (VSC) back-to-back high-voltage direct current (HVDC) systems using physics-informed neural networks. Furthermore, given the power system states, we present a neural network approach to estimate grid stability at different operating points. Validation via PSCAD/EMTDC simulations and a PyTorch neural network confirmed the adequacy of these models. [ABSTRACT FROM AUTHOR]

Partial Differential Equation (PDE) is among the most fundamental tools employed to model dynamic systems. Existing PDE modeling methods are typically derived from established knowledge and known phenomena, which are time-consuming and labor-intensive. Recently, discovering governing PDEs from collected actual data via Physics Informed Neural Networks (PINNs) provides a more efficient way to analyze fresh dynamic systems and establish PED models. This study proposes Sequentially Threshold Least Squares-Lasso (STLasso), a module constructed by incorporating Lasso regression into the Sequentially Threshold Least Squares (STLS) algorithm, which can complete sparse regression of PDE coefficients with the constraints of l norm. It further introduces PINN-STLasso, a physics informed neural network combined with Lasso sparse regression, able to find underlying PDEs from data with reduced data requirements and better interpretability. In addition, this research conducts experiments on canonical inverse PDE problems and compares the results to several recent methods. The results demonstrated that the proposed PINN-STLasso outperforms other methods, achieving lower error rates even with less data. [ABSTRACT FROM AUTHOR]

Simple Summary: Early cancer detection is crucial for favorable patient outcomes, with mammography playing a central role in breast cancer detection. However, challenges persist, such as limited sensitivity in dense breast tissue and low specificity leading to excessive invasive testing. Leveraging the distinct biological characteristics of malignant tumors, we employed high-sensitivity thermal imaging to identify temperature changes associated with cancer. This innovative approach integrates a novel imaging technique and a physics-based prediction model to accurately ascertain the presence of breast cancer, regardless of size, location, and breast density. Our goal is to develop this technique as a complementary tool to mammography for widespread screening and as a cost-effective, stand-alone method for specific populations underserved by mammography. Cancer is characterized by increased metabolic activity and vascularity, leading to temperature changes in cancerous tissues compared to normal cells. This study focused on patients with abnormal mammogram findings or a clinical suspicion of breast cancer, exclusively those confirmed by biopsy. Utilizing an ultra-high sensitivity thermal camera and prone patient positioning, we measured surface temperatures integrated with an inverse modeling technique based on heat transfer principles to predict malignant breast lesions. Involving 25 breast tumors, our technique accurately predicted all tumors, with maximum errors below 5 mm in size and less than 1 cm in tumor location. Predictive efficacy was unaffected by tumor size, location, or breast density, with no aberrant predictions in the contralateral normal breast. Infrared temperature profiles and inverse modeling using both techniques successfully predicted breast cancer, highlighting its potential in breast cancer screening. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive gradient-enhanced physics-informed neural network method(A-gPINN) is proposed to investigate the dynamics of solitons in tapered refractive index waveguides. A-gPINN method adopts adaptive sampling and incorporates the gradient information of the nonlinear partial differential equation into the neural network. Compared to traditional methods, A-gPINN can achieve a more accurate prediction of complicated soliton structures in a larger computational domain with less training data. Using this method, the evolution of self-similar bright solitons, self-similar soliton pairs, self-similar rogue waves, and self-similar Akhmediev breathers has been successfully and accurately predicted, while the coefficient variations of the generalized non-homogeneous nonlinear Schrödinger equation have been predicted reversely. Due to the superiority of this method, it turns to be a promising neural network method for studying soliton dynamics in optical fibers, and it also has application potential in other physical fields such as nonlinear optics and Bose Einstein condensation. [ABSTRACT FROM AUTHOR]

