## 1 Introduction  
Artificial neural networks (ANN), computational modelling tools, have found wide acceptance in many disciplines due to their adaptability to complex real world problems.  
ANNs have demonstrated their ability to model non-linear physics systems [1], involving complex physical behaviors, and were applied to the analysis of remotely sensed images with promising results. Some examples of applications are: retrieval of soil moisture and agricultural variables from microwave radiometry [2], estimation of snow water equivalent and snow water depth from microwave images [3], retrieval of leaf area index (LAI) and other biophysical variables from the MEdium Resolution Imaging Spectrometer (MERIS) and MODerate-resolution Imaging Spectroradiometer (MODIS) instruments [4], estimation of chlorophyll from MERIS [5], retrieval of volcanic ash and sulphur dioxide from hyperspectral data [6]. ANNs are also used, with good results, for rainfall prediction involving other geophysical data [7,8].  
Since an earthquake usually acts in a nonlinear way, the neural network algorithm can be an appropriate method for damage estimation purposes since it demonstrated to be a good non-linear approximator [9]. Recently, ANNs have been applied to detect damaged buildings, following an earthquake, by using high spatial resolution optical images acquired after the seismic event [10]. A neural network based-approach is being implemented to assess the status of buildings after earthquake excitation, predicting the displacement at different floors considering the wave energy propagating only into the ground floor [11].  
By using change features from satellite images, accurate and reliable damage mapping can be obtained, exploiting both optical and radar sensors [12, 13, 14]. In [PERSON] et al., 2016, an unsupervised algorithm for damage classification purposes has been developed [14].  
Currently, quantitative estimation of earthquake damage level as a continuous function, using an ANN, has not yet been exploited and the present study represents a first attempt at applying an ANN to both optical high resolution Sentinel-2 and Synthetic Aperture Radar (SAR) remote sensing data for collapse ratio modelling. To the best of our knowledge, the methodology based on ANN has not been utilized in modelling earthquake damage assessment.  
In the present study, two different neural networks using different Earth Observation (EO) datasets have been realized in order to model, as a continuous function, building damage. The first neural network (NN) experiment used, as input, only features obtained from optical data, whilst the second one (in a data fusion approach) also the features obtained from SAR images. NDI, KLD and MI features from optical data, and ICD and KLD from SAR data were used. Regarding the SAR data, KLD and MI parameters are very suitable features that can contribute to damage estimation [15]; the ICD demonstrated itself a very good damage proxy [13,16]. Concerning the optical data, the most significant performances are related to the NDI, KLD [17], and MI indexes [18]. These features show very good sensitivity to the collapse ratio.  
The case study is the Central Italy strong earthquake, which took place on August 2016. On 24 August 2016 at 1:36 UTC, a M6.0 earthquake occurred in the Apennines of Central (hereafter Amatrice earthquake) Italy at depth 8 km, over a NNW-SSE striking, WSW dipping normal fault [19], destroying the closest towns to the epicenter--Amatrice, Accumoli and Aquata del Tronto--and causing near 300 fatalities. This earthquake revealed the importance of a rapid earthquake damage assessment, right after a seismic event, which can address the civil protection interventions towards the most affected areas. This work allowed to quantitatively evaluate the performance of NNs in terms of CR retrieval accuracy and generalization capability.