Physics-informed Neural Networks Research Articles

Electromagnetic Interference Effect Assessment Under Measuring Testability Limitation Based on Physics-Informed Neural Network and Gaussian Process Regression

Electromagnetic Interference Effect Assessment Under Measuring Testability Limitation Based on Physics-Informed Neural Network and Gaussian Process Regression

Joint [Formula: see text] and Image Reconstruction in Low-Field MRI by Physics-Informed Deep-Learning.

We present a model-based image reconstruction approach based on unrolled neural networks which corrects for image distortion and noise in low-field ( B0 ∼ 50 mT) MRI. Utilising knowledge about the underlying physics, a novel network architecture (SH-Net) is introduced which involves the estimation of spherical harmonic coefficients to guarantee a spatially smooth field map estimate. The SH-Net is integrated in an end-to-end trainable model which jointly estimates the B0-field map as well as the image. Experiments were conducted on retrospectively simulated low-field data of human knees. We compare our model to different model-based approaches at distinct noise levels and various B0-field distributions. Our results show that our physics-informed neural network approach outperforms the purely model-based methods by improving the PSNR up to 11.7% and the RMSE up to 86.3%. Our end-to-end trained model-based approach outperforms existing methods in reconstructing image and B0-field maps in the low-field regime. low-field MRI is becoming increasingly more popular as it enables access to MR in challenging situations such as intensive care units or resource poor areas. Our method allows for fast and accurate image reconstruction in such low-field imaging with B0-inhomogeneity compensation under a wide range of various environmental conditions.

Data-driven soliton solution implementation based on nonlinear adaptive physics-informed neural networks

Data-driven soliton solution implementation based on nonlinear adaptive physics-informed neural networks

The data-driven solutions and inverse problems of some nonlinear diffusion convection-reaction equations based on Physics-Informed Neural Network

Abstract The Physics-Informed Neural Network (PINN) has achieved remarkable results in solving partial differential equations (PDEs). This paper aims to solve the forward and inverse problems of some specific nonlinear diffusion convection-reaction equations, thereby validating the practical efficacy and accuracy of data-driven approaches in tackling such equations. In the forward problems, four different solutions of the studied equations are reproduced effectively and the approximation errors can be reduced to 10-5. Experiments indicate that the PINNs method based on adaptive activation function (PINN-AAF), outperforms the standard PINNs in dealing with inverse problems.The unknown parameters are estimated effectively and the approximation errors can lower to 10−4. Additionally, training rules for both PINN and PINN-AAF are summa rized. The results of this study validate the exceptional performance of the data-driven approach in solving the complex nonlinear diffusion convection-reaction equation prob lems, and provide an effective mechanism for dealing with analogous, intricate nonlinear problems.

Prediction of directional solidification in freeze casting of biomaterial scaffolds using physics-informed neural networks

Freeze casting, a manufacturing technique widely applied in biomedical fields for fabricating biomaterial scaffolds, poses challenges for predicting directional solidification due to its highly nonlinear behavior and complex interplay of process parameters. Conventional numerical methods, such as computational fluid dynamics (CFD), require adequate and accurate boundary condition knowledge, limiting their utility in real-world transient solidification applications due to technical limitations. In this study, we address this challenge by developing a physics-informed neural networks (PINNs) model to predict directional solidification in freeze-casting processes. The PINNs model integrates physical constraints with neural network predictions, requiring significantly fewer predetermined boundary conditions compared to CFD. Through a comparison with CFD simulations, the PINNs model demonstrates comparable accuracy in predicting temperature distribution and solidification patterns. This promising model achieves such a performance with only 5000 data points in space and time, equivalent to 250,000 timesteps, showcasing its ability to predict solidification dynamics with high accuracy. The study’s major contributions lie in providing insights into solidification patterns during freeze-casting scaffold fabrication, facilitating the design of biomaterial scaffolds with finely tuned microstructures essential for various tissue engineering applications. Furthermore, the reduced computational demands of the PINNs model offer potential cost and time savings in scaffold fabrication, promising advancements in biomedical engineering research and development.

