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Fast and Precise Trajectory Simulation for Entry, Descent, and Landing Using A Multi-Model Monte Carlo Approach

Predicting landing radius and other quantities of interest (QoI) for entry, descent, and landing (EDL) applications requires a viable uncertainty propagation method for quantifying the impact of uncertainties in wind pattern variations, atmospheric uncertainties, etc. While standard MC simulation is the defacto standard for providing robust and unbiased predictions,it is often infeasible for expensive, high-fidelity EDL models. Low-fidelity models are commonly constructed to replace the high-fidelity model in MC simulation for computational speedup,but at the expense of accuracy and unbiasedness. Emerging multi-model MC methods are bridging this gap by combining predictions from two or more models of varying fidelity and computational cost for efficient and unbiased uncertainty propagation. This work explores the use of multi-model MC for increasing the speed and precision of trajectory simulation for EDL. It is shown that combining a high-fidelity EDL model with low-fidelity models (e.g,data-driven, reduced physics) yields substantial computational speedup versus standard MCwith only the high-fidelity model. Moreover, the unbiasedness of multi-model MC predictions is highlighted by showing increased accuracy versus an approach that leverages a low-fidelity surrogate model alone.

James E. Warner

Multi-Model Monte Carlo Estimators for Trajectory Simulation

Predicting landing radius and other quantities of interest (QoI) for entry, descent, andlanding (EDL) applications requires a viable uncertainty propagation method for quantifying the impact of uncertainties in aerodynamics, atmosphere, mass properties, etc. While standard Monte Carlo (MC) simulation is the de facto standard for producing robust and unbiasedstatistical estimators, it is often infeasible for expensive, high-fidelity models. Low-fidelity models are commonly constructed to replace the high-fidelity model in MC simulation for computational speedup, but at the expense of accuracy and unbiasedness. Emerging multi-model MC methods are bridging this gap by combining predictions from two or more modelsof varying fidelity and computational cost for efficient and unbiased uncertainty propagation.This works establishes a proof of concept for using multi-model MC to increase the speed and precision of trajectory simulation for EDL. It is shown that combining a high-fidelity EDL model with low-fidelity models (e.g., data-driven, reduced physics) in this manner has the potential to yield significant efficiency and accuracy gains for certain EDL QoIs versusa standard MC approach. Moreover, the unbiasedness of multi-model MC predictions ishighlighted by showing increased accuracy versus an approach that leverages a low-fidelity model alone.

James E Warner

Contextual classification of multispectral image data - An unbiased estimator for the context distribution

Recent investigations have demonstrated the effectiveness of a contextual classifier that combines spatial and spectral information employing a general statistical approach. This statistical classification algorithm exploits the tendency of certain ground-cover classes to occur more frequently in some spatial contexts than in others. Indeed, a key input to this algorithm is a statistical characterization of the context: the context distribution. Here a discussion is given of an unbiased estimator of the context distribution which, besides having the advantage of statistical unbiasedness, has the additional advantage over other estimation techniques of being amenable to an adaptive implementation in which the context distribution estimate varies according to local contextual information. Results from applying the unbiased estimator to the contextual classification of three real Landsat data sets are presented and contrasted with results from noncontextual classifications and from contextual classifications utilizing other context distribution estimation techniques.

Tilton, J. C.

Contextual classification of multispectral image data: An unbiased estimator for the context distribution

A key input to a statistical classification algorithm, which exploits the tendency of certain ground cover classes to occur more frequently in some spatial context than in others, is a statistical characterization of the context: the context distribution. An unbiased estimator of the context distribution is discussed which, besides having the advantage of statistical unbiasedness, has the additional advantage over other estimation techniques of being amenable to an adaptive implementation in which the context distribution estimate varies according to local contextual information. Results from applying the unbiased estimator to the contextual classification of three real LANDSAT data sets are presented and contrasted with results from non-contextual classifications and from contextual classifications utilizing other context distribution estimation techniques.

Tilton, J. C.

Estimation of context for statistical classification of multispectral image data

Recent investigations have demonstrated the effectiveness of a contextual classifier that combines spatial and spectral information employing a general statistical approach. This statistical classification algorithm exploits the tendency of certain ground cover classes to occur more frequently in some spatial contexts than in others. Indeed, a key input to this algorithm is a statistical characterization of the context: the context function. An unbiased estimator of the context function is discussed which, besides having the advantage of statistical unbiasedness, has the additional advantage over other estimation techniques of being amenable to an adaptive implementation in which the context-function estimate varies according to local contextual information. Results from applying the unbiased estimator to the contextual classification of three real Landsat data sets are presented and contrasted with results from noncontextual classifications and from contextual classifications utilizing other context-function estimation techniques.

Tilton, J. C.

Smoothed perturbation analysis algorithms for estimating the derivatives of occupancy-related functions in serial queueing networks

The authors present smoothed perturbation analysis (SPA) estimators for the derivative of a number of occupancy-related functions in serial queuing networks with finite buffer spaces. The functions are the average number of customers at a network as seen by an arrival, the probability that a customer is blocked at a particular queue, and the probability that a customer leaves a queue empty. In all three cases, the variable is a parameter of the distribution of service times at one of the queues. The derivative estimators considered are very simple and flexible, and they easily lend themselves to analysis of unbiasedness. Unlike most of the established SPA estimators, the present ones are not based on the computation of hazard rates.

Wardi, Y.

Envisioning the Future of International Earth Observations Collaboration: Area and Map Accuracy Estimation by Sampling

- Maps have errors, sometimes a lot of errors ⇒ obtaining information directly from map problematic; any use of the map will benefit from information about errors/uncertainty - IPCC: unbiasedness and uncertainty - By randomly drawing a sample from the study area, observing reference conditions at drawn locations, and constructing estimators – easily estimate areas and map accuracy ± uncertainty - Sampling design and analysis, relatively easy – collecting reference observations is not. Cloud-based solutions, e.g. AREA2, Collect Earth Online, facilitate the collection of reference observations - More research and guidance needed!

Pontus Olofsson

Debiasing Watermarks for Large Language Models via Maximal Coupling

Watermarking language models is essential for distinguishing between human and machine-generated text and thus maintaining the integrity and trustworthiness of digital communication. Here, we present a novel green/red list watermarking approach that partitions the token set into “green” and “red” lists, subtly increasing the generation probability for green tokens. To correct token distribution bias, our method employs maximal coupling, using a uniform coin flip to decide whether to apply bias correction, with the result embedded as a pseudorandom watermark signal. Theoretical analysis confirms this approach’s unbiased nature and robust detection capabilities. Experimental results show that it outperforms prior techniques by preserving text quality while maintaining high detectability, and it demonstrates resilience to targeted modifications aimed at improving text quality. This research provides a promising watermarking solution for language models, balancing effective detection with minimal impact on text quality.

97 MATHEMATICS AND COMPUTING