Recently, there has been a growing interest in the development of intelligent labelfree structural damage identification methods that utilize physics-informed neural networks (PINNs). However, penalizing the governing equation of training data is computationally time-consuming since the existence of high-order partial derivatives. To address this issue, a damage identification method for isotropic and homogeneous thin plates is proposed in this paper that utilizes transfer learning physics-informed neural networks (TL-PINNs). TL-PINNs are efficient PINNs that solve inverse problems by leveraging transfer learning. Transfer learning is a machine learning technique that leverages knowledge from a source task to enhance performance on a related but different target task. It involves reusing a source model trained on a source task and then fine-tuning it to a target model with a target task. In the proposed method, the source model is trained to minimize the mismatch between training data and its predictions. Then, it is finetuned as the target model by minimizing both the mismatch between training data and its predictions as well as residuals that penalize the governing equation of isotropic and homogeneous thin plates. It is resulting in fewer iterations being required in training to penalize the governing equation than those in PINNs, which is time-consuming for highorder partial derivatives using automatic differentiation. Hence, TL-PINNs have a substantial reduction in computational time compared to PINNs for damage identification. A trained TL-PINN from a measured flexural guided wavefield is referred to as a pseudopristine model since it can generate a wavefield that approximates that governed by an isotropic and homogeneous thin plate. This unique functionality arises from penalizing the governing equation in the target model and the fact that the governing equation does not consider the existence of the damage. Any local anomalies in the measured wavefield can be isolated by comparing them with the wavefield generated by the pseudo-pristine model and then intensified using the Teager energy operator. An accumulative damage index is formulated, and the damage can be identified within neighborhoods with high index values. The effectiveness of the proposed method is demonstrated through a numerical investigation. A parameter study is also conducted to investigate the robustness of TL-PINNs with different hyper-parameters.
63Domain- and task-specific transfer learning for medical segmentation tasks
Domain- and task-specific transfer learning for medical segmentation tasks
9What matters in a transferable neural network model for relation classification in the biomedical domain?
What matters in a transferable neural network model for relation classification in the biomedical domain?
65Adaptive transfer learning for PINN
Adaptive transfer learning for PINN
8An Extrinsic Approach Based on Physics-Informed Neural Networks for PDEs on Surfaces
In this paper, we propose an extrinsic approach based on physics-informed neural networks (PINNs) for solving the partial differential equations (PDEs) on surfaces embedded in high dimensional space. PINNs are one of the deep learning-based techniques. Based on the training data and physical models, PINNs introduce the standard feedforward neural networks (NNs) to approximate the solutions to the PDE systems. Using automatic differentiation, the PDEs information could be encoded into NNs and a loss function. To deal with the surface differential operators in the loss function, we combine the extrinsic approach with PINNs and then express that loss function in extrinsic form. Subsequently, the loss function could be minimized extrinsically with respect to the NN parameters. Numerical results demonstrate that the extrinsic approach based on PINNs for surface problems has good accuracy and higher efficiency compared with the embedding approach based on PINNs. In addition, the strong nonlinear mapping ability of NNs makes this approach robust in solving time-dependent nonlinear problems on more complex surfaces.
Read more2Transfer Learning for Indonesian Named Entity Recognition
Transfer learning enables machine learning system to use previously acquired knowledge from source task on target task. Source task and target task should be correlated. Successful transfer learning would improve system performance on target task especially when target data is small. In this paper, the source task is Indonesian part-of-speech (POS) tagging system and the target task is Indonesian named entity recognition (NER) tagging system. A bidirectional gated recurrent unit and conditional random field (GRU-CRF) sequence labeller is crafted as the model for the feature representation transfer to be applied. We compared F1 evaluation results between system that used transfer and system that did not use transfer and saw an improvement around 0.02 on the transferred model when 100% training data was used and around 0.15 when 1% training data was used.