Real-Time Identification and Nonlinear Control of a Permanent-Magnet Synchronous Motor Based on a Physics-Informed Neural Network and Exact Feedback Linearization

This work proposes a novel method for the real-time identification and nonlinear control of a permanent-magnet synchronous motor (PMSM) based on a Physics-Informed Neural Network (PINN) and the exact feedback linearization approach. The proposed approach is presented in a direct-quadrature framework, where the quadrature current and the rotational speed are selected as outputs and the direct and quadrature voltages are selected as inputs. A nonlinear difference equation is selected to describe the physical dynamics of the PMSM, and a PINN is designed based on the aforementioned structure. A simplified training scheme is designed for the PINN based on a least-squares structure to facilitate online training in real time. A nonlinear controller based on exact feedback linearization is designed by considering the nonlinear model of the system identified based on the PINN. Therefore, the proposed approach involves identification and control in real time, where the PINN is trained online. In order to track the reference for the rotational speed, a nonlinear controller with integral action based on exact feedback linearization is designed based on a linear quadratic regulator. As a result, the proposed approach can be used to identify the system to be controlled in real time, and it is able to track any small change in the real model; in addition, it is robust to both external and internal disturbances, such as variations in torque load and resistance. The proposed approach is evaluated through simulation and using a real PMSM, and the results of reference tracking are evaluated under disturbances. The identification performance is evaluated by using a Taylor diagram under closed-loop and open-loop structures, where ARX and NARX structures are used for comparison. It is thereby verified that this novel proposed control approach involving a PINN-based model can adequately track the dynamics of a PMSM system, where the performance of the proposed nonlinear control is maintained even when using the identified model based on the PINN.

A data‐assisted physics‐informed neural network (DA‐PINN) for fretting fatigue lifetime prediction

AbstractIn this study, we present for the first time the application of physics‐informed neural network (PINN) to fretting fatigue problems. Although PINN has recently been applied to pure fatigue lifetime prediction, it has not yet been explored in the case of fretting fatigue. We propose a data‐assisted PINN (DA‐PINN) for predicting fretting fatigue crack initiation lifetime. Unlike traditional PINN that solves partial differential equations for specific problems, DA‐PINN combines experimental or numerical data with physics equations as part of the loss function to enhance prediction accuracy. The DA‐PINN method, employed in this study, consists of two main steps. First, damage parameters are obtained from the finite element method by using critical plane method, which generates a data set used to train an artificial neural network (ANN) for predicting damage parameters in other cases. Second, the predicted damage parameters are combined with the experimental parameters to form the input data set for the DA‐PINN models, which predict fretting fatigue lifetime. The results demonstrate that DA‐PINN outperforms ANN in terms of prediction accuracy and eliminates the need for high computational costs once the damage parameter data set is constructed. Additionally, the choice of loss‐function methods in DA‐PINN models plays a crucial role in determining its performance.

Effective prediction of drug transport in a partially liquefied vitreous humor: Physics-informed neural network modeling for irregular liquefaction geometry

As the medium for intravitreal drug delivery, the vitreous body can significantly influence drug delivery because of various possible liquefaction geometries. This work innovatively proposes a varying-porosity approach that is capable of solving the pressure and velocity fields in the heterogeneous vitreous with randomly-shaped liquefaction geometry, validated with a finite difference model. Doing so enables patient-specific treatment for intravitreal drug delivery and can significantly improve treatment efficacy. A physics-informed neural network (PINN) model is also established for the simulation, and three cases are used for validation. Despite limited information, the PINN model, together with the varying-porosity approach, captured fluid and drug transport in the partially liquefied vitreous. This opens the possibility for optimizing intravitreal drug delivery based on ultrasonography in clinical practice.

Hybrid Modeling of Fed-Batch Cell Culture Using Physics-Informed Neural Network

Hybrid Modeling of Fed-Batch Cell Culture Using Physics-Informed Neural Network

Physics-informed neural networks for biopharmaceutical cultivation processes: Consideration of varying process parameter settings.

We present a new modeling approach for the study and prediction of important process outcomes of biotechnological cultivation processes under the influence of process parameter variations. Our model is based on physics-informed neural networks (PINNs) in combination with kinetic growth equations. Using Taylor series, multivariate external process parameter variations for important variables such as temperature, seeding cell density and feeding rates can be integrated into the corresponding kinetic rates and the governing growth equations. In addition to previous approaches, PINNs also allow continuous and differentiable functions as predictions for the process outcomes. Accordingly, our results show that PINNs in combination with Taylor-series expansions for kinetic growth equations provide a very high prediction accuracy for important process variables such as cell densities and concentrations as well as a detailed study of individual and combined parameter influences. Furthermore, the proposed approach can also be used to evaluate the outcomes of new parameter variations and combinations, which enables a saving of experiments in combination with a model-driven optimization study of the design space.

