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1. Probabilistic Symmetry for Multi-Agent Dynamics

   Sun, Sophia Huiwen; Walters, Robin; Li, Jinxi; Yu, Rose (June 2023, Proceedings of The 5th Annual Learning for Dynamics and Control Conference)

   Learning multi-agent dynamics is a core AI problem with broad applications in robotics and autonomous driving. While most existing works focus on deterministic prediction, producing probabilistic forecasts to quantify uncertainty and assess risks is critical for downstream decision-making tasks such as motion planning and collision avoidance. Multi-agent dynamics often contains internal symmetry. By leveraging symmetry, specifically rotation equivariance, we can improve not only the prediction accuracy but also uncertainty calibration. We introduce Energy Score, a proper scoring rule, to evaluate probabilistic predictions. We propose a novel deep dynamics model, Probabilistic Equivariant Continuous COnvolution (PECCO) for probabilistic prediction of multi-agent trajectories. PECCO extends equivariant continuous convolution to model the joint velocity distribution of multiple agents. It uses dynamics integration to propagate the uncertainty from velocity to position. On both synthetic and real-world datasets, PECCO shows significant improvements in accuracy and calibration compared to non-equivariant baselines. 

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2. Workflows for Construction of Spatio-Temporal Probabilistic Maps for Volcanic Hazard Assessment

   https://doi.org/10.3389/feart.2021.744655  

   Jones-Ivey, Renette; Patra, Abani; Bursik, Marcus (January 2022, Frontiers in Earth Science)

   Probabilistic hazard assessments for studying overland pyroclastic flows or atmospheric ash clouds under short timelines of an evolving crisis, require using the best science available unhampered by complicated and slow manual workflows. Although deterministic mathematical models are available, in most cases, parameters and initial conditions for the equations are usually only known within a prescribed range of uncertainty. For the construction of probabilistic hazard assessments, accurate outputs and propagation of the inherent input uncertainty to quantities of interest are needed to estimate necessary probabilities based on numerous runs of the underlying deterministic model. Characterizing the uncertainty in system states due to parametric and input uncertainty, simultaneously, requires using ensemble based methods to explore the full parameter and input spaces. Complex tasks, such as running thousands of instances of a deterministic model with parameter and input uncertainty require a High Performance Computing infrastructure and skilled personnel that may not be readily available to the policy makers responsible for making informed risk mitigation decisions. For efficiency, programming tasks required for executing ensemble simulations need to run in parallel, leading to twin computational challenges of managing large amounts of data and performing CPU intensive processing. The resulting flow of work requires complex sequences of tasks, interactions, and exchanges of data, hence the automatic management of these workflows are essential. Here we discuss a computer infrastructure, methodology and tools which enable scientists and other members of the volcanology research community to develop workflows for construction of probabilistic hazard maps using remotely accessed computing through a web portal. 

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3. New remote method to systematically extract bedrock channel width of small catchments across large spatial scales using high‐resolution digital elevation models

   https://doi.org/10.1002/esp.5560  

   Eidmann, Johanna Sophie; Gallen, Sean (February 2023, Earth Surface Processes and Landforms)

   Abstract Bedrock river width is an essential geometric parameter relevant to understanding flood hazards and gauging station rating curves, and is critical to stream power incision models and many other landscape evolution models. Obtaining bedrock river width measurements, however, typically requires extensive field campaigns that take place in rugged and steep topography where river access is often physically challenging. Although prior work has turned to measuring channel width from satellite imagery, these data present a snapshot in time, are typically limited to rivers ≥ 10–30 m wide due to the image resolution, and are physically restricted to areas devoid of vegetation. For these reasons, we are generally data limited, and the factors impacting bedrock channel width remain poorly understood. Due to these limitations, researchers often turn to assumptions of width‐scaling relationships with drainage area or discharge to estimate bedrock channel width. Here we present a new method of obtaining bedrock channel width at a desired river discharge through the incorporation of a high‐resolution bare‐earth digital elevation model (DEM) using MATLAB Topotoolbox and the HEC‐RAS river analysis system. We validate this method by comparing modeled results to US Geological Survey (USGS) field measurements at existing gauging stations, as well as field channel measurements. We show that this method can capture general characteristics of discharge rating curves and predict field‐measured channel widths within uncertainty. As high‐resolution DEMs become more available across the United States through the USGS three‐dimensional elevation program (3DEP), the future utility of this method is notable. Through developing and validating a streamlined, open‐source, and freely available workflow of channel width extraction, we hope this method can be applied to future research to improve the quantity of channel width measurements and improve our understanding of bedrock channels. 

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4. Effects of Robust Convex Optimization on Early-Stage Design Space Exploratory Behavior

   https://doi.org/10.1115/1.4048580  

   Pillai, Priya P.; Burnell, Edward; Wang, Xiqing; Yang, Maria C. (December 2020, Journal of Mechanical Design)

   null (Ed.)

   Abstract Engineers design for an inherently uncertain world. In the early stages of design processes, they commonly account for such uncertainty either by manually choosing a specific worst-case and multiplying uncertain parameters with safety factors or by using Monte Carlo simulations to estimate the probabilistic boundaries in which their design is feasible. The safety factors of this first practice are determined by industry and organizational standards, providing a limited account of uncertainty; the second practice is time intensive, requiring the development of separate testing infrastructure. In theory, robust optimization provides an alternative, allowing set-based conceptualizations of uncertainty to be represented during model development as optimizable design parameters. How these theoretical benefits translate to design practice has not previously been studied. In this work, we analyzed the present use of geometric programs as design models in the aerospace industry to determine the current state-of-the-art, then conducted a human-subjects experiment to investigate how various mathematical representations of uncertainty affect design space exploration. We found that robust optimization led to far more efficient explorations of possible designs with only small differences in an experimental participant’s understanding of their model. Specifically, the Pareto frontier of a typical participant using robust optimization left less performance “on the table” across various levels of risk than the very best frontiers of participants using industry-standard practices. 

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5. Early-Stage Uncertainty: Effects of Robust Convex Optimization on Design Exploration

   https://doi.org/10.1115/DETC2020-22626  

   Pillai, P.; Burnell, E.; Wang, X.; Yang, M. C. (August 2020, Proceedings of the ASME Design Engineering Technical Conferences)

   null (Ed.)

   Engineers design for an inherently uncertain world. In the early stages of design processes, they commonly account for such uncertainty either by manually choosing a specific worstcase and multiplying uncertain parameters with safety factors, or by using Monte Carlo simulations to estimate the probabilistic boundaries in which their design is feasible. The safety factors of this first practice are determined by industry and organizational standards, providing an inexpressive account of uncertainty; the second practice is time intensive, requiring the development of separate testing infrastructure. In theory, robust optimization provides an alternative, allowing set based conceptualizations of uncertainty to be represented during model development as optimizable design parameters. How these theoretical benefits translate to design practice has not previously been studied. In this work, we analyzed present use of geometric programs as design models in the aerospace industry to determine the current state-of-the-art, then conducted a human-subjects experiment to investigate how various mathematical representations of uncertainty affect design space exploration. We found that robust optimization led to far more efficient explorations of possible designs with only small differences in experimental participant’s understandings of their model. Specifically, the Pareto frontier of a typical participant using robust optimization left less performance “on the table” across various levels of risk than the very best frontiers of participants using industry-standard practices. 

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