Caracterización de anomalías mediante aprendizaje automático
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2024
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En este trabajo se analiza la viabilidad de resolver problemas inversos mediante técnicas de aprendizaje automático. Para ello, se estudia una ecuación específica que modela el comportamiento de un medio ante el paso de ondas a través de él. En una primera parte, se aborda la resolución del problema directo asociado al modelo matemático planteado mediante el método de elementos finitos. La resolución del modelo permitirá generar un conjunto de datos de soluciones de la ecuación a partir de ciertos parámetros determinados, lo cuál facilitará la experimentación posterior con la resolución del problema inverso, en la que se pretende inferir los parámetros a partir de la soluciones obtenidas. Una vez obtenido el conjunto de datos, se estudian teóricamente arquitecturas de redes neuronales con potencial para aproximar correctamente soluciones al problema inverso. Tras este estudio, se implementan tres redes neuronales: una red neuronal feedforward, una red convolucional y una red recurrente, con el fin de analizar su viabilidad para aproximar la solución del problema inverso. El estudio muestra el potencial de las redes neuronales convolucionales y recurrentes para resolver el problema planteado obteniendo errores pequeños en el conjunto de test.
This work analyzes the feasibility of solving inverse problems using machine learning techniques. To do so, a specific equation that models the behavior of a medium as waves pass through it is studied. In the first part, the solution of the direct problem associated with the proposed mathematical model is addressed using the finite element method. Solvig the model will allow the generation of a dataset of equation solutions given certain parameters of it, which will facilitate the experimentation with the solving of the inverse problem, where the aim is to infer the parameters from the obtained solutions. Once the dataset is obtained, the theory behind neural network architectures with potential to correctly approximate solutions to the inverse problem is studied. Following this study, three neural networks are implemented: a feedforward neural network, a convolutional neural network, and a recurrent neural network, in order to analyze their viability in approximating the solution of the inverse problem. The study shows the potential of convolutional and recurrent neural networks to solve the proposed problem, achieving low errors in the test set.
This work analyzes the feasibility of solving inverse problems using machine learning techniques. To do so, a specific equation that models the behavior of a medium as waves pass through it is studied. In the first part, the solution of the direct problem associated with the proposed mathematical model is addressed using the finite element method. Solvig the model will allow the generation of a dataset of equation solutions given certain parameters of it, which will facilitate the experimentation with the solving of the inverse problem, where the aim is to infer the parameters from the obtained solutions. Once the dataset is obtained, the theory behind neural network architectures with potential to correctly approximate solutions to the inverse problem is studied. Following this study, three neural networks are implemented: a feedforward neural network, a convolutional neural network, and a recurrent neural network, in order to analyze their viability in approximating the solution of the inverse problem. The study shows the potential of convolutional and recurrent neural networks to solve the proposed problem, achieving low errors in the test set.