Empowering Optimal Control with Machine Learning: A Perspective from Model Predictive Control

Solving complex optimal control problems have confronted computational challenges for a long time. Recent advances in machine learning have provided us with new opportunities to address these challenges. This paper takes model predictive control, a popular optimal control method, as the primary example to survey recent progress that leverages machine learning techniques to empower optimal control solvers. We also discuss some of the main challenges encountered when applying machine learning to develop more robust optimal control algorithms

Conic Optimization Theory: Convexification Techniques and Numerical Algorithms

Optimization is at the core of control theory and appears in several areas of this field, such as optimal control, distributed control, system identification, robust control, state estimation, model predictive control and dynamic programming. The recent advances in various topics of modern optimization have also been revamping the area of machine learning. Motivated by the crucial role of optimization theory in the design, analysis, control and operation of real-world systems, this tutorial paper offers a detailed overview of some major advances in this area, namely conic optimization and its emerging applications. First, we discuss the importance of conic optimization in different areas. Then, we explain seminal results on the design of hierarchies of convex relaxations for a wide range of nonconvex problems. Finally, we study different numerical algorithms for large-scale conic optimization problems.Comment: 18 page

Teaching data science in school: Digital learning material on predictive text systems

Data science and especially machine learning issues are currently the subject of lively discussions in society. Many research areas now use machine learning methods, which, especially in combination with increased computer power, has led to major advances in recent years. One example is natural language processing. A large number of technologies and applications that we use every day are based on methods from this area. For example, students encounter these technologies in everyday life through the use of Siri and Alexa but also when chatting with friends they are supported by assistance systems such as predictive text systems that give suggestions for the next word. This proximity to everyday life is used to give students a motivating approach to data science concepts. In this paper we will show how mathematical modeling of data science problems can be addressed with students from tenth grade or higher using digital learning material on predictive text systems

A Prescriptive Learning Analytics Framework: Beyond Predictive Modelling and onto Explainable AI with Prescriptive Analytics and ChatGPT

A significant body of recent research in the field of Learning Analytics has focused on leveraging machine learning approaches for predicting at-risk students in order to initiate timely interventions and thereby elevate retention and completion rates. The overarching feature of the majority of these research studies has been on the science of prediction only. The component of predictive analytics concerned with interpreting the internals of the models and explaining their predictions for individual cases to stakeholders has largely been neglected. Additionally, works that attempt to employ data-driven prescriptive analytics to automatically generate evidence-based remedial advice for at-risk learners are in their infancy. eXplainable AI is a field that has recently emerged providing cutting-edge tools which support transparent predictive analytics and techniques for generating tailored advice for at-risk students. This study proposes a novel framework that unifies both transparent machine learning as well as techniques for enabling prescriptive analytics, while integrating the latest advances in large language models. This work practically demonstrates the proposed framework using predictive models for identifying at-risk learners of programme non-completion. The study then further demonstrates how predictive modelling can be augmented with prescriptive analytics on two case studies in order to generate human-readable prescriptive feedback for those who are at risk using ChatGPT.Comment: revision of the original paper to include ChatGPT integratio

Measuring Women's Empowerment in Collective Households

Measuring women's empowerment within families is challenging. Social scientists often rely on close-ended survey questions on women's participation in household decisions, domestic abuse, and autonomy to measure women's power and agency. Recent advances in family economics have allowed researchers to identify and estimate structural measures of women's power and resource control based on the collective household model. We provide a brief overview of this literature. We then apply machine learning techniques to answer the following questions: How do such measures compare to women's responses to close-ended survey questions? Which survey questions are most predictive of model-based estimates of women's empowerment

MMGP: a Mesh Morphing Gaussian Process-based machine learning method for regression of physical problems under non-parameterized geometrical variability

When learning simulations for modeling physical phenomena in industrial designs, geometrical variabilities are of prime interest. While classical regression techniques prove effective for parameterized geometries, practical scenarios often involve the absence of shape parametrization during the inference stage, leaving us with only mesh discretizations as available data. Learning simulations from such mesh-based representations poses significant challenges, with recent advances relying heavily on deep graph neural networks to overcome the limitations of conventional machine learning approaches. Despite their promising results, graph neural networks exhibit certain drawbacks, including their dependency on extensive datasets and limitations in providing built-in predictive uncertainties or handling large meshes. In this work, we propose a machine learning method that do not rely on graph neural networks. Complex geometrical shapes and variations with fixed topology are dealt with using well-known mesh morphing onto a common support, combined with classical dimensionality reduction techniques and Gaussian processes. The proposed methodology can easily deal with large meshes without the need for explicit shape parameterization and provides crucial predictive uncertainties, which are essential for informed decision-making. In the considered numerical experiments, the proposed method is competitive with respect to existing graph neural networks, regarding training efficiency and accuracy of the predictions