ExREC 2026 abstracts

Oral presentations

“Learning Probabilistic Filters for Data Assimilation” Eviatar Bach

Filtering, the problem of estimating the probability distribution of a system`s states given partial and noisy observations, is generally intractable for high-dimensional, nonlinear systems. The ensemble Kalman filter (EnKF) approximates the filtering distribution with an ensemble of interacting particles, employing a Gaussian ansatz for the joint distribution of the state and observation at each observation time. The EnKF is robust, but the Gaussian ansatz limits accuracy. We address this shortcoming by using machine learning to map the forecast distribution and observation to the filtering distribution. We propose cost functions that are minimised uniquely at the true filtering distribution. By time-averaging over long trajectories in ergodic dynamical systems, the map can be learned and subsequently used for future filtering; this is a form of amortised Bayesian inference. We focus on learning ensemble-based filters within a mean field framework. We demonstrate the approach using a set transformer neural architecture, which is invariant to ensemble permutations. The learned filtering algorithms outperform state-of-the-art methods for filtering chaotic systems. They also perform well in challenging highly non-Gaussian and multimodal problems where the EnKF fails. Once learned at a given ensemble size, the learned map can be applied to other ensemble sizes with minimal fine-tuning.

“Conditions for skilful spatial and temporal tipping point early warning signals” Joe Clarke

As tipping points are extremely difficult to predict using an initial value modelling approach, forewarning of bifurcation tipping points instead often depends on the analysis of observational data, using approaches that aim to detect reducing system resilience. The most commonly used early warning indicators (EWIs) rely on the phenomenon of critical slowing down, which is the tendency for fluctuations of a state variable to get larger (increased variance) and longer lived (increased temporal autocorrelation), as the bifurcation is approached. This is measurable in low dimensional systems that remain close to a quasi-equilibrium state in the run-up to the bifurcation. However, in systems that are subject to rapid changes in external forcing, such as the contemporary Earth system, this condition is unlikely to be met and EWIs become less reliable. In addition, temporal EWIs require long observational time series. For these reasons, it makes sense to consider spatial EWIs that can make use of the spatial detail resolved by present-day observations, especially from remote sensing. In this talk, I explore the conditions under which spatial and temporal EWIs will each be reliable, using a simple spatially coupled model with a fold bifurcation. 

“Large deviations in systems with slow feedback” Francesco Coghi

“Tangent space precursors of extreme events and critical transitions” Riccardo Consonni

“Extreme events in atmosphere and ocean via sharp large deviations estimates” Tobias Grafke

Rare and extreme events are notoriously hard to handle in any complex stochastic system: They are simultaneously too rare to be reliably observable in experiments or numerics, but at the same time often too impactful to be ignored. Large deviation theory provides a classical way of dealing with events of extremely small probability, but generally only yields the exponential tail scaling of rare event probabilities. In this talk, I will discuss theory, and algorithms based upon it, that improve on this limitation, yielding sharp quantitative estimates of rare event probabilities from a single computation and without fitting parameters. Notably, these estimates require the computation of determinants of differential operators, which in relevant cases are not traceclass and require appropriate renormalization. We demonstrate that the Carleman-Fredholm operator determinant is the correct choice. Throughout, I will demonstrate the applicability of these methods to high-dimensional real-world systems, for example coming from atmosphere and ocean dynamics.

“Data-driven anticipation and prediction of Atlantic Meridional Overturning Circulation collapse using non-autonomous spatio-temporal dynamical modelling” Frank Kwasniok

Data-driven methodologies for identifying, anticipating and predicting critical transitions in high-dimensional model or observational data sets are introduced, based on explicit non-stationary low-order modelling of the tipping dynamics, allowing for dynamical understanding of the underlying tipping mechanism and genuine prediction of the future system state by extrapolation. A set of spatial modes carrying the tipping dynamics are identified and a stochastic model of appropriate complexity is estimated in the subspace spanned by these modes. Analysis of the reconstructed dynamics provides information on the proximity to a bifurcation point and the type of the impending bifurcation. In a first step, we focus on linear stability analysis and derive non-autonomous dynamic and optimal mode decompositions (non-aut-DMD, non-aut-OMD) as extensions of the stationary DMD and OMD. In a second step, we estimate nonlinear stochastic low-order models. Different competing tipping mechanisms can be compared and assessed using likelihood inference and information criteria. The method allows to quantify the likelihood or risk of a critical transition at some point in the future having observed a certain amount of data up to present.

The methodologies are here applied to a data set from a simulation of AMOC collapse with a complex climate model, actually a freshwater hosing experiment with the FAMOUS GCM. The AMOC on-state is found to lose stability via a subcritical Hopf bifurcation; however, the transition to the off-state occurs far ahead of the bifurcation point. The early collapse can be explained by a combination of rate-induced and noise-induced tipping.