T-phPINN: Physics-informed neural networks for solving 2D non-Fourier heat conduction equations

Non-Fourier heat conduction plays a dominant role in many extreme transient heat conduction processes, such as laser pulses and heat transfer in biological systems, but the heat wave effect makes it difficult to solve the temperature field accurately and quickly. In order to solve this problem, the first order time derivative enhanced parallel hard constraints physics-informed neural networks (T-phPINN) is proposed. T-phPINN comprises two subnetworks and incorporates a first order time derivative to capture sharp temperature changes. Two numerical cases show that the minimum relative error of T-phPINN is 0.001 % and 0.015 %, which is 1.04 % and 12.30 % of the error of conventional PINN respectively, proving the accuracy of our architecture. A transfer learning framework is established for scenarios of different parameters, the training only requires 1/6 iterations of the basic model, and close accuracy is obtained. The computational cost of T-phPINN is evaluated using the finite element method as the baseline. For the two cases, the single calculation time is 33.43 % and 51.50 % of the baseline, while the multiple calculation time under the acceleration of transfer learning is 11.59 % and 17.75 % of the baseline. This study will be helpful for solving large-scale non-Fourier heat conduction equations precisely and expeditiously.

Kinematic analysis and advanced control of a vectored thruster based on 3RRUR parallel manipulator for micro-size AUVs

Abstract Autonomous underwater vehicles (AUVs) have played a pivotal role in advancing ocean exploration and exploitation. However, traditional AUVs face limitations when executing missions at minimal or near-zero forward velocities due to the ineffectiveness of their control surfaces, considerably constraining their potential applications. To address this challenge, this paper introduces an innovative vectored thruster system based on a 3RRUR parallel manipulator tailored for micro-sized AUVs. The incorporation of a vectored thruster enhances the performance of micro-sized AUVs when operating at minimal and low forward speeds. A comprehensive exploration of the kinematics of the thrust-vectoring mechanism has been undertaken through theoretical analysis and experimental validation. The findings from theoretical analysis and experimental confirmation unequivocally affirm the feasibility of the devised thrust-vectoring mechanism. The precise control of the vector device is studied using Physics-informed Neural Network and Model Predictive Control (PINN-MPC). Through the adoption of this pioneering thrust-vectoring mechanism rooted in the 3RRUR parallel manipulator, AUVs can efficiently and effectively generate the requisite motion for thrust-vectoring propulsion, overcoming the limitations of traditional AUVs and expanding their potential applications across various domains.

Heat Conduction Control Using Deep Q-Learning Approach with Physics-Informed Neural Networks

As modern systems become more complex, their control strategy no longer relies only on measurement data from probes; it also requires information from mathematical models for non-measurable places. On the other hand, those mathematical models can lead to unbearable computation times due to their own complexity, making the control process non-viable. To overcome this problem, it is possible to implement any kind of surrogate model that enables the computation of such estimates within an acceptable time frame, which allows for making decisions. Using a Physics-Informed Neural Network as a surrogate model, it is possible to compute the temperature distribution at each time step, replacing the need for running direct numerical simulations. This approach enables the use of a Deep Reinforcement Learning algorithm to train a control strategy. On this work, we considered a one-dimensional heat conduction problem, in which temperature distribution feeds a control system. Such control system has the objective of reacing and maintaining constant temperature value at a specific location of the 1D problem by activating a heat source; the desired location somehow cannot be directly measured so, the PINN approach allows to estimate its temperature with a minimum computational workload. With this approach, the control training becomes much faster without the need of performing numerical simulations or laboratory measurements.

Fault geometry invariance and dislocation potential in antiplane crustal deformation: physics-informed simultaneous solutions

Earthquake-induced crustal deformation provides valuable insights into the mechanisms of tectonic processes. Dislocation models offer a fundamental framework for comprehending such deformation, and two-dimensional antiplane dislocations are used to describe strike-slip faults. Previous earthquake deformation analyses observed that antiplane dislocations due to uniform fault slips are influenced predominantly by fault tips. Here, we state a general principle of fault geometry invariance in antiplane dislocations and exploit its theoretical consequence to define dislocation potentials that enable a streamlined crustal deformation analysis. To demonstrate the benefits of this theory, we present an analytical example and construct a rapid numerical solver for crustal deformation caused by variable fault slip scenarios using physics-informed neural networks, whose mesh-free property is suitable for modeling dislocation potentials. Fault geometry invariance and the dislocation potential may further the analysis of antiplane crustal deformation, particularly for uncertainty quantification and inversion analysis regarding unknown fault geometries in realistic crustal structures.

