Probabilistic transfer learning methodology to expedite high fidelity simulation of reactive flows

Reduced order models based on the transport of a lower dimensional manifold representation of the thermochemical state, such as Principal Component (PC) transport and Machine Learning (ML) techniques, have been developed to reduce the computational cost associated with the Direct Numerical Simulations (DNS) of reactive flows. Both PC transport and ML normally require an abundance of data to exhibit sufficient predictive accuracy, which might not be available due to the prohibitive cost of DNS or experimental data acquisition. To alleviate such difficulties, similar data from an existing dataset or domain (source domain) can be used to train ML models, potentially resulting in adequate predictions in the domain of interest (target domain). This study presents a novel probabilistic transfer learning (TL) framework to enhance the trust in ML models in correctly predicting the thermochemical state in a lower dimensional manifold and a sparse data setting. The framework uses Bayesian neural networks, and autoencoders, to reduce the dimensionality of the state space and diffuse the knowledge from the source to the target domain. The new framework is applied to one-dimensional freely-propagating flame solutions under different data sparsity scenarios. The results reveal that there is an optimal amount of knowledge to be transferred, which depends on the amount of data available in the target domain and the similarity between the domains. TL can reduce the reconstruction error by one order of magnitude for cases with large sparsity. The new framework required 10 times less data for the target domain to reproduce the same error as in the abundant data scenario. Furthermore, comparisons with a state-of-the-art deterministic TL strategy show that the probabilistic method can require four times less data to achieve the same reconstruction error.

Scaling While Privacy Preserving: A Comprehensive Synthetic Tabular Data Generation and Evaluation in Learning Analytics

Privacy poses a significant obstacle to the progress of learning analytics (LA), presenting challenges like inadequate anonymization and data misuse that current solutions struggle to address. Synthetic data emerges as a potential remedy, offering robust privacy protection. However, prior LA research on synthetic data lacks thorough evaluation, essential for assessing the delicate balance between privacy and data utility. Synthetic data must not only enhance privacy but also remain practical for data analytics. Moreover, diverse LA scenarios come with varying privacy and utility needs, making the selection of an appropriate synthetic data approach a pressing challenge. To address these gaps, we propose a comprehensive evaluation of synthetic data, which encompasses three dimensions of synthetic data quality, namely resemblance, utility, and privacy. We apply this evaluation to three distinct LA datasets, using three different synthetic data generation methods. Our results show that synthetic data can maintain similar utility (i.e., predictive performance) as real data, while preserving privacy. Furthermore, considering different privacy and data utility requirements in different LA scenarios, we make customized recommendations for synthetic data generation. This paper not only presents a comprehensive evaluation of synthetic data but also illustrates its potential in mitigating privacy concerns within the field of LA, thus contributing to a wider application of synthetic data in LA and promoting a better practice for open science.

Enhancing Polynomial Chaos Expansion Based Surrogate Modeling using a Novel Probabilistic Transfer Learning Strategy

In the field of surrogate modeling, polynomial chaos expansion (PCE) allows practitioners to construct inexpensive yet accurate surrogates to be used in place of the expensive forward model simulations. For black-box simulations, non-intrusive PCE allows the construction of these surrogates using a set of simulation response evaluations. In this context, the PCE coefficients can be obtained using linear regression, which is also known as point collocation or stochastic response surfaces. Regression exhibits better scalability and can handle noisy function evaluations in contrast to other non-intrusive approaches, such as projection. However, since over-sampling is generally advisable for the linear regression approach, the simulation requirements become prohibitive for expensive forward models. We propose to leverage transfer learning whereby knowledge gained through similar PCE surrogate construction tasks (source domains) is transferred to a new surrogate-construction task (target domain) which has a limited number of forward model simulations (training data). The proposed transfer learning strategy determines how much, if any, information to transfer using new techniques inspired by Bayesian modeling and data assimilation. The strategy is scrutinized using numerical investigations and applied to an engineering problem from the oil and gas industry.

Transfer learning for predicting source terms of principal component transport in chemically reactive flow

The objective of this study is to evaluate whether the number of requisite training samples can be reduced with the use of various transfer learning models for predicting, for example, the chemical source terms of the data-driven reduced-order model that represents the homogeneous ignition process of a hydrogen/air mixture. Principal component analysis is applied to reduce the dimensionality of the hydrogen/air mixture in composition space. Artificial neural networks (ANNs) are used to tabulate the reaction rates of principal components, and subsequently, a system of ordinary differential equations is solved. As the number of training samples decreases at the target task (i.e.,for T0 > 1000 K and various phi), the reduced-order model fails to predict the ignition evolution of a hydrogen/air mixture. Three transfer learning strategies are then applied to the training of the ANN model with a sparse dataset. The performance of the reduced-order model with a sparse dataset is found to be remarkably enhanced if the training of the ANN model is restricted by a regularization term that controls the degree of knowledge transfer from source to target tasks. To this end, a novel transfer learning method is introduced, parameter control via partial initialization and regularization (PaPIR), whereby the amount of knowledge transferred is systemically adjusted for the initialization and regularization of the ANN model in the target task. It is found that an additional performance gain can be achieved by changing the initialization scheme of the ANN model in the target task when the task similarity between source and target tasks is relatively low.

