Training of supermodels - in the context of weather and climate forecasting

Given a set of imperfect weather or climate models, predictions can be improved by combining the models dynamically into a so called `supermodel'. The models are optimally combined to compensate their individual errors. This is different from the standard multi-model ensemble approach (MME), where the model output is statistically combined after the simulations. Instead, the supermodel can create a trajectory closer to observations than any of the imperfect models. By intervening during the forecast, errors can be reduced at an early stage and the ensemble can exhibit different dynamical behavior than any of the individual models. In this way, common errors between the models can be removed and new, physically correct behavior can appear. In our simplified context of models sharing the same evolution function and phase space, we can define either a connected or a weighted supermodel. A connected supermodel uses nudging to bring the models closer together, while in a weighted supermodel all model states are replaced at regular time intervals (i.e., restarted) by the weighted average of the individual model states. To obtain optimal connection coefficients or weights, we need to train the supermodel on the basis of historical observations. A standard training approach such as minimization of a cost function requires many model simulations, which is computationally very expensive. This thesis has focused on developing two new methods to efficiently train supermodels. The first method is based on an idea called cross pollination in time, where models exchange states during the training. The second method is a synchronization-based learning rule, originally developed for parameter estimation. The techniques are developed on low-order systems, such as Lorenz63, and later applied to different versions of the intermediate-complexity global coupled atmosphere-ocean-land model SPEEDO. Here the observations are from the same models, but with different parameters. The applicability of the method to real observations is tested using sensitivity to noisy and incomplete data. The characteristics the individual models should have in order to be combined together into a supermodel are identified, as well as which physical variables should be connected in a supermodel, and which ones should not. Both training methods result in supermodels that outperform both the individual models and the MME, for short term predictions as well as long term simulations. Furthermore, we show that the novel use of negative weights can improve predictions in cases where model errors do not cancel (for instance, all models are too warm with respect to the truth). A crucial advantage of the proposed training schemes is that in the present context relatively short training periods suffice to find good solutions. Although the validity of our conclusions in the context of real observations and model scenarios has yet to be proved, our results are very encouraging. In principle, the methods are suitable to train supermodels constructed using state-of-the art weather and climate models.Doktorgradsavhandlin

Bispectrum Inversion with Application to Multireference Alignment

We consider the problem of estimating a signal from noisy circularly-translated versions of itself, called multireference alignment (MRA). One natural approach to MRA could be to estimate the shifts of the observations first, and infer the signal by aligning and averaging the data. In contrast, we consider a method based on estimating the signal directly, using features of the signal that are invariant under translations. Specifically, we estimate the power spectrum and the bispectrum of the signal from the observations. Under mild assumptions, these invariant features contain enough information to infer the signal. In particular, the bispectrum can be used to estimate the Fourier phases. To this end, we propose and analyze a few algorithms. Our main methods consist of non-convex optimization over the smooth manifold of phases. Empirically, in the absence of noise, these non-convex algorithms appear to converge to the target signal with random initialization. The algorithms are also robust to noise. We then suggest three additional methods. These methods are based on frequency marching, semidefinite relaxation and integer programming. The first two methods provably recover the phases exactly in the absence of noise. In the high noise level regime, the invariant features approach for MRA results in stable estimation if the number of measurements scales like the cube of the noise variance, which is the information-theoretic rate. Additionally, it requires only one pass over the data which is important at low signal-to-noise ratio when the number of observations must be large

Improving weather and climate predictions by training of supermodels

Recent studies demonstrate that weather and climate predictions potentially improve by dynamically combining different models into a so-called “supermodel”. Here, we focus on the weighted supermodel – the supermodel's time derivative is a weighted superposition of the time derivatives of the imperfect models, referred to as weighted supermodeling. A crucial step is to train the weights of the supermodel on the basis of historical observations. Here, we apply two different training methods to a supermodel of up to four different versions of the global atmosphere–ocean–land model SPEEDO. The standard version is regarded as truth. The first training method is based on an idea called cross pollination in time (CPT), where models exchange states during the training. The second method is a synchronization-based learning rule, originally developed for parameter estimation. We demonstrate that both training methods yield climate simulations and weather predictions of superior quality as compared to the individual model versions. Supermodel predictions also outperform predictions based on the commonly used multi-model ensemble (MME) mean. Furthermore, we find evidence that negative weights can improve predictions in cases where model errors do not cancel (for instance, all models are warm with respect to the truth). In principle, the proposed training schemes are applicable to state-of-the-art models and historical observations. A prime advantage of the proposed training schemes is that in the present context relatively short training periods suffice to find good solutions. Additional work needs to be done to assess the limitations due to incomplete and noisy data, to combine models that are structurally different (different resolution and state representation, for instance) and to evaluate cases for which the truth falls outside of the model class