In Nuclear Power Plants (NPPs), online condition monitoring and the fault detection of structures, systems and components (SSCs) can aid in guaranteeing safe operation. The use of data-driven methods for these tasks is limited by the requirement of physically consistent outcomes, particularly in safety-critical systems. Considering the importance of regulating valves (e.g., safety relief valves and main steam isolation valves), this work proposes a multistage Physics-Informed Neural Network (PINN) for fault detection in such components. Two stages of the PINN are built by developing the process model of the regulating valve, which integrates the basic valve sizing equation into the loss function to jointly train the two stages of the PINN. In the 1st stage, a shallow Neural Network (NN) with only one hidden layer is developed to estimate the equivalent flow coefficient (a key performance indicator of regulating valves) using the displacement of the valve as input. In the 2nd stage, a Deep Neural Network (DNN) is developed to estimate the flow rate expected in normal conditions using inputs such as the estimated flow coefficient from the 1st stage, the differential pressure, and the fluid temperature. Then, the residual, i.e., the difference between the estimated and measured flow rates, is fed into a Deep Support Vector Data Description (DeepSVDD) to detect the occurrence of faults. Moreover, the deviation between the estimated flow coefficients of normal and faulty conditions is used to interpret the consistency of the detection result with physics. The proposed method is, first, applied to a simulation case implemented to emulate the operating characteristics of regulating the valves of NPPs and then validated on a real-world case study based on the DAMADICS benchmark. Compared to state-of-the-art fault detection methods, the obtained results from the proposed method show effective fault detection performance and reasonable flow coefficient estimation, thus guaranteeing the physical consistency of the detection results. [ABSTRACT FROM AUTHOR]

• The study reveals that heat conduction model is sufficient to describe melt pool size in SLS of polymer. • The hybrid PINN and FEM model can parametrically and rapidly simulate temperature profiles and melt region morphologies. • Results demonstrate high fidelity in both temperature levels and final melt region compared to pure FEM models. • The hybrid model effectively addresses process parameter selection in real-world production scenarios. The state of the melt region as well as the temperature field are critical indicators reflecting the stability of the process and subsequent product quality in selective laser sintering (SLS). The present study compares various simulation models for analyzing melt pool morphologies, specifically considering their complex transient evolution. While thermal fluid dynamic simulations offer comprehensive insights into melt regions, their inherent high computational time demand is a drawback. In SLS, the polymer's high viscosity and low conductivity limit liquid flow, thereby promoting a slow evolution of the melt region formation. Based on this observation, utilizing low-complexity pure heat conduction simulation can be adequate for describing melt region morphologies as compared to the more complex thermal fluid dynamic simulations. In the present work, we propose such a purely conduction based finite element (FE) model and use it in combination with an AI-powered partial differential equation (PDE) solver based on a parametric physics-informed neural network (PINN). We specifically conduct the simulations for the sintering process, where large thermal gradients are present, with the parametric PINN based model, whereas we employ the finite element method (FEM) for the cooling phase in which gradients and cooling rates are several orders lower, thus enabling the prediction of sintering temperature and melt region morphology under various configurations. The combined hybrid model demonstrates less than 7% deviation in temperatures and less than 1% in melt pool sizes as compared to the pure FEM-based models, with faster computational times of 0.7 s for sintering and 20 min for cooling. Moreover, the hybrid model is utilized for multi-track simulation with parametric variations with the purpose of optimizing the manufacturing process. Our model provides an approach to determine the most suitable combinations of settings that enhance manufacturing speed while preventing issues such as lack of fusion and material degradation. [ABSTRACT FROM AUTHOR]

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Physics‐informed neural networks (PINNs) have emerged as a promising approach for solving a wide range of numerical problems. Nevertheless, conventional PINNs frequently face challenges in model convergence and stability when optimizing complex loss functions containing complex gradients. In this study, a new mesh‐based PINN method, called M‐PINN, is proposed drawing the ideas of the finite element method (FEM). By partitioning the solution domain into several subdomains and incorporating finite element data distribution constraints to the prior estimates of the predicted data distribution of PINN on the solution domain, the M‐PINN approach effectively reduces the optimization difficulty of conventional PINNs. Moreover, it is sometimes difficult to directly obtain precise boundary conditions in some practical applications. This method can be used to solve PINN problems with unknown boundary conditions, thus having wider applicability. In this study, the efficiency of M‐PINN was demonstrated through a standard 2D linear elastic solid mechanics simulation experiment, and its applicability was investigated in depth. The results indicate that the M‐PINN method outperforms traditional PINN and exhibits superior applicability and convergence, especially in cases involving unknown boundary conditions. [ABSTRACT FROM AUTHOR]