Robust scalable initialization for Bayesian variational inference with multi-modal Laplace approximations

For predictive modeling relying on Bayesian inversion, fully independent, or ``mean-field'', Gaussian distributions are often used as approximate probability density functions in variational inference since the number of variational parameters is twice the number of unknown model parameters. The resulting diagonal covariance structure coupled with unimodal behavior can be too restrictive when dealing with highly non-Gaussian behavior, including multimodality. High-fidelity surrogate posteriors in the form of Gaussian mixtures can capture any distribution to an arbitrary degree of accuracy while maintaining some analytical tractability. Variational inference with Gaussian mixtures with full-covariance structures suffers from a quadratic growth in variational parameters with the number of model parameters. Coupled with the existence of multiple local minima due to nonconvex trends in the loss functions often associated with variational inference, these challenges motivate the need for robust initialization procedures to improve the performance and scalability of variational inference with mixture models. In this work, we propose a method for constructing an initial Gaussian mixture model approximation that can be used to warm-start the iterative solvers for variational inference. The procedure begins with an optimization stage in model parameter space in which local gradient-based optimization, globalized through multistart, is used to determine a set of local maxima, which we take to approximate the mixture component centers. Around each mode, a local Gaussian approximation is constructed via the Laplace method. Finally, the mixture weights are determined through constrained least squares regression. Robustness and scalability are demonstrated using synthetic tests. The methodology is applied to an inversion problem in structural dynamics involving unknown viscous damping coefficients.

Will ChatGPT get you caught? Rethinking of Plagiarism Detection

The rise of Artificial Intelligence (AI) technology and its impact on education has been a topic of growing concern in recent years. The new generation AI systems such as chatbots have become more accessible on the Internet and stronger in terms of capabilities. The use of chatbots, particularly ChatGPT, for generating academic essays at schools and colleges has sparked fears among scholars. This study aims to explore the originality of contents produced by one of the most popular AI chatbots, ChatGPT. To this end, two popular plagiarism detection tools were used to evaluate the originality of 50 essays generated by ChatGPT on various topics. Our results manifest that ChatGPT has a great potential to generate sophisticated text outputs without being well caught by the plagiarism check software. In other words, ChatGPT can create content on many topics with high originality as if they were written by someone. These findings align with the recent concerns about students using chatbots for an easy shortcut to success with minimal or no effort. Moreover, ChatGPT was asked to verify if the essays were generated by itself, as an additional measure of plagiarism check, and it showed superior performance compared to the traditional plagiarism-detection tools. The paper discusses the need for institutions to consider appropriate measures to mitigate potential plagiarism issues and advise on the ongoing debate surrounding the impact of AI technology on education. Further implications are discussed in the paper.

A heteroencoder architecture for prediction of failure locations in porous metals using variational inference

In this work we employ an encoder-decoder convolutional neural network to predict the failure locations of porous metal tension specimens based only on their initial porosities. The process we model is complex, with a progression from initial void nucleation, to saturation, and ultimately failure. The objective of predicting failure locations presents an extreme case of class imbalance since most of the material in the specimens do not fail. In response to this challenge, we develop and demonstrate the effectiveness of data- and loss-based regularization methods. Since there is considerable sensitivity of the failure location to the particular configuration of voids, we also use variational inference to provide uncertainties for the neural network predictions. We connect the deterministic and Bayesian convolutional neural networks at a theoretical level to explain how variational inference regularizes the training and predictions. We demonstrate that the resulting predicted variances are effective in ranking the locations that are most likely to fail in any given specimen.

Learning Analytics in Massive Open Online Courses

Educational technology has obtained great importance over the last fifteen years. At present, the umbrella of educational technology incorporates multitudes of engaging online environments and fields. Learning analytics and Massive Open Online Courses (MOOCs) are two of the most relevant emerging topics in this domain. Since they are open to everyone at no cost, MOOCs excel in attracting numerous participants that can reach hundreds and hundreds of thousands. Experts from different disciplines have shown significant interest in MOOCs as the phenomenon has rapidly grown. In fact, MOOCs have been proven to scale education in disparate areas. Their benefits are crystallized in the improvement of educational outcomes, reduction of costs and accessibility expansion. Due to their unusual massiveness, the large datasets of MOOC platforms require advanced tools and methodologies for further examination. The key importance of learning analytics is reflected here. MOOCs offer diverse challenges and practices for learning analytics to tackle. In view of that, this thesis combines both fields in order to investigate further steps in the learning analytics capabilities in MOOCs. The primary research of this dissertation focuses on the integration of learning analytics in MOOCs, and thereafter looks into examining students' behavior on one side and bridging MOOC issues on the other side. The research was done on the Austrian iMooX xMOOC platform. We followed the prototyping and case studies research methodology to carry out the research questions of this dissertation. The main contributions incorporate designing a general learning analytics framework, learning analytics prototype, records of students' behavior in nearly every MOOC's variables (discussion forums, interactions in videos, self-assessment quizzes, login frequency), a cluster of student engagement...