“Large-Deviation-Based Importance Sampling for Rare Transition Paths in Overdamped Langevin Dynamics.” Rivkah Moshe

“How to simulate extreme events with climate models and what this can be useful for” Robin Noyelle

The changes in frequency and intensity of extreme meteorological and climatological events will likely dominate the impacts of climate change on societies and ecosystems. Understanding how they respond to anthropogenic and natural forcings is thus of paramount importance. However, by definition these events are rare and are thus seldom seen in both observations and climate model simulations. Recently, methods known as rare event algorithms have been developed and used with climate models to sample more of these extreme events. In this talk I will present two such methods – the GKTL algorithm and ensemble boosting, explain what kind of extreme events they are expected to sample and how we can leverage them to answer physical equations about the climate system. I will show applications of these methods to hot summers, megadroughts, extreme temperature and extreme precipitation events. Finally, I will propose some ways forward for the use of rare event algorithms in the climate science context.

“Addressing the Lack of Data Issue: Bayesian Generalized Extreme Value Statistics & AI Emulator Driven Rare Event Algorithms” Peter Werner

Obtaining reliable statistics of rare events is of great practical importance. For example, extreme temperature events, e.g., the annual maximum surface air temperature, are of interest, since they are representative of the maximum thermal stress from the environment that electrical power infrastructure should ideally be capable of withstanding. Assessment of the decrease in efficiency of power generation, in case of power plants, or its subsequent transport through the influence on the thermal rating of power lines necessitates data on rare extreme temperature events, too. Due to the data scarcity from observations that is inherent to rare events, more sophisticated approaches are required to overcome this issue, which are the subject of this talk.

A purely statistical approach [1] to describe annual temperature extremes will be discussed in the first part of the talk. It involves the fit of a non-stationary generalized extreme value distribution (GEV) using the software package ANKIALE [2] using a Bayesian setup and allows to predict the statistics of extremely rare events based on both observation datasets and climate model outputs. The employed Bayesian approach provides uncertainty or error estimates on the obtained
parameters, too, allowing to make statements about the reliability of the predictions. As an application of the method, electrical power infrastructure in continental France is considered.

The second part of the talk addresses recent advances in AI emulators of physical models that allow to simulate large ensembles, including extreme events, at a fraction of the cost of the original model. However, these emulators may suffer from biases that degrade return period estimates. To address this, AI+RES was introduced [3]. It is a hybrid framework coupling AI weather emulators with genealogical particle analysis type rare event algorithms. The algorithm uses an emulator ensemble forecast to estimate the committor function — the theoretically optimal score function — at each resampling step, guiding the simulation toward rare event realizations. This enables unbiased return period estimates and the study of the dynamics of very rare events, such as onceper-millennium heatwaves, at two orders of magnitude lower computational cost.

[1] Robin, Y. and Ribes, A.: Nonstationary extreme value analysis for event attribution combining climate models and observations, Adv. Stat. Clim. Meteorol. Oceanogr., 6, 205–221, https://doi.org/10.5194/ascmo-6-205-2020, 2020.
[2] Robin, Y., Vrac, M., Ribes, A., Barbaux, O., and Naveau, P.: A Bayesian statistical method to estimate the climatology of extreme temperature under multiple scenarios: the ANKIALE package, Geosci. Model Dev., 19, 2349–2372, https://doi.org/10.5194/gmd-19-2349-2026, 2026.
[3] Amaury Lancelin, Alex Wikner, Laurent Dubus, Clément Le Priol, Dorian S. Abbot, Freddy Bouchet, Pedram Hassanzadeh and Jonathan Weare: AI-boosted rare event sampling to characterize extreme weather (2026), [preprint] https://doi.org/10.48550/arXiv.2510.2706

Poster presentations

“Nonstationarity in rare hydrological drought projections in UK” Srinidhi Jha

“Scale-Preserving Autoencoders for High-Dimensional Heavy-Tailed Data” Ashley Turner

High-dimensional and heavy-tailed data arise in fields such as climate science, finance, insurance and astronomy. Such data often exhibit low-dimensional structure, motivating dimension reduction and latent-space modelling. However, when the downstream objective is magnitude-focussed, such as extreme-value analysis, generic nonlinear dimension reduction can destroy the radial scaling and tail behaviour of the original data distribution.

This talk will begin with motivating dimension reduction in high-dimensional statistical modelling, recalling some relevant extreme-value theory, including regular variation, tail indices and tail measures and a review of standard autoencoders as nonlinear dimension-reduction architectures.

Homogeneous Autoencoders are then presented as a scale-preserving autoencoder architecture for heavy-tailed data. We show why unconstrained autoencoders may reconstruct data accurately while substantially distorting latent radial properties and tail behaviour, and propose an architecture combining a homogeneous encoder with an asymptotically homogeneous decoder. Together, these maps transport radial magnitudes analytically between observation and latent space, yield explicit tail-index and tail-measure transformations under regular variation, and preserve the original radial tail index under the encoder-decoder round trip. The methodology is demonstrated on synthetic heavy-tailed manifold-supported data and ERA5 atmospheric fields, where Homogeneous Autoencoders match the reconstructive performance of parameter-matched standard autoencoders while preserving latent and round-trip radial tail diagnostics by construction.