We performed uncertainty analysis and further numerical studies on the data-enabled physics-informed neural network (DEPINN). The purpose of DEPINN is to accurately and efficiently use a small amount of prior data to solve the neutron diffusion eigenvalue equations based on the physics-informed neural network. However, in practical engineering experiments, these prior data are acquired through different kinds of sensors, which are inevitably polluted by noise. Numerical results of three typical benchmark problems show that the classical DEPINN is not so robust with respect to noise. To improve the noise robustness, we propose an interval loss function to deal with the noisy prior data term; the weight of the noisy prior data term is also set to be noise dependent. Numerical results show that the proposed framework effectively enhances the robustness of DEPINN and improves the efficiency of utilizing the noisy prior data and thus promotes the engineering application of DEPINN. [ABSTRACT FROM AUTHOR]

This article presents a model that can automatically produce a power amplifier's (PA) design parameters, that is, transmission lines (TLs) dimension, from a dataset of user‐specified design goals like gain, efficiency, linearity, and scattering (S‐) parameters. Based on the applied boundary conditions, a synthetic dataset is generated with the best range of design parameters (W and L). This dataset is utilized for training the physics‐informed neural network (PINN) model with user‐specified design goals as input and design parameters as target to produce the optimum value of W and L as the resultant output. Furthermore, utilizing the obtained dimensions, design, simulation, fabrication, and measurement of a PA are performed to validate our proposed model. The results of large signal measurements of PA are drain efficiency (DE) of 26.9%, power added efficiency (PAE) of 24.7%, output power (Pout) of 30.98 dBm at an input power Pin$$ \left({P}_{in}\right) $$ of 19 dBm, and gain of 12.41 dB at an operating frequency of 1.625 GHz. It has been observed that the design parameters produced by the model have a significant agreement with the validated output. Also, the statistical error analysis is done by calculating the error metrics between the validated output and the actual output of the PA design. [ABSTRACT FROM AUTHOR]

Friction-induced vibration is very common in engineering areas, such as aerospace, high-speed railways, robotics, and human/artificial joints. Analysing the dynamic behaviour of systems containing a multiple-contact point frictional interface is an important topic. However, accurately simulating nonsmooth/discontinuous dynamic behaviour due to friction is challenging. This paper presents a new physics-informed neural network approach for solving nonsmooth dynamic problems involved in the friction-induced vibration or friction-involved vibration. Compared with schemes of the conventional time-stepping methodology, this novel computational framework integrates the theoretical formulations of nonsmooth multibody dynamics into the training process of the neural network. We found that this new framework can not only more accurately simulate nonsmooth dynamic behaviours, but also could be a promising method to improve the efficiency as it eliminates the need for extremely small time steps typically associated with the conventional time-stepping methodology for multibody systems. Specifically, four kinds of high-accuracy Physics-informed-neural network (PINN) strategies were proposed: (1) single PINN; (2) dual PINN; (3) advanced single PINN; and (4) advanced dual PINN. Two typical dynamics problems with nonsmooth contact were simulated, including a 1-dimensional contact problem with stick–slip and a 2-dimensional contact problem considering separation–reattachment and stick–slip. Both single and dual PINN methods showed their advantages in dealing with the 1-dimensional stick–slip problem, which outperformed conventional methods across friction models that are difficult to simulate with the conventional time-stepping method. In contrast, the advanced single and advanced dual PINN methods provided better accuracy in simulating the 2-dimensional problem, even in the cases where conventional methods failed to simulate. [ABSTRACT FROM AUTHOR]

