Systems & control transactions最新文献

Physics-Informed Symbolic Regression (PISR) offers a pathway to discover human-interpretable solutions to partial differential equations (PDEs). This work investigates three fitness metrics within a PISR framework: PDE fitness, Bayesian Information Criterion (BIC), and a fitness metric proportional to the probability of a model given the data. Through experiments with Laplace's equation, Burgers' equation, and a nonlinear wave equation, we demonstrate that incorporating information theoretic criteria like BIC can yield higher fidelity models while maintaining interpretability. Our results show that BIC-based PISR achieved the best performance, identifying an exact solution to Laplace's equation and finding solutions with $R^2$ -values of 0.998 for Burgers' equation and 0.957 for the nonlinear wave equation. The inclusion of the Bayes D-optimality criterion in estimating model probability strongly constrained solution complexity, limiting models to 3-4 parameters and reducing accuracy. These findings suggest that a two-stage approach-using simpler complexity metrics during initial solution discovery followed by a post-hoc identifiability analysis may be optimal for discovering interpretable and mathematically identifiable PDE solutions.

Planning and scheduling are integral components of process supply chains. The presence of data correlation, particularly multivariate demand data dependency, can pose significant challenges to the decision-making process. This necessitates the consideration of dependency structures inherent in the underlying data to generate good-quality, feasible solutions to optimisation problems such as planning and scheduling. This work proposes a chance-constrained optimisation framework integrated with copulas, a non-parametric data estimation technique to forecast uncertain demand levels in accordance with specified risk thresholds in the context of a planning and scheduling problem. We focus on the integrated planning and scheduling problem following a bi-level optimisation formulation. The estimated demand forecasts are subsequently utilised within the Data-driven Optimisation of bi-level Mixed-Integer NOnlinear problems (DOMINO) framework to solve the integrated optimisation problem, and derive decisions with guaranteed demand satisfaction rates. Computational experiments demonstrate that our proposed copula-based chance-constrained optimisation framework can incorporate demand correlation and achieve higher joint demand satisfaction rate, lower total costs with higher efficiency.

Following the discovery of the least squares method in 1805 by Legendre and later in 1809 by Gauss, surrogate modeling and machine learning have come a long way. From identifying patterns and trends in process data to predictive modeling, optimization, fault detection, reaction network discovery, and process operations, machine learning became an integral part of all aspects of process design and process systems engineering. This is enabled, at the same time necessitated, by the vast amounts of data that are readily available from processes, increased digitalization, automation, increasing computation power, and simulation software that can model complex phenomena that span over several temporal and spatial scales. Although this paper is not a comprehensive review, it gives an overview of the recent history of machine learning models that we use every day and how they shaped process design problems from the recent advances to the exploration of their prospects.