Search for: All records

This tutorial paper focuses on safe physics- informed machine learning in the context of dynamics and control, providing a comprehensive overview of how to integrate physical models and safety guarantees. As machine learning techniques enhance the modeling and control of complex dynamical systems, ensuring safety and stability remains a critical challenge, especially in safety-critical applications like autonomous vehicles, robotics, medical decision-making, and energy systems. We explore various approaches for embedding and ensuring safety constraints, including structural priors, Lyapunov and Control Barrier Functions, predictive control, projections, and robust optimization techniques. Additionally, we delve into methods for uncertainty quantification and safety verification, including reachability analysis and neural network verification tools, which help validate that control policies remain within safe operating bounds even in uncertain environments. The paper includes illustrative examples demonstrating the implementation aspects of safe learning frameworks that combine the strengths of data-driven approaches with the rigor of physical principles, offering a path toward the safe control of complex dynamical systems. 

Physics-informed machine learning (PIML) is a set of methods and tools that systematically integrate machine learning (ML) algorithms with physical constraints and abstract mathematical models developed in scientific and engineering domains. As opposed to purely data-driven methods, PIML models can be trained from additional information obtained by enforcing physical laws such as energy and mass conservation. More broadly, PIML models can include abstract properties and conditions such as stability, convexity, or invariance. The basic premise of PIML is that the integration of ML and physics can yield more effective, physically consistent, and data-efficient models. This paper aims to provide a tutorial-like overview of the recent advances in PIML for dynamical system modeling and control. Specifically, the paper covers an overview of the theory, fundamental concepts and methods, tools, and applications on topics of: 1) physics-informed learning for system identification; 2) physics-informed learning for control; 3) analysis and verification of PIML models; and 4) physics-informed digital twins. The paper is concluded with a perspective on open challenges and future research opportunities. 

Abstract Sedimentary nitrogen isotope (as δ¹⁵N) records from the Southern Ocean provide critical constraints on surface nutrient consumption in the past and the role of Southern Ocean biophysical changes in setting atmosphericpCO₂. We present a field assessment of how surface nitrate consumption is reflected in δ¹⁵N values of total nitrogen and diatom‐bound nitrogen pools of particles and sediments across the Southern Ocean along 170°W during late austral summer. Mixed layer nitrate δ¹⁵N values increase northwards associated with greater nitrate drawdown. Particles and sediments are expected to follow this trend. Contrary to expectations, surface ocean particle total nitrogen and diatom‐bound δ¹⁵N values decreased northward during the late summer, likely due to recycling of nitrogen and the assimilation of regenerated ammonium, as well as nitrate. The relationship between δ¹⁵N values of the total nitrogen and diatom‐bound pools remains relatively constant across this Southern Ocean transect, suggesting that the isotopic composition of these two surface ocean nitrogen pools are largely set by the δ¹⁵N value(s) of the assimilated nutrient(s). Surface sediment δ¹⁵N values do increase away from the region of maximum biogenic silica deposition, suggesting that the recycled nitrogen isotopic signal observed in late summer particles may not significantly impact the sedimentary record. However, the enrichment in δ¹⁵N values of the diatom‐bound pool is greater than what is expected from progressive utilization of the surface nitrate alone and not yet explained.