# A Review of Blast Loading in the Urban Environment
## 3 Numerical Methods
### Neural Networks  
In general terms, neural networks are computational-based models whose architecture and function are said to be _\"loosely inspired by the human brain\"_([PERSON] et al., 2018). They consist of an  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Pressure Sensor ID** & **Analysis (kPa)** & **Experiment (kPa)** & **Percentage Difference** \\ \hline H1 & 2324 & 2281 & 1.9\% \\ H2 & 782 & 728 & 6.9\% \\ H3 & 398 & 312 & 21.6\% \\ H4 & 303 & 224 & 26.0\% \\ V1 & 2324 & 2432 & \(-\)4.6\% \\ V2 & 1310 & 1272 & 2.9\% \\ V3 & 7  
assembly of many _\"highly connected processing units\"_--termed the nodes or neurons [109]. The nodes are connected via unidirectional communication channels, which have individual weightings attributed to them. The weightings dictate the strength of a given connection, and knowledge storage is achieved in the form of collected weighting values. Nodes activate based on threshold values, which are functions of the sum of the inputs received from other nodes. Collectively, this allows a neural network to learn, which enables sought-after characteristics such as the capability to produce outputs when presented with an incomplete set of inputs. Furthermore, neural networks can apply a certain level of generalisation provided by the database from which they are trained--typically, this would be known input-output pairs. Training rules can be implemented that adjust the weighting of connections so that a model can obtain the desired outputs within a specified tolerable accuracy (usually 5 to 10 %).  
[PERSON] and [PERSON] [109] explored the prediction of blast loads in urban streets from a bomb detonation using neural networks. A database consisting of 49 individual analyses of a blast within a straight street from CFD blast simulations (Air3D) was used to train and validate the neural network; NeuroShell 2, Release 4.0 in this case. Peak impulse and pressure data were treated as the outputs of the configuration. Multiple neural networks were produced, each with a unique network configuration. The network that showed the least absolute mean error between the expected and estimated outputs was selected.  
The outputs from the neural network are stated to show _\"very good agreement with those obtained from the CFD simulations\"_, with the positive impulse values receiving a particular mention as being _\"very close\"_ (see Figure 9, adapted from [109]). A closing remark states _\"it has been proven that a neural network can be used as an effective tool for rapid prediction of blast effects in urban environments\"_. Whilst this seems to be the case presented by [PERSON] and [PERSON] [109], it should be noted that the geometries of the neural network models were the same as the database models. It may be more appropriate to say that neural networks can be used as an effective prediction tool, provided they are suitably trained using a thorough dataset to improve performance, similar to a conclusion determined by [PERSON] et al. [110]. Likewise, [PERSON] et al. [111] use data-rich experimental work (30 pressure vs. time data sets per test) for the training of a numerical model, although no further detail is provided about the model.  
Other blast-related applications of data-driven [112; 113] and neural network-based predictive approaches [114; 115; 116] have been shown to have  
Figure 9: Neural network and CFD overpressure outputs for a straight street blast, adapted from [PERSON] and [PERSON] [109].  
tional times compared to CFD simulations. [PERSON] et al. [117] showcased a neural network that was capable of running as much as six orders of magnitude faster than a CFD simulation for a 3D scenario, with similar results reported by [PERSON] and [PERSON] [118]. [PERSON] and [PERSON] [119] also compared neural network-based modelling to CFD simulations and stated that their results _\"demonstrate the potential for machine learning algorithms to revolutionise CFD analysis for blast loading\"_.