PaperlayerView exact revision on arXiv

Source-linked AI summary

Predicting Subsurface Abnormalities Growth using Physics-Informed Neural Networks

Mehrdad Shafiei Dizaji, Hoda Azari

arXiv:2609.01417v1cs.LG

TL;DR

Bridge-deck assessment needs more detailed and reliable forecasting than visual inspection and conventional data-dependent models provide. The paper combines deep learning with electromagnetic-wave physics to predict future GPR data, reporting improved predictive capability when physics is included. The approach is positioned as a foundation for more accurate NDE and infrastructure deterioration assessment.

  • Problem

    Bridge deterioration assessment is limited by subjective visual inspection and by model-driven approaches requiring substantial data and offering weak generalization without physical understanding.

  • Method

    The paper develops a PINN that combines GPR time-series deep learning with electromagnetic wave propagation physics and uses CNN, SFCA, ConvLSTM, and attention components.

  • Results

    Omitting physics causes a significant drop in predictive capability, including edge-information loss and poorer replication of measured-data patterns.

  • Takeaways & Limitations

    Integrating physics into deep learning provides a foundation for more accurate and reliable NDE techniques for civil-infrastructure monitoring.

  • Takeaways & Limitations

    Further optimization and extensive validation across more diverse datasets are needed to improve efficiency, accuracy, and applicability.

Abstract

from arXiv · show

The research explores the pioneering integration of Physics-Informed Neural Networks (PINNs) into the domain of Ground-Penetrating Radar (GPR) data prediction. This research presents a detailed development framework for a specialized PINN model, proficient at interpreting and forecasting GPR data, much like how medical imaging models predict tumor behavior. By harnessing the synergy between deep learning algorithms and the physical laws governing subsurface structures or in medical terms, human tissues the model effectively embeds the physics of electromagnetic wave propagation into its architecture. This ensures that predictions not only align with fundamental physical principles but also mirror the precision needed in medical diagnostics for detecting and monitoring tumors. The suggested deep learning structure comprises three components: a CNN, a spatial feature channel attention (SFCA) mechanism, and ConvLSTM, along with temporal feature frame attention (TFFA) modules. The attention mechanism computes channel attention and temporal attention weights using self-adaptation, thereby fine tuning the visual and temporal feature responses to extract the most pertinent and significant visual and temporal features. By integrating physics directly into the neural network, our model has shown enhanced accuracy in forecasting GPR data. This improvement is vital for conducting effective assessments of bridge deck conditions and other evaluations related to civil infrastructure. The use of Physics Informed Neural Networks (PINNs) has demonstrated the potential to transform the field of Non-Destructive Evaluation (NDE) by enhancing the precision of infrastructure deterioration predictions. Moreover, it offers a deeper insight into the fundamental mechanisms of deterioration, viewed through the prism of physics-based models.

1. Introduction

Bridge decks deteriorate rapidly, while visual inspection is subjective, unreliable, and incomplete. The research therefore examines spatial-temporal learning and NDE data to forecast localized deterioration more precisely.

  • Bridge decks deteriorate faster than other bridge components and consume the largest share of maintenance, repair, and replacement resources.
  • Visual inspection-based condition assessment is subjective, reliability-limited, and not comprehensive.NDE provides detailed, unbiased information for quantifying and monitoring bridge deck deterioration.
  • Spatial-temporal AI frameworks are proposed to identify localized deterioration and forecast its progression over time with more granular analysis.
  • Convolutional neural networks extract spatial patterns, whereas LSTM-based networks capture temporal features from sequential and time-series data.
  • ConvLSTM combines convolution with LSTM units to model spatial structures in image sequences and is applied here to forecast future B-scan GPR data.

2. Physics Informed Convolutional Neural Networks

The paper addresses data and generalization challenges in model-driven approaches by combining deep learning with electromagnetic wave physics for GPR forecasting. Its PINN uses neural approximations, physics residuals, and trainable material parameters during optimization.

  • Model-driven approaches require substantial training data, may rely on unrealistic simulations, and can generalize poorly without physical understanding.
  • PINNs integrate governing physical laws, including Maxwell-based electromagnetic wave propagation, directly into neural-network learning.
  • The model uses time-series NDE maps with ConvLSTM and attention layers to exploit spatial and temporal coherence when predicting future NDE maps.
  • The wave equation accounts for propagation and attenuation through conductive media using permeability and permittivity, supporting GPR subsurface modeling.
  • The objective combines data-fitting and physics-enforcing mean squared errors, with α controlling their relative contribution as a trainable variable.MSE_f enforces the structure imposed by the governing equation at collocation points.
  • The neural network approximates E(t, x), while automatic differentiation produces a physics-informed residual constrained by electromagnetic wave propagation.Training seeks parameters that fit both observed data and the differential-equation residual.
  • The training concept is illustrated as physics-informed neural-network training in Figure 2.

3. Deep Network Model Architecture

The proposed architecture combines CNN-based spatial extraction, ConvLSTM sequence modeling, and adaptive SFCA and TFFA attention mechanisms to forecast GPR data. These components selectively emphasize relevant spatial channels and temporal frames.

  • The architecture combines CNN, SFCA, ConvLSTM, and TFFA modules to extract salient spatial and temporal GPR features.Attention weights are calculated through self-adaptation.
  • CNN Architecture in PINN: The CNN uses inception blocks, convolution, pooling, and regression layers to recognize spatial features.Sensitivity analysis is used to optimize convolutional-layer settings.
  • ConvLSTM Module in PINN: ConvLSTM processes GPR frames sequentially while preserving spatial information through convolutional operations.Its connected blocks exchange generated and previous information across the sequence.
  • Spatial-Feature Channel Attention (SFCA): SFCA uses channel statistics and ConvLSTM hidden states to adaptively weight feature responses.The reweighted channels emphasize relevant information and suppress ineffective features.
  • Temporal-Feature Frame Attention (TFFA): TFFA assigns importance weights to hidden states so the model focuses on critical frames rather than treating every input frame equally.The weighted hidden sequence is encoded into a fixed-length vector for regression.