Accurately modeling the system dynamics of autonomous underwater vehicles (AUVs) is imperative to facilitating the implementation of intelligent control. In this research, we introduce a physics-informed neural network (PINN) method to model the dynamics of AUVs by integrating dynamical equations with deep neural networks. This integration leverages the nonlinear expressive power of deep neural networks, alongside the robust foundation of physical prior knowledge, resulting in an AUV model proficient in long-term motion forecasting. The experimental results indicate that this method is capable of effectively extracting AUV system dynamics from datasets, exhibiting strong generalization capabilities and achieving robust long-term motion prediction. Furthermore, a model predictive control method is proposed, using the learned PINN as the predictive model to accurately track the closed-loop trajectory. This research offers novel perspectives on the dynamics modeling of AUVs and has the potential to be applied in other relevant research endeavors. [ABSTRACT FROM AUTHOR]

This article proposes a new approach to train physics‐augmented neural networks with observable data to represent mechanical constitutive laws. To train the neural network and learn thermodynamics potentials, the proposed method does not rely on strain‐stress or strain‐free energy pairs but needs only partial strain or displacement measurements inside the structure. The neural network is trained thanks to an unsupervised procedure in which the modified constitutive relation error (mCRE) is minimized. The mCRE functional provides a bias‐aware data assimilation framework with a rich physical sense as the constitutive relation error (CRE) part can be interpreted as a modeling error continuously defined over the structure, and can be used as a prediction quality in the inference phase. This article also extends previous works on the mCRE by introducing a new minimization procedure in the case of nonlinear state laws. As typical structural health monitoring applications may require that the neural networks should be trained online, an important focus is thus made on automatic and adaptive tuning of sensitive hyperparameters (learning rate, weighting between losses, number of epochs and initialization). It is shown that when the training database is rich enough with respect to the loading cases, the proposed method achieves remarkable performance regarding the quality of the learned model, noise robustness, and low sensitivity to user‐defined hyperparameters. The method is evaluated on two test cases: a non‐quadratic potential in the small strain regime with synthetic optic fiber measurements, and a Mooney–Rivlin model in the hyperelastic case with synthetic digital image correlation observations. [ABSTRACT FROM AUTHOR]

Challenges in the operation of power systems arise from several factors such as the interconnection of large power systems, integration of new energy sources and the increase in electrical energy demand. These challenges have required the development of fast and reliable tools for evaluating the operation of power systems. The load margin (LM) is an important index in evaluating the stability of power systems, but traditional methods for determining the LM consist of solving a set of differential-algebraic equations whose information may not always be available. Data-Driven techniques such as Artificial Neural Networks were developed to calculate and monitor LM, but may present unsatisfactory performance due to difficulty in generalization. Therefore, this article proposes a design method for Physics-Informed Neural Networks whose parameters will be tuned by bio-inspired algorithms in an optimization model. Physical knowledge regarding the operation of power systems is incorporated into the PINN training process. Case studies were carried out and discussed in the IEEE 68-bus system considering the N-1 criterion for disconnection of transmission lines. The PINN load margin results obtained by the proposed method showed lower error values for the Root Mean Square Error (RMSE), Mean Square Error (MSE) and Mean Absolute Percentage Error (MAPE) indices than the traditional training Levenberg-Marquard method. [ABSTRACT FROM AUTHOR]

The use of light-weight tensile membrane structures (TMS) has gained widespread acceptance, especially for covering vast areas. Their tension only behavior leads to high efficiency in material utilization. Designing of TMS starts with ‘form-finding’ to find the membrane’s initial equilibrium state under specified prestress and boundary constraints. Existing techniques of form-finding are generally sensitive to the parameters of the selected method and the choice of initial shape; these methods pay high computational costs especially when the number of degrees of freedom is very high. In this paper, a new linear partial differential equation, defined as the ‘modified Laplace equation,’ is derived for form-finding of minimal and non-minimal TMS by extending the vibrating membrane analogy. This equation is solved using physics-informed neural network to determine the stable configuration of the TMS. Varied TMS case studies demonstrate the accuracy and efficacy of the proposed mesh-less framework. Issues of dependency on initial shape, arbitrariness in parameter selection, non-convergence due to high-dimensionality, and meshing complex geometries are mitigated in the proposed form-finding framework. However, this method is only applicable for frame-supported TMS. [ABSTRACT FROM AUTHOR]