Read more23Physics Informed Neural Network using Finite Difference Method
In recent engineering applications using deep learning, physics-informed neural network (PINN) is a new development as it can exploit the underlying physics of engineering systems. The novelty of PINN lies in the use of partial differential equations (PDE) for the loss function. Most PINNs are implemented using automatic differentiation (AD) for training the PDE loss functions. A lesser well-known study is the use of finite difference method (FDM) as an alternative. Unlike an AD based PINN, an immediate benefit of using a FDM based PINN is low implementation cost. In this paper, we propose the use of finite difference method for estimating the PDE loss functions in PINN. Our work is inspired by computational analysis in electromagnetic systems that traditionally solve Laplace’s equation using successive over-relaxation. In the case of Laplace’s equation, our PINN approach can be seen as taking the Laplacian filter response of the neural network output as the loss function. Thus, the implementation of PINN can be very simple. In our experiments, we tested PINN on Laplace’s equation and Burger’s equation. We showed that using FDM, PINN consistently outperforms non-PINN based deep learning. When comparing to AD based PINNs, we showed that our method is faster to compute as well as on par in terms of error reduction.
Read more299CAN-PINN: A fast physics-informed neural network based on coupled-automatic–numerical differentiation method
CAN-PINN: A fast physics-informed neural network based on coupled-automatic–numerical differentiation method
10Quantifying local and global mass balance errors in physics-informed neural networks
Physics-informed neural networks (PINN) have recently become attractive for solving partial differential equations (PDEs) that describe physics laws. By including PDE-based loss functions, physics laws such as mass balance are enforced softly in PINN. This paper investigates how mass balance constraints are satisfied when PINN is used to solve the resulting PDEs. We investigate PINN’s ability to solve the 1D saturated groundwater flow equations (diffusion equations) for homogeneous and heterogeneous media and evaluate the local and global mass balance errors. We compare the obtained PINN’s solution and associated mass balance errors against a two-point finite volume numerical method and the corresponding analytical solution. We also evaluate the accuracy of PINN in solving the 1D saturated groundwater flow equation with and without incorporating hydraulic heads as training data. We demonstrate that PINN’s local and global mass balance errors are significant compared to the finite volume approach. Tuning the PINN’s hyperparameters, such as the number of collocation points, training data, hidden layers, nodes, epochs, and learning rate, did not improve the solution accuracy or the mass balance errors compared to the finite volume solution. Mass balance errors could considerably challenge the utility of PINN in applications where ensuring compliance with physical and mathematical properties is crucial.
Read more787Transfer learning enhanced physics informed neural network for phase-field modeling of fracture
Transfer learning enhanced physics informed neural network for phase-field modeling of fracture
63Indoor airflow field reconstruction using physics-informed neural network
Indoor airflow field reconstruction using physics-informed neural network
19Transfer learning-enhanced finite element-integrated neural networks
• The finite element-integrated neural network (FEINN) is enhanced by transfer learning strategy. • The impacts of the FEM mesh on FEINN are investigated and fully discussed. • Scale transfer learning, material transfer learning, load transfer learning strategies are evaluated. • FEINN is successfully accelerated in solving elastic, elastoplastic, multiple material boundary value problems. Physics informed neural networks (PINNs) have attracted increasing attention in computational solid mechanics due to their success in solving complex partial differential equations (PDEs). Nevertheless, the low efficiency and precision always hinder the application of PINNs in boundary value problems. To address this issue, this study proposed a transfer learning enhanced hybrid framework that integrates the finite element method with PINNs to accelerate the training process. The finite element-integrated neural network framework (FEINN) is first introduced, leveraging finite elements for domain discretization and the weak-form governing equation for defining the loss function. A mesh parametric study is subsequently conducted, aiming to identify the optimal discretization configuration by exploring various element sizes, element types, and orders of shape functions. Furthermore, various transfer learning strategies are proposed and fully evaluated to improve the training efficiency and precision of FEINN, including scale transfer learnings (STLs) from coarse mesh to refine mesh and from small domain to large domain, material transfer learnings (MTLs) from elastic material to elastoplastic material and from elastic material to elastic material problems, as well as load transfer learnings (LTLs) form displacement load condition to force load condition. A series of experiments are conducted to showcase the effectiveness of FEINN, identifying the most efficient discretization configuration and validating the efficacy of transfer learning strategies across elastic, elastoplastic, and multi-material scenarios. The results indicate that the element type and size, and shape function order have significant impacts on training efficiency and accuracy. Moreover, the transfer learning techniques can significantly improve the accuracy and training efficiency of FEINN.
