Fast Non-Parametric Learning to Accelerate Mixed-Integer Programming for Online Hybrid Model Predictive Control

Today's fast linear algebra and numerical optimization tools have pushed the frontier of model predictive control (MPC) forward, to the efficient control of highly nonlinear and hybrid systems. The field of hybrid MPC has demonstrated that exact optimal control law can be computed, e.g., by mixed-integer programming (MIP) under piecewise-affine (PWA) system models. Despite the elegant theory, online solving hybrid MPC is still out of reach for many applications. We aim to speed up MIP by combining geometric insights from hybrid MPC, a simple-yet-effective learning algorithm, and MIP warm start techniques. Following a line of work in approximate explicit MPC, the proposed learning-control algorithm, LNMS, gains computational advantage over MIP at little cost and is straightforward for practitioners to implement

Graphic Thinking and Digital Processes: Three Built Case Studies of Digital Materiality

Think strategic link between computer programming; digital modeling; the data; matter and CNC manufacturing in the various stages of the architectural project is key to update our discipline with new technologies. Our proposal to articulate and digital graphic thought processes; developable folded geometries and compositions is rooted in an expanded graphic thinking through multiple conceptual tools that are already part of the operational structure of our discipline

Machine Learning for Fluid Mechanics

The field of fluid mechanics is rapidly advancing, driven by unprecedented volumes of data from field measurements, experiments and large-scale simulations at multiple spatiotemporal scales. Machine learning offers a wealth of techniques to extract information from data that could be translated into knowledge about the underlying fluid mechanics. Moreover, machine learning algorithms can augment domain knowledge and automate tasks related to flow control and optimization. This article presents an overview of past history, current developments, and emerging opportunities of machine learning for fluid mechanics. It outlines fundamental machine learning methodologies and discusses their uses for understanding, modeling, optimizing, and controlling fluid flows. The strengths and limitations of these methods are addressed from the perspective of scientific inquiry that considers data as an inherent part of modeling, experimentation, and simulation. Machine learning provides a powerful information processing framework that can enrich, and possibly even transform, current lines of fluid mechanics research and industrial applications.Comment: To appear in the Annual Reviews of Fluid Mechanics, 202

An Algorithmic Theory of Dependent Regularizers, Part 1: Submodular Structure

We present an exploration of the rich theoretical connections between several classes of regularized models, network flows, and recent results in submodular function theory. This work unifies key aspects of these problems under a common theory, leading to novel methods for working with several important models of interest in statistics, machine learning and computer vision. In Part 1, we review the concepts of network flows and submodular function optimization theory foundational to our results. We then examine the connections between network flows and the minimum-norm algorithm from submodular optimization, extending and improving several current results. This leads to a concise representation of the structure of a large class of pairwise regularized models important in machine learning, statistics and computer vision. In Part 2, we describe the full regularization path of a class of penalized regression problems with dependent variables that includes the graph-guided LASSO and total variation constrained models. This description also motivates a practical algorithm. This allows us to efficiently find the regularization path of the discretized version of TV penalized models. Ultimately, our new algorithms scale up to high-dimensional problems with millions of variables