Optimal measurement locations for parameter estimation of distributed parameter systems

Identifying the parameters with the largest influence on the predicted outputs of a model revealswhich parameters need to be known more precisely to reduce the overall uncertainty on themodel output. A large improvement of such models would result when uncertainties in the keymodel parameters are reduced. To achieve this, new experiments could be very helpful,especially if the measurements are taken at the spatio-temporal locations that allow estimate the parameters in an optimal way. After evaluating the methodologies available for optimal sensor location, a few observations were drawn. The method based on the Gram determinant evolution can report results not according to what should be expected. This method is strongly dependent of the sensitivity coefficients behaviour. The approach based on the maximum angle between subspaces, in some cases, produced more that one optimal solution. It was observed that this method depends on the magnitude of outputs values and report the measurement positions where the outputs reached their extrema values. The D-optimal design method produces number and locations of the optimal measurements and it depends strongly of the sensitivity coefficients, but mostly of their behaviours. In general it was observed that the measurements should be taken at the locations where the extrema values (sensitivity coefficients, POD modes and/or outputs values) are reached. Further improvements can be obtained when a reduced model of the system is employed. This is computationally less expensive and the best estimation of the parameter is obtained, even with experimental data contaminated with noise. A new approach to calculate the time coefficients belonging to an empirical approximator based on the POD-modes derived from experimental data is introduced. Additionally, an artificial neural network can be used to calculate the derivatives but only for systems without complex nonlinear behaviour. The latter two approximations are very valuable and useful especially if the model of the system is unknown.EThOS - Electronic Theses Online ServiceUniversidad del Zulia, Maracaibo, VenezuelaGBUnited Kingdo

Data-Driven Forecasting of High-Dimensional Chaotic Systems with Long Short-Term Memory Networks

We introduce a data-driven forecasting method for high-dimensional chaotic systems using long short-term memory (LSTM) recurrent neural networks. The proposed LSTM neural networks perform inference of high-dimensional dynamical systems in their reduced order space and are shown to be an effective set of nonlinear approximators of their attractor. We demonstrate the forecasting performance of the LSTM and compare it with Gaussian processes (GPs) in time series obtained from the Lorenz 96 system, the Kuramoto-Sivashinsky equation and a prototype climate model. The LSTM networks outperform the GPs in short-term forecasting accuracy in all applications considered. A hybrid architecture, extending the LSTM with a mean stochastic model (MSM-LSTM), is proposed to ensure convergence to the invariant measure. This novel hybrid method is fully data-driven and extends the forecasting capabilities of LSTM networks.Comment: 31 page

Machine learning algorithms for fluid mechanics

Neural networks have become increasingly popular in the field of fluid dynamics due to their ability to model complex, high-dimensional flow phenomena. Their flexibility in approximating continuous functions without any preconceived notion of functional form makes them a suitable tool for studying fluid dynamics. The main uses of neural networks in fluid dynamics include turbulence modelling, flow control, prediction of flow fields, and accelerating high-fidelity simulations. This thesis focuses on the latter two applications of neural networks. First, the application of a convolutional neural network (CNN) to accelerate the solution of the Poisson equation step in the pressure projection method for incompressible fluid flows is investigated. The CNN learns to approximate the Poisson equation solution at a lower computational cost than traditional iterative solvers, enabling faster simulations of fluid flows. Results show that the CNN approach is accurate and efficient, achieving significant speedup in the Taylor-Green Vortex problem. Next, predicting flow fields past arbitrarily-shaped bluff bodies from point sensor and plane velocity measurements using neural networks is focused on. A novel conformal-mapping-aided method is devised to embed geometry invariance for the outputs of the neural networks, which is shown to be critical for achieving good performance for flow datasets incorporating a diverse range of geometries. Results show that the proposed methods can accurately predict the flow field, demonstrating excellent agreement with simulation data. Moreover, the flow field predictions can be used to accurately predict lift and drag coefficients, making these methods useful for optimizing the shape of bluff bodies for specific applications.Open Acces

Some models are useful, but how do we know which ones? Towards a unified Bayesian model taxonomy

Probabilistic (Bayesian) modeling has experienced a surge of applications in almost all quantitative sciences and industrial areas. This development is driven by a combination of several factors, including better probabilistic estimation algorithms, flexible software, increased computing power, and a growing awareness of the benefits of probabilistic learning. However, a principled Bayesian model building workflow is far from complete and many challenges remain. To aid future research and applications of a principled Bayesian workflow, we ask and provide answers for what we perceive as two fundamental questions of Bayesian modeling, namely (a) "What actually is a Bayesian model?" and (b) "What makes a good Bayesian model?". As an answer to the first question, we propose the PAD model taxonomy that defines four basic kinds of Bayesian models, each representing some combination of the assumed joint distribution of all (known or unknown) variables (P), a posterior approximator (A), and training data (D). As an answer to the second question, we propose ten utility dimensions according to which we can evaluate Bayesian models holistically, namely, (1) causal consistency, (2) parameter recoverability, (3) predictive performance, (4) fairness, (5) structural faithfulness, (6) parsimony, (7) interpretability, (8) convergence, (9) estimation speed, and (10) robustness. Further, we propose two example utility decision trees that describe hierarchies and trade-offs between utilities depending on the inferential goals that drive model building and testing

Artificial neural networks for vibration based inverse parametric identifications: A review