Summary: This paper examines the controllability of a novel Lyapunov‐based model reference adaptive control (MRAC) system designed with a meta‐learning‐based physics‐informed neural network (MLPINN) for linear and nonlinear single‐input and single‐output (SISO) plants without labeled data (MLPINN‐MRAC system). It is devised with the benefits of several techniques: the integration of the identification process in a training mode into an online control mode (straightforward design); no labeled data generation for online identification by a physics‐informed neural network; the prevention of degradation in tracking performance by meta‐learning, as the system triggers a meta‐learning process only when an error threshold detects the deterioration (high efficiency and the reduction of computation cost); quick adaptation to new inputs and an updated control input for each sub‐time span by transfer learning. It is worth noting that the frequency of the meta‐learning event detection significantly affects the step response stability of the nonlinear plant. To achieve a better quality of the stabilization, more frequent event detection is necessary for both beginning and end intervals in control. Sixteen triggering events are enough to shape the acceptable step response of the nonlinear plant, and 44 triggering events achieve the plant's desired step response with its minor modeling error. While, as for the linear plant, a single triggering event is sufficient to attain its tolerable step response and modeling error, implying that intensive event detection is not critical in the identification. It is obvious that the MLPINN‐MRAC system functions well and is more beneficial and efficient for the nonlinear plant. [ABSTRACT FROM AUTHOR]

To describe unsteady multiphase flows in porous media, it is important to consider the non-Newtonian properties of fluids by including rheological laws in the hydrodynamic model. This leads to the formation of a nonlinear system of partial differential equations. To solve this direct problem, it is necessary to linearize the equation system. Algorithm construction for inverse problem solution is problematic since the numerical solution is unstable. The application of implicit methods is reduced to matrix equations with a high rank of the coefficient matrix, which requires significant computational resources. The authors of this paper investigated the possibility of parameterized function (physics-informed neural networks) application to solve direct and inverse problems of non-Newtonian fluid flows in porous media. The results of laboratory experiments to process core samples and field data from a real oil field were selected as examples of application of this method. Due to the lack of analytical solutions, the results obtained via the finite difference method and via real experiments were proposed for validation. [ABSTRACT FROM AUTHOR]

Abstract The rapid growth of artificial intelligence is revolutionizing classical engineering society, offering novel approaches to material and structural design and analysis. Among various scientific machine learning techniques, physics-informed neural network (PINN) has been one of the most researched subjects, for its ability to incorporate physics prior knowledge into model training. However, the intrinsic continuity requirement of PINN demands the adoption of domain decomposition when multiple materials with distinct properties exist. This greatly complicates the gradient computation of design features, restricting the application of PINN to structural shape optimization. To address this, we present a novel framework that employs neural network coordinate projection for shape optimization within PINN. This technique allows for direct mapping from a standard shape to its optimal counterpart, optimizing the design objective without the need for traditional transition functions or the definition of intermediate material properties. Our method demonstrates a high degree of adaptability, allowing the incorporation of diverse constraints and objectives directly as training penalties. The proposed approach is tested on magnetostatic problems for iron core shape optimization, a scenario typically plagued by the high permeability contrast between materials. Validation with finite-element analysis confirms the accuracy and efficiency of our approach. The results highlight the framework’s capability as a viable tool for shape optimization in complex material design tasks.

This work presents a deep neural network (DNN)-based approach for identifying the modal field distributions of closed non-radiating waveguides. Specifically, physics-informed neural networks (PINNs) are used to solve the Helmholtz partial differential equation. The PINN architecture includes incorporation of boundary conditions and selection of initial conditions to obtain required modes inside the waveguides. In this paper, furthermore, the use of this method is illustrated for waveguides consisting of inhomogeneous and anisotropic media, where we apply a domain decomposition-based deep learning method. Our approach successfully identifies all eigenmode distributions with an error of less than −12 dB as compared to analytical and full-wave simulation results. Notably, we further enhance the efficiency of our approach by utilizing transfer learning, achieving a 23 times reduction in solution time. Our results demonstrate PINNs as an alternative to traditional methods in accurately calculating waveguide modal field distributions and its applicability to other partial differential equation based EM problems.

