## 1 Introduction  
In biomechanics, internal forces exerted during the execution of motor tasks can be estimated by combining a biomechanical model, able to predict the forces acting on each involved joint, with the design of an optimization criterion to determine the contribution of each muscle to the overall force [1]. This approach has been applied in a variety of application fields, ranging from the analysis of gait [2] and running [3], to the study of upper limb movements [4]. For instance, different studies in the literature proposed a biomechanical model of the human shoulder complex, for quasi-static and dynamic estimation of the muscle forces and joint reaction forces in the gleno-humeral joint, combining inverse dynamics and static optimization to estimate the associated muscle forces [5; 6; 7]. Other studies present a conceptual 3D bipedal nonlinear model for Sit-To-Stand task with optimal controller design for exoskeleton torques [8] or a coupled optimization problem for a 2D model to solve for controller, which shows that central nervous system is able to solve the limb coordination problem when recovering from balance perturbations [9]. In the biomechanics of cycling it is important to evaluate how the athlete executes the required motor task, in order to have objective parameters that quantify the performance [10]. This aspect can be analyzed in terms of power exerted while cycling, using different techniques [11], or investigating the role of muscle activity while performing the task [12; 13; 14]. To this aim, previous studies proposed an inverse dynamics approach [15; 16; 17; 18] to predict muscle force patterns by the measurement of the external forces exerted on the pedal. These predictions were compared against muscle activity, as estimated from surface Electromyography (sEMG) data [19], after proper preprocessing [20]. The use of standard optimization algorithms, to solve the equations that describe the inverse dynamics of cycling, can represent a limit to the development of a real time device. Being able to estimate muscle forces in real time can be used on the field to assess and monitor athlete performance. The purpose of this study was to develop a new optimization algorithm based on artificial Neural Networks (NN), in order to reduce the computational complexity of the deterministic one used in the previous study [15], while maintaining the quality of estimation. Concerning the NN, Multilayer Perceptrons (MLP) with a single hidden layer have been proven capable of approximating any function with any desired accuracy, provided that associated conditions are satisfied [21; 22; 23; 24; 25]. They are probably the most commonly used NN and have been applied to a wide variety of problems, including function approximation, prediction, and simulation. Although one hidden layer is adequate to enable NN to approximate any given function, some researchers argued that NN with more than one hidden layer might require fewer hidden neurons to approximate the same function. It was theoretically shown in [26] that, given a desired degree of interpolation accuracy, NNs with two hidden layers require considerably fewer hidden neurons compared to NNs with one hidden layer. From a more practical perspective it has been shown in [27], through extensive experiments, that single-hidden-layer NNs are superior to networks with more than one hidden layer with the same level of complexity mainly due to the fact that the latter are more prone to fall into local minima. In engineering applications, there is a clear tendency toward using NNs with only one hidden layer [28]. Generally, feed forward NN have been a natural choice as trainable pattern classifiers because of their function approximation and generalization capabilities [29]. The function approximation capability allows them to form arbitrary nonlinear discriminant surfaces, while the generalization ability allows responding consistently to datanever shown to the network itself.