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Concept# Artificial neural network

Summary

Artificial neural networks (ANNs, also shortened to neural networks (NNs) or neural nets) are a branch of machine learning models that are built using principles of neuronal organization discovered by connectionism in the biological neural networks constituting animal brains.
An ANN is based on a collection of connected units or nodes called artificial neurons, which loosely model the neurons in a biological brain. Each connection, like the synapses in a biological brain, can transmit a signal to other neurons. An artificial neuron receives signals then processes them and can signal neurons connected to it. The "signal" at a connection is a real number, and the output of each neuron is computed by some non-linear function of the sum of its inputs. The connections are called edges. Neurons and edges typically have a weight that adjusts as learning proceeds. The weight increases or decreases the strength of the signal at a connection. Neurons may have a threshold such that a signal is

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Mammalian motor control is implemented by a combination of different networks and system, working coherently to plan the movement of the body or a limb and to execute this movement a dynamical environment. While it is believed that complex, voluntary movements are planned in the motor areas of the cortex, the execution of the movement is controlled by a combination of cortical and cerebellar networks together with central pattern generators and reflex circuits in the spinal cord. In this thesis, we propose an abstract model that captures the basic properties of mammalian motor control, using the example of two different movements: arm movements as well as locomotion.
Our model consists of three parts: first a high-level network, that learns movements, using a combination of actor-critic based reinforcement learning and Optimal Control theory. The second part corresponds to spinal reflex circuits that execute basic movements of the musculo-skeletal system. They are modeled by a simple neural network, that learns the dynamic properties of the muscoloskeletal system by the mechanism of spontaneous motor activity (muscle twithing) combined with a Hebbian learning rule. We demonstrate that this network can learn the antagonistic control of joint movements. The final part of the model is a cerebellar network, that translates a complex movement trajectory, such as reaching, and activates the spinal reflex circuits to execute the movement. The mapping between the cerebellar neurons and the spinal reflex circuits are trained with artificial neural networks. Using a musculoskeletal arm model, we demonstrate that the proposed neural motor control model can generate the movement to arbitrary goal position.

The explosive growth of machine learning in the age of data has led to a new probabilistic and data-driven approach to solving very different types of problems. In this paper we study the feasibility of using such data-driven algorithms to solve classic physical and mathematical problems. In particular, we try to model the solution of an inverse continuum mechanics problem in the context of linear elasticity using deep neural networks. To better address the inverse function, we start first by studying the simplest related task,consisting of a building block of the actual composite problem. By empirically proving the learnability of simpler functions, we aim to draw conclusions with respect to the initial problem.The basic inverse problem that motivates this paper is that of a 2D plate with inclusion under specific loading and boundary conditions. From measurements at static equilibrium,we wish to recover the position of the hole. Although some analytical solutions have been formulated for 3D-infinite solids - most notably Eshelby’s inclusion problems - finite problems with particular geometries, material inhomogeneities, loading and boundary conditions require the use of numerical methods which are most often efficient solutions to the forward problem, the mapping from the parameter space to the measurement/signal space, i.e. in our case computing displacements and stresses knowing the size and position of the inclusion. Using numerical data generated from the well-defined forward problem,we train a neural network to approximate the inverse function relating displacements and stresses to the position of the inclusion. The preliminary results on the 2D-finite problem are promising, but the black-box nature of neural networks is a huge issue when it comes to understanding the solution.For this reason, we study a 3D-infinite continuous isotropic medium with unique concentrated load, for which the Green’s function gives an analytical mathematical expression relating relative position of the point force and the displacements in the solid. After de-riving the expression of the inverse, namely recovering the relative position of the force from the Green’s matrix computed at a given point in the medium, we are able to study the sensitivity of the inverse function. From both the expression of the Green’s function and its inverse, we highlight what issues might arise when training neural networks to solve the inverse problem. As the Green’s function is not bijective, bijection must been forced when training for regression. Moreover, due to displacements growing to infinity as we approach the singularity at zero, the training domain must be constrained to be some distance away from the singularity. As we train a neural network to fit the inverse of the Green’s function, we show that the input parameters should include the least possible redundant information to ensure the most efficient training.We then extend our analysis to two point forces. As more loads are added, bijection is harder to enforce as permutations of forces must be taken into account and more collisions may arise, i.e. multiple specific combinations of forces might yield the same measurements.One obvious solution is to increase the number of nodes where displacements are measured to limit the possibility of collision. Through new experiments, we show again that the best training is achieved for the least possible amount of nodes, as long as the training data generated is indeed bijective. As the medium is elastic, we propose a neural network architecture that matches the composite nature of the inverse problem. We also present another formulation of the problem which is invariant to permutations of the forces,namely multilabel classification, and yields good performance in the two-load case.Finally, we study the composite inverse function for 2, 3, 4 and 5 forces. By comparing training and accuracy for different neural network architectures, we expose the model easiest to train. Moreover, the evolution of the final accuracy as more loads are added indicates that deep-neural networks (DNNs) are not well suited to fit a non-linear mapping from and to a high-dimensional space. The results are more convincing for multilabel classification.

2020A big challenge in algorithmic composition is to devise a model that is both easily trainable and able to reproduce the long-range temporal dependencies typical of music. Here we investigate how artificial neural networks can be trained on a large corpus of melodies and turned into automated mu- sic composers able to generate new melodies coherent with the style they have been trained on. We employ gated-recurrent unit (GRU) networks that have been shown to be particularly efficient in learning complex sequential activations with arbitrary long time lags. Our model processes rhythm and melody in parallel while modeling the relation between these two properties. Using such an approach, we were able to generate interesting complete melodies or suggest possible continuations of a melody fragment that is coherent with the characteristics of the fragment itself.

2016