The construction of models from data is a significant contributor to the energetic costs of computation. Because of this, understanding how foundational thermodynamic bounds apply to modeling algorithms will be increasingly important. Here, we study the thermodynamic costs of a basic and fundamental modeling algorithm: simple linear regression. Following Landauer, we approximate the thermodynamic lower bound on irreversibly performing both exact linear regression and linear regression via stochastic gradient descent as implemented on floating-point numbers. From this, we derive energycost aware scaling laws for the optimal dataset size for training a linear regression model given a generalization error dependent demand for inference. Additionally, we discuss a method to lower bound the entropy production from the mismatch cost for algorithms with continuous input variables.

ABSTRACT Legged rovers provide enhanced mobility compared to wheeled platforms, enabling navigation on steep and irregular planetary terrains. However, traditional legged locomotion might be energetically inefficient and potentially dangerous to the rover on loose and inclined surfaces, such as crater walls and cave slopes. This paper introduces a preliminary study that compares the Cost of Transport (CoT) of walking and torso-based sliding locomotion for quadruped robots across different slopes, friction conditions and speed levels. By identifying intersections between walking and sliding CoT curves, we aim to define threshold conditions that may trigger transitions between the two strategies. The methodology combines physics-based simulations in Isaac Sim with particle interaction validation in ANSYS-Rocky. Our results represent an initial step towards adaptive locomotion strategies for planetary legged rovers.

However, as we grow older, our bodies become less energy efficient, turning simple daily activities like walking around a block into a daunting effort. Although the effect of aging on the energetic costs of walking is well-documented, we do not yet have a complete understanding of what causes the progressive increase in energetic cost. One of the challenges to understanding this phenomenon is that current technologies for assessing metabolic energy consumption require measuring several minutes of breathing. These measurements are too slow to gain insight into the energetic cost of different phases of the gait cycle. The Disability and Rehabilitation Engineering program (DARE) and the Established Program to Stimulate Competitive Research (EPSCoR) from the National Science Foundation (NSF) are funding a collaborative project at the University of Nebraska at Omaha (UNO) and at the University of Nebraska at Lincoln (UNL) aimed at investigating the metabolic cost of different phases of the walking gait cycle. It is expected that this inter-campus collaboration between researchers from different disciplines will enable the development more creative solutions than single-discipline research.