4. Training Details and Network Implementation

The model is trained and evaluated using an Adam-based workflow with train, validation, and test partitions and MSE as both loss and evaluation criterion. Experiments examine architecture choices, regularization, and the effect of adding ConvLSTM layers.

  • The dataset is split into 75% training, 10% validation, and 15% testing, with MSE used for training and evaluation.After 400 steps, training and validation MSE are 0.1 and 2.4, respectively.
  • The model uses Adam with β1 = 0.9, β2 = 0.999, batch size 4, weight decay 0.1, and learning-rate warmup and decay.TensorFlow and Keras are used for implementation, with Xavier initialization and L2 regularization.
  • Training Issues and Overfitting: Adding a ConvLSTM layer improved the network’s performance to an MSE of 0.12.The added layer enabled learning of a more complex time function.

5. Experiment Setup: Bridge Evaluation and Accelerated Structural Testing (BEAST)

The experiments use GPR data from the BEAST full-scale bridge testing facility, where accelerated environmental and traffic loading produces bridge-deck deterioration. The data are processed and cropped into image sequences for model training.

  • BEAST is a full-scale bridge testing facility in Piscataway, New Jersey, designed for controlled accelerated deterioration experiments.Its specimen is a 30 by 50 ft multi-girder steel composite bridge with an 8-inch concrete deck.
  • The BEAST specimen undergoes accelerated live loading, freeze-thaw and hot-dry cycles, and deicing-agent exposure to simulate 15–20 years of wear in months.The planned loading includes over 8 million 60-kip cycles and 400 environmental cycles.
  • GPR measurements from BEAST are stored as DZT files and processed with RADAN before model training.Processing includes cropping and formatting the raw measurements.
  • The 2051 by 512-point images are cropped into 256 by 256-pixel images and divided into train, test, and validation sets.The cropped images are organized into sequences for prediction.

6. Performance of PINN

The proposed PINN outperforms the compared network configurations, with attention blocks improving validation accuracy and predictions closely tracing ground truth.

  • Attention blocks improve the model’s validation accuracy during training.The comparison evaluates different network modules using training loss functions.
  • MSE values on the validation or test data generally range from 4 to 7.The reported mean MSE indicates strong predictive performance.
  • The PINN achieves the best prediction results, with a mean MSE of 4.
  • The CNN performs worst, recording a mean MAE value of 70.

7. Results and discussion

The PINN forecasts subsequent GPR data from preceding sequences and shows improved predictive accuracy with more training data, whereas removing physics causes substantial degradation.

  • The PINN predicts the subsequent GPR time step from input sequences of GPR data.Its output is generated from patterns and dependencies learned during training.
  • Measured and predicted GPR data are directly compared to illustrate the model’s forecasting performance on test data.Figure 15 presents measurements in the top row and predictions in the bottom row for 1000, 2000, and 3000 samples.
  • Prediction accuracy improves as the volume of training data increases.The model is trained with different dataset sizes and validated on a new test setup.
  • Omitting physics causes a significant drop in predictive capability, including edge information loss and inaccurate replication of measured patterns.The comparison is shown in Figure 16.

8. Ablation Study: Hyperparameter Tuning for DLVM

The ablation study evaluates architectural, trainable-parameter, sequence-size, and optimizer choices, identifying configurations associated with stable convergence and improved performance.

  • CNN architecture: The study compares inception-, VGG-, and ResNet-based CNN configurations to measure architectural performance.These configurations are evaluated as alternative CNN architectures.
  • CNN architecture: The inception-based network converges more stably and performs better than the VGG- and ResNet-based CNNs.The VGG-based network oscillates in its losses, whereas the Inception configuration is comparatively stable.
  • Epsilon and alpha variation: Epsilon converges to 1, while alpha converges within 0.5-0.6 after training.Both parameters are trainable variables whose initial values are varied during training.
  • Sequence size effect: The sequence size is selected as 6 because larger sequences reduce generalization, whereas smaller ones lose global information.The limited total data means changing sequence size also changes the number of training samples.
  • Optimizer comparison: The experiment compares SGD, SGDLR, and Adam, using an initial learning rate of 0.001 for each optimizer.SGDLR produces results very similar to SGD, and comparisons are shown for validation loss and accuracy.

Conclusion

The study reports that integrating physics into deep learning improves GPR prediction and may strengthen NDE for infrastructure assessment. It identifies broader applications, reduced data needs, real-time analysis, and further validation and integration as future directions.

  • Physics-informed learning improved the model’s accuracy in predicting GPR data for bridge deck and civil infrastructure assessments.The approach embeds physical laws into the neural network so predictions align with empirical data and established physical theories.
  • The model integrates spatial and temporal information from existing NDE data, increasing the depth and reliability of analysis compared with treating data points in isolation.
  • PINNs show potential for more accurate infrastructure deterioration forecasts and improved understanding of deterioration mechanisms through physics-based models.
  • Implications for Future Research and Practice: The methodology may extend beyond GPR to other NDE applications and civil engineering domains, including seismic analysis and material science.
  • Implications for Future Research and Practice: Physics-informed models may achieve high accuracy with less data and support rapid prediction from real-time data for live monitoring systems.These advantages are particularly relevant where data collection is expensive or logistically challenging, although deployment would require integration with existing NDE tools and systems.
  • Implications for Future Research and Practice: Future work should optimize the network and training processes, validate the model across more diverse datasets, and integrate it into existing NDE systems.
Loading 2609.01417v1…