## 6 Concluding Remarks  
It is widely believed that one of the advantages of ANNs is their ability to model complex non-linear relationships between several input/output parameters, without any need for prior knowledge of the nature of the relationships between these parameters. While this is generally true, however a large training dataset (usually hundreds of data points) will be required for the ANN to fully capture such complex non-linear relationships. In many engineering applications, such as fracture mechanics for instance, the input/output relations are complex and highly non-linear; and at the same time, the curation of large experimental datasets is usually not feasible. This paper introduces a novel assisted-ANN modeling approach that enables the ANN to be trained using small datasets and still achieve high prediction accuracy. This approach is demonstrated, and its capabilities are investigated by applying it for evaluating the residual strength of panels with MSD cracks. The purpose of the assisted-ANN modeling approach proposed here is to assist the ANN learning process, when the training dataset is relatively small, and therefore improve the accuracy of the output predictions. This is done by including additional inputs (called assistance parameters) that are obtained from the known analytical input/output relations. So, in essence, our approach merges the well-known and well-established analytical relations (between the different input/output parameters) with the ANN technique to improve the ability of ANN to estimate the residual strength of panels with MSD cracks. The inputs that are usually used in ANN modeling are geometry and material related, and they are \"independent\" from each other. In contrary to the inputs used in the traditional approach, the added assistance parameters being used in the assisted approach are basically \"dependent\" on the other input parameters, and they are calculated using the existing analytical relations (or obtained using computational techniques). The results presented in this paper demonstrate that the assisted-ANN modeling approach clearly improves the residual strength predictions' accuracy, in comparison to the traditional approach. Using the assisted approach, an average prediction error (MAE\({}_{\text{P}}\)) of less than 3% is achieved. Also, the relative reduction in the prediction error, compared to the traditional approach, reached up to 46% in some cases. The main conclusions of this study can be summarized in the following points:  
* Different types of parameters can be used as assistance parameters, and one or more assistance parameters can be used at the same time. The assistance parameters can be obtained using any well-established relation that partially or fully relate some (or all) of the inputs with the output (e.g., the SIF correction factors are partial relations while the linkup model is a full relation). The amount of the achieved accuracy improvement depends on the level and the accuracy of the assistance parameter(s) being used. * The fact that the SIF correction factors can be successfully used as assistance input parameters makes the proposed assisted-ANN approach to be useful in a very wide variety of fracture mechanics applications (both for fatigue crack growth and static fracture). The assisted-ANN approach should prove to be very helpful in cases where the number of data points available for training the ANN is limited, which is generally the case in many experimental investigations in the fracture mechanics field. * The lower the accuracy of the predictions obtained using the traditional approach, the more the improvement that is achieved using the assisted approach. For the SGC algorithm (it gives the least accurate results), the relative error reduction achieved by the assisted approach reached \(-46\%\); whereas for the BR algorithm (it gives the most accurate results), the relative error reduction achieved by the assisted approach reached \(-22\%\) only.