Trustworthy AI-based crack-tip segmentation using domain-guided explanations

Technical Summary: Trustworthy AI-based Crack-Tip Segmentation using Domain-Guided Explanations

Problem Statement
Deep learning (DL) models, particularly in high-stakes scientific applications like fracture mechanics, face a "black-box" challenge where their lack of interpretability undermines trust and reliability. While post-hoc Explainable AI (XAI) methods, such as Class Activation Mapping (CAM), offer insights into model decisions, they often produce explanations that are misleading, unfaithful to the underlying model, or inconsistent across different methods. Furthermore, existing approaches to integrating explanations into training (e.g., Learning by Self-Explaining) often rely on secondary critic models or human feedback, which can be tedious, time-consuming, and fail to explicitly incorporate established domain knowledge. In the specific context of crack-tip segmentation in Digital Image Correlation (DIC) data, models may learn to focus on physically irrelevant artifacts (e.g., noise near the crack path) rather than the underlying stress fields, leading to poor generalization on out-of-distribution data.

Methodology
The authors propose Attention-Guided Training (AGT), a framework that integrates faithful XAI techniques, quantitative evaluation metrics, and domain-specific priors directly into the model training loop. The methodology proceeds in three main stages:

1. XAI Method Selection and Quantitative Evaluation:
   The authors first adapt CAM-based methods for semantic segmentation tasks. They systematically evaluate various gradient-based (e.g., Grad-CAM, Grad-CAM++) and gradient-free (e.g., Score-CAM, Eigen-CAM) techniques using four objective criteria proposed by Nauta et al. [29]:

   • Correctness (Faithfulness): How well the explanation reflects the model's true behavior.
   • Completeness: The extent to which the explanation covers relevant features.
   • Continuity: Stability of explanations under small input perturbations.
   • Compactness: The size of the explanation region.
     Through this evaluation, Grad-CAM++ applied to encoder layers was identified as the most suitable method for the crack-tip segmentation task.

2. Domain Knowledge Integration:
   Instead of relying on human annotation or unverified critic models, AGT utilizes analytical domain knowledge as the target for model attention. Specifically, the authors use Williams' series expansion [35], a theoretical solution for the stress and displacement fields near a crack tip in linear-elastic fracture mechanics. From DIC displacement data, they compute the von Mises equivalent stress field. This theoretical stress field serves as the "target explanation" ($\hat{\Phi}$).

3. The AGT Training Process:
   The training utilizes a two-phase approach:

   • Phase 1 (Pretraining): A standard DL approach using only the prediction loss (Dice loss) to ensure the model learns the segmentation task and produces meaningful initial explanations.
   • Phase 2 (Attention-Guided): A joint loss function is introduced to align the model's attention with the domain-guided target. The total loss ($L_{total}$) is defined as:
     $$L_{total} = \text{Dice}(y, \hat{y}) + \lambda \cdot SC(\Phi, \hat{\Phi})$$
     Where $y$ and $\hat{y}$ are predictions and ground truth, $\Phi$ is the current Grad-CAM++ explanation, $\hat{\Phi}$ is the target stress-field explanation, and $SC$ is the cosine similarity. The hyperparameter $\lambda$ balances the two terms.

Key Contributions

• Framework Development: Introduction of AGT, a framework that moves XAI from a post-hoc interpretability tool to an active component of the training process, guided by physical laws rather than just data patterns.
• Quantitative XAI Evaluation: Demonstration that post-hoc explanations for segmentation models vary significantly in quality and that rigorous, objective metrics are necessary to select the most faithful method (identifying Grad-CAM++ as optimal for this task).
• Domain-Guided Attention: The explicit formulation of a loss term that penalizes deviations between model attention and physically meaningful stress fields (Williams' solution), ensuring the model focuses on regions of high mechanical relevance.
• Comparative Analysis: A systematic comparison of AGT using physical targets (Binary Williams, Gradual Williams) versus non-physical/misleading targets (randomly placed attention maps) and a standard unguided baseline.

Results
The study was validated on crack-tip segmentation in DIC data from fatigue crack growth experiments.

• Predictive Performance: Models trained with physical attention targets (BW and GW) achieved significantly lower validation Dice losses (mean $\approx 0.67$) compared to non-physical targets and the unguided reference (mean $\ge 0.70$).
• Generalization and Reliability: On out-of-distribution datasets (specifically $S950,1.6$), the Binary Williams (BW) strategy demonstrated superior reliability (94% valid predictions) compared to all other strategies (max 86%). This indicates that aligning attention with physical stress fields enhances robustness against distribution shifts.
• Explanation Faithfulness: Quantitative metrics showed that physical AGT strategies improved the correctness (faithfulness) of explanations (lower AUC values), whereas non-physical strategies degraded explanation quality. The unguided baseline showed no change in correctness over extended training, confirming that the improvements were due to the attention guidance, not just additional epochs.
• Hyperparameter Sensitivity: Empirical testing identified an optimal range for $\lambda$ between 0.5 and 3. Values that were too high caused over-correction and loss of salient features, while values that were too low had insufficient effect.

Significance and Claims
The paper claims that AGT successfully addresses the trade-off between model accuracy and interpretability in scientific machine learning. By anchoring the training process to established physical theories (Williams' series), the framework ensures that deep learning models not only predict accurately but also "think" in ways consistent with domain experts. This leads to models that are more robust, trustworthy, and generalizable, particularly in scenarios where data is noisy or scarce.

The authors emphasize that this approach moves XAI beyond mere visualization; it becomes a mechanism to inject expert knowledge into the learning process. They acknowledge that finding suitable domain priors that can be mathematically formulated for attention guidance is a significant challenge, but where applicable, AGT offers a principled path toward trustworthy AI in fracture mechanics and potentially other scientific domains. The work does not claim to solve all XAI issues but provides a specific, validated pathway for integrating physical constraints into deep learning training to enhance both performance and explainability.