Improving weather and climate predictions by training of supermodels

Recent studies demonstrate that weather and climate predictions potentially improve by dynamically combining different models into a so-called "supermodel". Here, we focus on the weighted supermodel - the supermodel's time derivative is a weighted superposition of the time derivatives of the imperfect models, referred to as weighted supermodeling. A crucial step is to train the weights of the supermodel on the basis of historical observations. Here, we apply two different training methods to a supermodel of up to four different versions of the global atmosphere-ocean-land model SPEEDO. The standard version is regarded as truth. The first training method is based on an idea called cross pollination in time (CPT), where models exchange states during the training. The second method is a synchronization-based learning rule, originally developed for parameter estimation. We demonstrate that both training methods yield climate simulations and weather predictions of superior quality as compared to the individual model versions. Supermodel predictions also outperform predictions based on the commonly used multi-model ensemble (MME) mean. Furthermore, we find evidence that negative weights can improve predictions in cases where model errors do not cancel (for instance, all models are warm with respect to the truth). In principle, the proposed training schemes are applicable to state-of-the-art models and historical observations. A prime advantage of the proposed training schemes is that in the present context relatively short training periods suffice to find good solutions. Additional work needs to be done to assess the limitations due to incomplete and noisy data, to combine models that are structurally different (different resolution and state representation, for instance) and to evaluate cases for which the truth falls outside of the model class

Experimental Evaluation of Hybrid Fibre−Wireless System for 5G Networks

This article describes a novel experimental study considering a multiband fibre–wireless system for constructing the transport network for fifth-generation (5G) networks. This study describes the development and testing of a 5G new radio (NR) multi-input multi-output (MIMO) hybrid fibre–wireless (FiWi) system for enhanced mobile broadband (eMBB) using digital pre-distortion (DPD). Analog radio over fibre (A-RoF) technology was used to create the optical fronthaul (OFH) that includes a 3 GHz supercell in a long-range scenario as well as a femtocell scenario using the 20 GHz band. As a proof of concept, a Mach Zehnder modulator with two independent radio frequency waveforms modifies a 1310 nm optical carrier using a distributed feedback laser across 10 km of conventional standard single-mode fibre. It may be inferred that a hybrid FiWi-based MIMO-enabled 5G NR system based on OFH could be a strong competitor for future mobile haul applications. Moreover, a convolutional neural network (CNN)-based DPD is used to improve the performance of the link. The error vector magnitude (EVM) performance for 5G NR bands is predicted to fulfil the Third Generation Partnership Project’s (3GPP) Release 17 standards

Design optimization and performance analysis methodology for PMSMs to improve efficiency in hydraulic applications

