Car-Following Models: A Multidisciplinary Review

Recent advances of data-driven machine learning have revolutionized fields like computer vision, reinforcement learning, and many scientific and engineering domains. In many real-world and scientific problems, systems that generate data are governed by physical laws. Recent work shows that it provides potential benefits for machine learning models by incorporating the physical prior and collected data, which makes the intersection of machine learning and physics become a prevailing paradigm. By integrating the data and mathematical physics models seamlessly, it can guide the machine learning model towards solutions that are physically plausible, improving accuracy and efficiency even in uncertain and high-dimensional contexts. In this survey, we present this learning paradigm called Physics-Informed Machine Learning (PIML) which is to build a model that leverages empirical data and available physical prior knowledge to improve performance on a set of tasks that involve a physical mecha …

Reduced models describing the Lagrangian dynamics of the Velocity Gradient Tensor (VGT) in Homogeneous Isotropic Turbulence (HIT) are developed under the Physics-Informed Machine Learning (PIML) framework. We construct the pressure Hessian and sub-filter contributions using the integrity bases and invariants of VGT and express them with extended Tensor Basis Neural Network (TBNN). We observe that the PIML model provides an improved representation for the magnitude and orientation of the small-scale pressure Hessian contributions. Statistics of the flow, as indicated by the joint PDF of second and third invariants of the VGT, show good agreement with the ``ground-truth'' DNS data.

Physics-informed machine learning (PIML), referring to the combination of prior knowledge of physics, which is the high level abstraction of natural phenomenons and human behaviours in the long history, with data-driven machine learning models, has emerged as an effective way to mitigate the shortage of training data, to increase models' generalizability and to ensure the physical plausibility of results. In this paper, we survey an abundant number of recent works in PIML and summarize them from three aspects: (1) motivations of PIML, (2) physics knowledge in PIML, (3) methods of physics knowledge integration in PIML. We also discuss current challenges and corresponding research opportunities in PIML.

Although an increased availability of computational resources has enabled high-fidelity simulations of turbulent flows, the RANS models are still the dominant tools for industrial applications. However, the predictive capabilities of RANS models are limited by potential inaccuracy driven by hypotheses in the Reynolds stress closure. Recently, a Physics-Informed Machine Learning (PIML) approach has been proposed to learn the functional form of Reynolds stress discrepancy in RANS simulations based on available data. It has been demonstrated that the learned discrepancy function can be used to improve Reynolds stresses in different flows where data are not available. However, owing to a number of challenges, the improvements have been demonstrated only in the Reynolds stress prediction but not in the corresponding propagated quantities of interest. In this work, we introduce the procedures toward a complete PIML framework for predictive turbulence modeling, including learning Reynolds str …

A fundamental challenge in physics-informed machine learning (PIML) is the design of robust PIML methods for out-of-distribution (OOD) forecasting tasks. These OOD tasks require learning-to-learn from observations of the same (ODE) dynamical system with different unknown ODE parameters, and demand accurate forecasts even under out-of-support initial conditions and out-of-support ODE parameters. In this work we propose a solution for such tasks, which we define as a meta-learning procedure for causal structure discovery (including invariant risk minimization). Using three different OOD tasks, we empirically observe that the proposed approach significantly outperforms existing state-of-the-art PIML and deep learning methods.