Read more2Structural Damage Identification Based on Transfer Learning and Power Spectral Density
This paper proposes a novel method for structural damage identification that integrates the power spectral density (PSD) of structural acceleration responses with densely connected convolutional networks (DenseNet). The method transforms the training object of the DenseNet into a numerical matrix (PSD matrix) for structural damage identification. Leveraging transfer learning, the DenseNet models are initially trained on simulated data and further fine‐tuned using experimental data to enhance robustness and generalization. Results demonstrate that frequency‐domain signals processed by PSD significantly enhance model performance, achieving lower mean squared error (MSE), higher Pearson’s correlation coefficient ( R value), and reduced mean absolute error (MAE) compared to time‐domain signals. The effectiveness of this method was verified on a six‐story frame structure. This study underscores the efficacy of transfer learning in bridging the gap between simulated and real‐world data, thereby facilitating effective structural health monitoring and damage identification.
Read more25Upwind, No More: Flexible Traveltime Solutions Using Physics-Informed Neural Networks
The eikonal equation plays an important role across multidisciplinary branches of science and engineering. In geophysics, the eikonal equation, and its characteristics, are used in addressing two fundamental questions pertaining to seismic waves: what paths do the seismic waves take (its spreading)? and how long do they take? There have been numerous attempts to solve the eikonal equation, which can be broadly categorized as finite-difference and physics informed neural network (PINN) based approaches. While the former has been developed and optimized over the years, it still inherits some numerical inaccuracies and also the cost scales exponentially with the velocity model size. More importantly, it requires upwind calculations to satisfy the viscosity solution. PINNs, on the other hand, have shown great promise due to several features allowing for higher accuracy and scalability than conventional approaches. In this paper, we demonstrate another unique feature of PINN solutions, specifically its flexibility resulting from the global nature of its NN functional optimization, allowing for functional gradients referred to as automatic differentiation. This feature allows us to overcome the inability of conventional methods to handle large areas of missing information (gap) in the velocity model. We find empirically that the PINNs interpolation-extrapolation inherent capability enables us to circumvent a scenario when traveltime modelling is performed on velocity models containing gaps. Such a capability is crucial when performing traveltime modelling using the global tomographic Earth velocity model.
Read more38Heat Transfer Prediction With Unknown Thermal Boundary Conditions Using Physics-Informed Neural Networks
Simulating convective heat transfer using traditional numerical methods requires explicit definition of thermal boundary conditions on all boundaries of the domain, which is almost impossible to fulfill in real applications. Here, we address this ill-posed problem using machine learning techniques by assuming that we have some extra measurements of the temperature at a few locations in the domain, not necessarily located on the boundaries with the unknown thermal boundary condition. In particular, we employ physics-informed neural networks (PINNs) to represent the velocity and temperature fields while simultaneously enforce the Navier-Stokes and energy equations at random points in the domain. In PINNs, all differential operators are computed using automatic differentiation, hence avoiding discretization in either space or time. The loss function is composed of multiple terms, including the mismatch in the velocity and temperature data, the boundary and initial conditions, as well as the residuals of the Navier-Stokes and energy equations. Here, we develop a data-driven strategy based on PINNs to infer the temperature field in the prototypical problem of convective heat transfer in flow past a cylinder. We assume that we have just a couple of temperature measurements on the cylinder surface and a couple more temperature measurements in the wake region, but the thermal boundary condition on the cylinder surface is totally unknown. Upon training the PINN, we can discover the unknown boundary condition while simultaneously infer the temperature field everywhere in the domain with less than 5% error in the Nusselt number prediction. In order to assess the performance of PINN, we carried out a high fidelity simulation of the same heat transfer problem (with known thermal boundary conditions) by using the high-order spectral/hp-element method (SEM), and quantitatively evaluated the accuracy of PINN’s prediction with respect to SEM. We also propose a method to adaptively select the location of sensors in order to minimize the number of required temperature measurements while increasing the accuracy of the inference in heat transfer.
Read more47Deep neural network methods for solving forward and inverse problems of time fractional diffusion equations with conformable derivative
Deep neural network methods for solving forward and inverse problems of time fractional diffusion equations with conformable derivative
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