## 1 Introduction
The use of simulated data was shown to be technically effective and economical compared to generating an experimental dataset; however, the attainable accuracy of such approach is practically limited by the accuracy of the simulation method used to generate the dataset. [PERSON] et al. [38] proposed an approach called \"functional virtual population\" to assist learning of the scheduling knowledge in dynamic manufacturing systems using small datasets. Using as few as 40 virtual samples, the proposed ANN model was attested to enhance learning accuracy. [PERSON] and [PERSON] [39] introduced a method of multiple runs adopted during the design of an ANN model for predicting the compressive strength of trabecular bone. Although a small dataset with only 35 data points is used for training, a two-layer back-propagation neural network (BPNN) model achieved significantly high accuracy with 98.3% correlation coefficient between predicted and experimental values. [PERSON] et al. [9] used the results of multiple experimental duplicates for the same input variables in developing an ANN model to evaluate polyvinylchloride composites' properties. Their results showed that the use of the individual duplicates data (instead of the averaged value) helps in enhancing the accuracy of the ANN model. [PERSON] et al. [14] performed pre-training using a stacked auto-encoder to optimize the initial weights in deep networks. They used this approach for predicting solidification cracking susceptibility of stainless steels using a small dataset (containing 487 data points) and concluded that their approach leads to better performance of DNNs. [PERSON] et al. [35] compared four models for the prediction of the flow stress of Nb-Ti micro-alloyed steel. The compared models included the original Arrhenius-type model and the same model modified by intelligent algorithms such as ANN and genetic algorithm. The results showed that the Arrhenius-type model with errors revised by ANN gives the best prediction accuracy among all other models, even with a small training dataset. [PERSON] et al. [36] proposed the use of a generalized regression neural network (GRNN) optimized by fruit-fly optimization algorithm (FOA) to improve the predictive accuracy when using small training datasets. Using a small dataset comprising only 14 data points, the proposed approach was used for modeling the relationship between alloying elements and fracture toughness of steel alloys. Based on their results, the GRNN-FOA model was found to be successful in predicting toughness with high accuracy and good generalization ability. [PERSON] et al. [40] utilized support vector machine to obtain posterior probability information, then an ANN model whose inputs included the samples and their posterior probabilities was constructed. Using a small dataset, the inclusion of simulation and real data results showed improved learning accuracy by the proposed algorithm. In this paper, we introduce a novel assisted-ANN modeling approach and use it for estimating the residual strength of panels with MSD. This proposed approach improves the accuracy of the ANN model predictions, and most importantly, it enables the ANN to be trained using small datasets and still achieve high prediction accuracy. 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. This proposed approach is especially useful in cases where there are many input parameters that affect the output, and at the same time, the number of data points available for training the ANN model is limited. Our approach relies on calculating characteristic quantities using the known relations between the different inputs/outputs and using these calculated quantities as assistance input parameters for the ANN (in addition to the traditional independent inputs).