Pla de Doctorats Industrials de la Generalitat de CatalunyaIn the recent years, water pumping and other hydraulic applications are increasingly demanding motors capable to operate under different working conditions, including variable pressure and volumetric flow demands. Moreover, the technical evolution trend of pumping components is to minimize the size, offering compact and adaptable hydraulic units. Hence, the need to optimize the electric motor part to reduce the volume according this trend, maximizing the efficiency, decreasing material and fabrication costs, reducing noise and improving thermal dissipation have originated the research field of this project. So far different methodologies have been focused on designing electrical machines considering few aspects, such as the rated conditions with some size limitations. In addition, the optimization strategies have been based on single operation conditions, improving multiple aspects but not considering the overall performance of the machine and its influence with the working system. This research changes the design and optimization paradigm, focusing on defining beforehand the desired performance of the electrical machine in relation with the application system. The customization is not limited to an operating point but to the whole performance space, which in this case is the torque-speed area. Thus, the designer has plenty of freedom to study the system, and define the desired motor performance establishing the size, thermal and mechanical limitations from the beginning of the process. Moreover, when designing and optimizing electrical machines, the experimental validation is of major importance. From an industrial scope so far, the testing methodologies are focused on evaluating point by point the electrical machine performance, being a robust and trustable way to measure and validate the electrical machine characteristics. Nevertheless,this method requires a large time to prepare the experimental setup and to evaluate the whole motor performance. For this reason, there is a special interest on improving parameter estimation and performance evaluation techniques for electrical machines to reduce evaluation time, setup complexity and increase the number of physical magnitudes to measure in order to have deeper information. This research also develops methodologies to extend the electrical machine experimental validation providing information to evaluate the motor performance. This doctoral thesis has been developed with a collaboration agreement between UPC and the company MIDTAL TALENTOS S.L. The thesis is included within the Industrial Doctorates program 2018 DI 019 promoted by the Generalitat de Catalunya.En los últimos años, el bombeo de agua, entre otras aplicaciones hidráulicas, exige cada vez más motores capaces de operar en diferentes condiciones de trabajo, incluyendo las demandas variables de presión y caudal volumétrico. Además, la evolución técnica de los componentes de bombeo está cada vez más minimizando el tamaño ofreciendo unidades hidráulicas compactas y adaptables. De ahí la necesidad de optimizar la parte del motor eléctrico para reducir el volumen de acuerdo con esta tendencia, maximizando la eficiencia, disminuyendo los costos de material y fabricación, reduciendo el ruido y mejorando la disipación térmica. Todos estos factores han creado el campo de investigación sobre el cual se desarrolla este proyecto. Hasta ahora las metodologías se han centrado en diseñar las máquinas eléctricas considerando unos pocos aspectos técnicos, como las condiciones nominales con algunas limitaciones de tamaño. Además, las estrategias de optimización se han basado en condiciones de operación única, mejorando múltiples aspectos sin considerar el rendimiento general de la máquina y su influencia en el sistema de trabajo. Esta investigación cambia el paradigma de diseño y optimización centrándose en definir de antemano el rendimiento deseado de la máquina eléctrica en relación con el sistema de aplicación. La personalización no se limita a un punto de funcionamiento sino a todo el espacio de operación, que en este caso se expresa en el espacio par-velocidad. Así, el diseñador tiene libertad para estudiar el sistema, definir el rendimiento deseado del motor estableciendo el tamaño, limitaciones térmicas y mecánicas desde el inicio del proceso. Además, a la hora de diseñar y optimizar máquinas eléctricas, la validación experimental es de gran importancia. En el ámbito industrial hasta ahora, las metodologías de ensayo han sido enfocadas a evaluar punto por punto la máquina eléctrica, siendo una forma robusta y confiable de medir y validar sus características. Sin embargo, este método requiere mucho tiempo para preparar la configuración experimental y evaluar el motor en toda su zona de operación. Por esta razón, existe un interés especial en mejorar la estimación de parámetros y las técnicas de evaluación de la operación de las máquinas eléctricas reduciendo tiempo, complejidad y aumentando el número de magnitudes físicas a medir teniendo más información sobre la máquina. Esta investigación también desarrolla metodologías para extender la validación experimental de la máquina eléctrica proporcionando información para evaluar el rendimiento del motor. Esta tesis doctoral ha sido desarrollada con un convenio de colaboración entre la Universidad Politécnica de Cataluña UPC y la empresa MIDTAL TALENTOS S.L. La tesis se engloba dentro del plan de Doctorados Industriales 2018 DI 019 impulsado por la Generalitat de Catalunya.Postprint (published version

Framework for an Ocean-Connected Supermodel of the Earth System

A supermodel connects different models interactively so that their systematic errors compensate and achieve a model with superior performance. It differs from the standard non-interactive multi-model ensembles (NI), which combines model outputs a-posteriori. Supermodels with Earth system models (ESMs) has not been developed because it is technically challenging to combine models with different state space. Here, we formulate the first supermodel framework for ESMs and use data assimilation to synchronise models. The ocean of three ESMs is synchronised every month by assimilating pseudo sea surface temperature (SST) observations generated by them on a common grid to handle discrepancies in grid and resolution. We compare the performance of two supermodel approaches to that of the NI. In the first (EW), the models are connected to the equal-weight multi-model mean, while in the second (SINGLE), they are connected to a single model. Both versions achieve synchronisation in the ocean and in the atmosphere, where the ocean drives the variability. The time variability of the supermodel multi-model mean SST is reduced compared to observations, most where synchronisation is not achieved and is lower-bounded by NI. The damping is larger in EW, for which variability in the individual models is also damped. Hence, under partial synchronisation, the unsynchronized variability gets damped in the multi-model average pseudo-observations, causing a deflation during the assimilation. The SST bias in individual models of EW is reduced compared to that of NI, and so is its multi-model mean in the synchronised regions. A trained supermodel remains to be tested.publishedVersio