Physics-Informed Neural Networks (PINNs) have proven highly effective for solving high-dimensional Partial Differential Equations (PDEs), having demonstrated tremendous potential in a variety of challenging scenarios. However, traditional PINNs (vanilla PINNs), typically based on fully connected neural networks (FCNN), often face issues with convergence and parameter redundancy. This paper proposes a novel approach that utilizes a multi-input residual network, incorporating a multi-step training paradigm to facilitate unsupervised training. This improved method, which we named MultiInNet PINNs, can enhance the convergence speed and the stability of traditional PINNs. Our experiments demonstrate that MultiInNet PINNs achieve better convergence with fewer parameters than other networks like FCNN, ResNet, and UNet. Specifically, the multi-step training increases convergence speed by approximately 45%, while the MultiInNet enhancement contributes an additional 50%, leading to a total improvement of about 70%. This accelerated convergence speed allows PINNs to lower computational costs by achieving faster convergence. Moreover, our MultiInNet PINNs provides a potential method for handling initial and boundary conditions (I/BCs) separately within PINNs.

Predicting future discontinuous phenomena that are unobservable from training data sets has long been a challenging problem in scientific machine learning. We introduce a novel paradigm to predict the emergence and evolution of various discontinuities of hyperbolic partial differential equations (PDEs) based on given training data over a short window with limited discontinuity information. Our method is inspired by the classical Roe solver [P. L. Roe, J Comput Phys., vol. 43, 1981], a basic tool for simulating various hyperbolic PDEs in computational physics. By carefully designing the computing primitives, the data flow, and the novel pseudoinverse processing module, we enable our data‐driven predictor to satisfy all the essential mathematical criteria of a Roe solver and hence deliver accurate predictions of hyperbolic PDEs. We demonstrate through various examples that our data‐driven Roe predictor outperforms original human‐designed Roe solver and deep neural networks with weak priors in terms of accuracy and robustness. [ABSTRACT FROM AUTHOR]

The rapid growth of artificial intelligence is revolutionizing classical engineering society, offering novel approaches to material and structural design and analysis. Among various scientific machine learning techniques, physics-informed neural network (PINN) has been one of the most researched subjects, for its ability to incorporate physics prior knowledge into model training. However, the intrinsic continuity requirement of PINN demands the adoption of domain decomposition when multiple materials with distinct properties exist. This greatly complicates the gradient computation of design features, restricting the application of PINN to structural shape optimization. To address this, we present a novel framework that employs neural network coordinate projection for shape optimization within PINN. This technique allows for direct mapping from a standard shape to its optimal counterpart, optimizing the design objective without the need for traditional transition functions or the definition of intermediate material properties. Our method demonstrates a high degree of adaptability, allowing the incorporation of diverse constraints and objectives directly as training penalties. The proposed approach is tested on magnetostatic problems for iron core shape optimization, a scenario typically plagued by the high permeability contrast between materials. Validation with finite-element analysis confirms the accuracy and efficiency of our approach. The results highlight the framework's capability as a viable tool for shape optimization in complex material design tasks. [ABSTRACT FROM AUTHOR]

Nonlinear projection equations (NPEs) provide a unified framework for solving various constrained nonlinear optimization and engineering problems. This paper presents a deep learning approach for solving NPEs by incorporating neurodynamic optimization and physics‐informed neural networks (PINNs). First, we model the NPE as a system of ordinary differential equations (ODEs) using neurodynamic optimization, and the objective becomes solving this ODE system. Second, we use a modified PINN to serve as the solution for the ODE system. Third, the neural network is trained using a dedicated algorithm to optimize both the ODE system and the NPE. Unlike conventional numerical integration methods, the proposed approach predicts the end state without computing all the intermediate states, resulting in a more efficient solution. The effectiveness of the proposed framework is demonstrated on a collection of classical problems, such as variational inequalities and complementarity problems. [ABSTRACT FROM AUTHOR]

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