Vibration behavior of any solid structure reveals certain dynamic characteristics and property parameters of that structure. Inverse problems dealing with vibration response utilize the response signals to find out input factors and/or certain structural properties. Due to certain drawbacks of traditional solutions to inverse problems, ANNs have gained a major popularity in this field. This paper reviews some earlier researches where ANNs were applied to solve different vibration-based inverse parametric identification problems. The adoption of different ANN algorithms, input-output schemes and required signal processing were denoted in considerable detail. In addition, a number of issues have been reported, including the factors that affect ANNs’ prediction, as well as the advantage and disadvantage of ANN approaches with respect to general inverse methods Based on the critical analysis, suggestions to potential researchers have also been provided for future scopes

Learning-Based Modeling of Weather and Climate Events Related To El Niño Phenomenon via Differentiable Programming and Empirical Decompositions

This dissertation is the accumulation of the application of adaptive, empirical learning-based methods in the study and characterization of the El Niño Southern Oscillation. In specific, it focuses on ENSO’s effects on rainfall and drought conditions in two major regions shown to be linked through the strength of the dependence of their climate on ENSO: 1) the southern Pacific Coast of the United States and 2) the Nile River Basin. In these cases, drought and rainfall are tied to deep economic and social factors within the region. The principal aim of this dissertation is to establish, with scientific rigor, an epistemological and foundational justification of adaptive learning models and their utility in the both the modeling and understanding of a wide-reaching climate phenomenon such as ENSO. This dissertation explores a scientific justification for their proven accuracy in prediction and utility as an aide in deriving a deeper understanding of climate phenomenon. In the application of drought forecasting for Southern California, adaptive learning methods were able to forecast the drought severity of the 2015-2016 winter with greater accuracy than established models. Expanding this analysis yields novel ways to analyze and understand the underlying processes driving California drought. The pursuit of adaptive learning as a guiding tool would also lead to the discovery of a significant extractable components of ENSO strength variation, which are used with in the analysis of Nile River Basin precipitation and flow of the Nile River, and in the prediction of Nile River yield to p=0.038. In this dissertation, the duality of modeling and understanding is explored, as well as a discussion on why adaptive learning methods are uniquely suited to the study of climate phenomenon like ENSO in the way that traditional methods lack. The main methods explored are 1) differentiable Programming, as a means of construction of novel self-learning models through which the meaningfulness of parameters arises from emergent phenomenon and 2) empirical decompositions, which are driven by an adaptive rather than rigid component extraction principle, are explored further as both a predictive tool and as a tool for gaining insight and the construction of models

Uncertainty quantification for an electric motor inverse problem - tackling the model discrepancy challenge

In the context of complex applications from engineering sciences the solution of identification problems still poses a fundamental challenge. In terms of Uncertainty Quantification (UQ), the identification problem can be stated as a separation task for structural model and parameter uncertainty. This thesis provides new insights and methods to tackle this challenge and demonstrates these developments on an industrial benchmark use case combining simulation and real-world measurement data. While significant progress has been made in development of methods for model parameter inference, still most of those methods operate under the assumption of a perfect model. For a full, unbiased quantification of uncertainties in inverse problems, it is crucial to consider all uncertainty sources. The present work develops methods for inference of deterministic and aleatoric model parameters from noisy measurement data with explicit consideration of model discrepancy and additional quantification of the associated uncertainties using a Bayesian approach. A further important ingredient is surrogate modeling with Polynomial Chaos Expansion (PCE), enabling sampling from Bayesian posterior distributions with complex simulation models. Based on this, a novel identification strategy for separation of different sources of uncertainty is presented. Discrepancy is approximated by orthogonal functions with iterative determination of optimal model complexity, weakening the problem inherent identifiability problems. The model discrepancy quantification is complemented with studies to statistical approximate numerical approximation error. Additionally, strategies for approximation of aleatoric parameter distributions via hierarchical surrogate-based sampling are developed. The proposed method based on Approximate Bayesian Computation (ABC) with summary statistics estimates the posterior computationally efficient, in particular for large data. Furthermore, the combination with divergence-based subset selection provides a novel methodology for UQ in stochastic inverse problems inferring both, model discrepancy and aleatoric parameter distributions. Detailed analysis in numerical experiments and successful application to the challenging industrial benchmark problem -- an electric motor test bench -- validates the proposed methods

Reinforcement learning in large state action spaces

Reinforcement learning (RL) is a promising framework for training intelligent agents which learn to optimize long term utility by directly interacting with the environment. Creating RL methods which scale to large state-action spaces is a critical problem towards ensuring real world deployment of RL systems. However, several challenges limit the applicability of RL to large scale settings. These include difficulties with exploration, low sample efficiency, computational intractability, task constraints like decentralization and lack of guarantees about important properties like performance, generalization and robustness in potentially unseen scenarios. This thesis is motivated towards bridging the aforementioned gap. We propose several principled algorithms and frameworks for studying and addressing the above challenges RL. The proposed methods cover a wide range of RL settings (single and multi-agent systems (MAS) with all the variations in the latter, prediction and control, model-based and model-free methods, value-based and policy-based methods). In this work we propose the first results on several different problems: e.g. tensorization of the Bellman equation which allows exponential sample efficiency gains (Chapter 4), provable suboptimality arising from structural constraints in MAS(Chapter 3), combinatorial generalization results in cooperative MAS(Chapter 5), generalization results on observation shifts(Chapter 7), learning deterministic policies in a probabilistic RL framework(Chapter 6). Our algorithms exhibit provably enhanced performance and sample efficiency along with better scalability. Additionally, we also shed light on generalization aspects of the agents under different frameworks. These properties have been been driven by the use of several advanced tools (e.g. statistical machine learning, state abstraction, variational inference, tensor theory). In summary, the contributions in this thesis significantly advance progress towards making RL agents ready for large scale, real world applications