Physics-informed neural networks (PINNs) have enabled significant improvements in modelling physical processes described by partial differential equations (PDEs) and are in principle capable of modeling a large variety of differential equations. PINNs are based on simple architectures, and learn the behavior of complex physical systems by optimizing the network parameters to minimize the residual of the underlying PDE. Current network architectures share some of the limitations of classical numerical discretization schemes when applied to non-linear differential equations in continuum mechanics. A paradigmatic example is the solution of hyperbolic conservation laws that develop highly localized nonlinear shock waves. Learning solutions of PDEs with dominant hyperbolic character is a challenge for current PINN approaches, which rely, like most grid-based numerical schemes, on adding artificial dissipation. Here, we address the fundamental question of which network architectures are best suited to learn the complex behavior of non-linear PDEs. We focus on network architecture rather than on residual regularization. Our new methodology, called physics-informed attention-based neural networks (PIANNs), is a combination of recurrent neural networks and attention mechanisms. The attention mechanism adapts the behavior of the deep neural network to the non-linear features of the solution, and break the current limitations of PINNs. We find that PIANNs effectively capture the shock front in a hyperbolic model problem, and are capable of providing high-quality solutions inside the convex hull of the training set.

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ResumenEn este trabajo se presenta el desarrollo e implementación de un monitor cardiaco capaz de cumplir con características de portabilidad, facilidad de uso y tiempo prolongado de operación. El diseño se divide en dos fases. En la primera, cada etapa del monitor cardiaco se implementa priorizando su consumo individual de energía. En la segunda fase, se integran las etapas para conformar el monitor cardiaco, constituido por una fuente de alimentación, una interfaz con el paciente, un micro controlador, una interfaz inalámbrica y una aplicación que se ejecuta en un teléfono inteligente. Para cumplir con las dos fases de diseño se exponen inicialmente los fundamentos teóricos y el desarrollo actual de la monitorización cardiaca. Posteriormente, para cada etapa se describen los requerimientos funcionales y las variables relevantes para su diseño. También se detallan los procesos de implementación y los procedimientos de prueba y sus resultados. Con esta investigación se pretende contribuir con una alternativa de diseño de un monitor cardiaco, que puede utilizarse por un periodo no menor a 30 días. Los resultados demostraron que el equipo desarrollado permite la monitorización cardiaca remota, facilita la movilidad de pacientes y además elimina la necesidad además elimina la necesidad de continuas recargas de energía.Palabras Clave: interfaz inalámbrica; monitor cardiaco; teléfono inteligente. AbstractThis paper describes the development and implementation of a heart monitor capable of meeting portability features, easy to use and a prolonged time of operation. The design is divided into two phases. In the first, each stage of the cardiac monitor is implemented prioritizing their individual energy consumption. In the second phase, the stages are integrated to form the cardiac monitor, consisting of a power supply, an interface with the patient, a micro controller, a wireless interface and an application running on a smartphone. To fulfill the two design phases are initially exposed the theoretical foundations and the current development of cardiac monitoring. Subsequently, for each stage, the functional requirements are described and the relevant variables for the design. Also, implementation processes and test procedures and results are detailed. This research is intended to contribute to an alternative design of a heart monitor, which can be used for not less than 30 days period. The results showed that the equipment developed allows remote cardiac monitoring, facilitates the mobility of patients and also eliminates the need for continuous energy refills.

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