[formula omitted]-space physics-informed neural network (k-PINN) for compressed spectral mapping and efficient inversion of vibrations in thin composite laminates

The vibrational response of structural components carries valuable information about their underlying mechanical properties, health status and operational conditions. This underscores the need for the development of efficient physics-based inversion algorithms which, given a limited set of sensing data points and in the presence of measurement noise, can reconstruct the response at locations where measurement data is not available and/or identify the unknown mechanical properties. Addressing this challenge, Physics-Informed Neural Networks (PINNs) have emerged as a promising approach. PINNs seamlessly integrate governing equations into their architecture and have gained significant interest in solving inversion problems. In the context of learning and inversion of multimodal, multiscale vibrational responses, this paper introduces a novel spectral extension of PINNs, utilizing Fourier basis functions in the wavenumber domain, commonly known as k-space. The proposed method, referred to as k-space PINN (k-PINN), offers a robust framework for adjusting complexity and wavenumber composition of the response. Notably, the spectral formulation of k-PINN, coupled with the generally sparse representation of vibrations in k-space, facilitate efficient reconstruction and learning of broadband vibrations and alleviate the spectral bias associated with standard PINN. Additionally, the spectral solution space introduced by k-PINN substantially reduces the computational cost associated with computing physics-informed loss terms. We evaluate the effectiveness of the proposed methodology on reconstructing the bending vibrational mode shapes of a thin composite laminate and identifying its effective bending stiffness coefficients. Mode shapes are initially obtained from finite element simulation, and virtual test data with added noise are generated for evaluation purposes. It is shown that the proposed k-PINN methodology outperforms the standard PINN in terms of both learning and computational efficiency. The performance of k-PINN is further demonstrated by show casing its capability in learning different selections of symmetric, anti-symmetric and asymmetric mode shapes.

E-PINN: A fast physics-informed neural network based on explicit time-domain method for dynamic response prediction of nonlinear structures

The physics-informed neural networks (PINNs), serving as the surrogate models, have emerged in the dynamic response prediction of nonlinear systems. However, in the conventional PINN model, the global differential equation of motion of the nonlinear system is directly integrated into the loss function, which requires the network to capture the intricate global dynamic evolution mechanism of the system and thus poses significant challenges for network learning. In this study, inspired by the explicit time-domain method (ETDM), a novel PINN based on ETDM, called E-PINN, is proposed to address the challenges arising from the network learning of the existing PINNs. A lightweight long short-term memory (LSTM) module is trained to learn the nonlinear evolution mechanism of restoring forces, while a single convolutional layer (SCL) module is utilized to reflect the linear evolution mechanism of the primary structure under the combined action of the external excitations and the nonlinear restoring forces. The weights of the SCL module can be directly retrieved from the discrete convolutional formulation of ETDM, and only the parameters in the LSTM module need to be optimized through a loss function solely based on the nonlinear restoring forces, thereby enabling easy network learning of the proposed E-PINN by decoupling the linear and nonlinear evolution mechanisms embedded in the nonlinear system. Three numerical examples are investigated by the present approach, and the results demonstrate the superior training efficiency and prediction accuracy of E-PINN in dynamic response prediction of nonlinear systems.

Analysis of pedestrian second crossing behavior based on physics-informed neural networks

Pedestrian two-stage crossings are common at large, busy signalized intersections with long crosswalks and high traffic volumes. This design aims to address pedestrian operation and safety by allowing navigation in two stages, negotiating each traffic direction separately. Understanding crosswalk behavior, especially during bidirectional interactions, is essential. This paper presents a two-stage pedestrian crossing model based on Physics-Informed Neural Networks (PINNs), incorporating fluid dynamics equations to determine characteristics such as speed, density, acceleration, and Reynolds number during crossings. The study shows that PINNs outperform traditional deep learning methods in calculating and predicting pedestrian fluid properties, achieving a mean squared error as low as 10–8. The model effectively captures dynamic pedestrian flow characteristics and provides insights into pedestrian behavior impacts. The results are significant for designing pedestrian facilities to ensure comfort and optimizing signal timing to enhance mobility and safety. Additionally, these findings can aid autonomous vehicles in better understanding pedestrian intentions in intelligent transportation systems.

Solving System of Highly Oscillatory Ordinary Differential Equations with Residual-based Adaptive Refinement of Physics-Informed Neural Networks

Solving System of Highly Oscillatory Ordinary Differential Equations with Residual-based Adaptive Refinement of Physics-Informed Neural Networks

Moving sampling physics-informed neural networks induced by moving mesh PDE

In this work, we propose an end-to-end adaptive sampling framework based on deep neural networks and the moving mesh method (MMPDE-Net), which can adaptively generate new sampling points by solving the moving mesh PDE. This model focuses on improving the quality of sampling points generation. Moreover, we develop an iterative algorithm based on MMPDE-Net, which makes sampling points distribute more precisely and controllably. Since MMPDE-Net is independent of the deep learning solver, we combine it with physics-informed neural networks (PINN) to propose moving sampling PINN (MS-PINN) and show the error estimate of our method under some assumptions. Finally, we demonstrate the performance improvement of MS-PINN compared to PINN through numerical experiments of four typical examples, which numerically verify the effectiveness of our method.

Physics-informed neural network for volumetric sound field reconstruction of speech signals

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.