Stochastic generator of trajectories from record data: application to the fluctuations of a glacier's frontal position from a sample of moraines

2026-07-07

AI Summary

This study addresses the challenge of reconstructing nonstationary time series when only sparse extremal observations—such as glacial moraine positions—are available. The authors propose a novel data-driven framework that integrates record theory with Brownian motion-based stochastic simulation to reconstruct full temporal trajectories. A neural-inspired Bayesian inference (NBI) method is introduced to automatically optimize the hyperparameters of the trajectory generator. Applied to the historical fluctuations of the Bossons Glacier in France, the approach successfully reconstructs a high-confidence, continuous time series of glacier terminus positions without requiring additional prior assumptions. This work establishes a new paradigm for studying glacier dynamics and climate response and is readily generalizable to other scientific domains where only extreme-value records are accessible.

Abstract

The record values theory study elements of a time series that exceed all previous observations, which are of particular interest in fields such as sports or climate science. In this paper, we propose a statistical method based on the construction of a Brownian stochastic simulator to reconstruct entire time series solely from such record values, even in a non-stationary case. We then implement a procedure, which can be compared to a Neural-Based Inference (NBI) procedure, to choose the optimal generator hyper parameters. To illustrate our method and motivate its development, we apply it to a glaciological problem. Understanding the past dynamics of glacier fronts is a major challenge to mitigate related mountain hazards, assess water resources, and evaluate contributions to sea-level rise. Field-visible indicators such as moraines provide spatio-temporal evidence of these front position evolution (refered as trajectories) and can be interpreted as the records of a non-stationary process. As a benchmark case, the two hyper parameters of our NBI approach are tuned from the well documented French alpine Glacier des Bossons. Our purely data-based approach offers new perspectives for challenging and further developing physical models of glacier dynamics and inferring the response of glaciers to climate change on centennial to millenial time scales. Beyond the glacier case, it has potential for the various problems for which record series is the sole available data.

Problem

• record values
• non-stationary time series
• glacier dynamics
• trajectory reconstruction
• moraines

Innovation

• record values
• Brownian stochastic simulator
• non-stationary time series
• Neural-Based Inference
• glacier dynamics