In-context learning to predict critical transitions in dynamical systems

Critical transitions - abrupt, often irreversible changes in system dynamics - arise across human and natural systems, often with catastrophic consequences. Real-world observations of such shifts remain scarce, preventing the development of reliable early warning systems. Conventional statistical and spectral indicators, such as increasing variance, tend to fail under realistic conditions of limited data and correlated noise, whereas existing deep learning classifiers do not extrapolate beyond their training data distribution. In this work, we introduce TipPFN, an in-context learning (ICL) framework that uses a prior-data fitted network to infer a system's proximity to a critical transition. Trained on our novel synthetic data generator, which is based on canonical bifurcation scenarios coupled to diverse, randomized stochastic dynamics, TipPFN flexibly capitalizes on contexts of various sizes, complexity and dimensionalities. We demonstrate robust, state-of-the-art early detection of critical transitions in previously unseen tipping regimes, sim-to-real examples, and real-world observations in both ICL and zero-shot settings.

Earth-o1: A Grid-free Observation-native Atmospheric World Model

Despite the unprecedented volume of multimodal data provided by modern Earth observation systems, our ability to model atmospheric dynamics remains constrained. Traditional modeling frameworks force heterogeneous measurements into predefined spatial grids, inherently limiting the full exploitation of raw sensor data and creating severe computational bottlenecks. Here we present Earth-o1, an observation-native atmospheric world model that overcomes these structural limitations. Rather than relying on conventional atmospheric dynamical modeling systems or traditional data assimilation, Earth-o1 directly learns the continuous, three-dimensional physical evolution of the Earth system from ungridded observational data. By integrating diverse sensor inputs into a unified, grid-free dynamical field, the model autonomously advances the atmospheric state in space and time. We show that this fundamentally distinct paradigm enables direct, real-time forecasting and cross-sensor inference without the overhead of explicit numerical solvers. In hindcast evaluations, Earth-o1 achieves surface forecast skill comparable to the operational Integrated Forecasting System (IFS). These results establish that continuous, observation-driven world models -- a new class of fully observation-native geophysical simulators -- can match the fidelity of established physical frameworks, providing a scalable data-driven foundation for a digital twin of the Earth.

Physics-Constrained Adaptive Flow Matching for Climate Downscaling

Regional climate information at kilometer scales is essential for assessing the impacts of climate change, but generating it with global climate models is too expensive due to their high computational costs. Machine learning models offer a fast alternative, yet they often violate basic physical laws and degrade when applied to climates outside of their training distribution. We present Physics-Constrained Adaptive Flow Matching (PC-AFM), a generative downscaling model that addresses both problems. Building on the Adaptive Flow Matching (AFM) model of Fotiadis et al. (2025) as our baseline, we add soft conservation constraints that keep the downscaled output consistent with the large-scale input for precipitation and humidity, and use gradient surgery via the ConFIG algorithm to prevent these constraints from interfering with the generative objective. We train the model on Central Europe climate data, evaluate it on a 10-time downscaling task (63km to 6.3km) over six variables (near-surface temperature, precipitation, specific humidity, surface pressure, and horizontal wind components) across a comprehensive set of metrics including bias, ensemble skill scores, power spectra, and conservation error, and test the generalization on two held-out climate regions. Within the training distribution, PC-AFM reduces conservation errors and improves ensemble calibration while matching the baseline on standard skill metrics. Outside the training distribution, where unconstrained models develop large systematic errors by extrapolating learned statistics, PC-AFM halves precipitation wet bias, reduces conservation error and improves extreme-quantile accuracy, all without any information about the target climate at inference time. These results indicate that physical consistency is a practical requirement for deploying generative downscaling models in real-world applications.

Accurate and Efficient Hybrid-Ensemble Atmospheric Data Assimilation in Latent Space with Uncertainty Quantification

Data assimilation (DA) combines model forecasts and observations to estimate the optimal state of the atmosphere with its uncertainty, providing initial conditions for weather prediction and reanalyses for climate research. Yet, existing traditional and machine-learning DA methods struggle to achieve accuracy, efficiency and uncertainty quantification simultaneously. Here, we propose HLOBA (Hybrid-Ensemble Latent Observation-Background Assimilation), a three-dimensional hybrid-ensemble DA method that operates in an atmospheric latent space learned via an autoencoder (AE). HLOBA maps both model forecasts and observations into a shared latent space via the AE encoder and an end-to-end Observation-to-Latent-space mapping network (O2Lnet), respectively, and fuses them through a Bayesian update with weights inferred from time-lagged ensemble forecasts. Both idealized and real-observation experiments demonstrate that HLOBA matches dynamically constrained four-dimensional DA methods in both analysis and forecast skill, while achieving end-to-end inference-level efficiency and theoretical flexibility applies to any forecasting model. Moreover, by exploiting the error decorrelation property of latent variables, HLOBA enables element-wise uncertainty estimates for its latent analysis and propagates them to model space via the decoder. Idealized experiments show that this uncertainty highlights large-error regions and captures their seasonal variability.

Power Ensemble Aggregation for Improved Extreme Event AI Prediction

This paper addresses the critical challenge of improving predictions of climate extreme events, specifically heat waves, using machine learning methods. Our work is framed as a classification problem in which we try to predict whether surface air temperature will exceed its q-th local quantile within a specified timeframe. Our key finding is that aggregating ensemble predictions using a power mean significantly enhances the classifier's performance. By making a machine-learning based weather forecasting model generative and applying this non-linear aggregation method, we achieve better accuracy in predicting extreme heat events than with the typical mean prediction from the same model. Our power aggregation method shows promise and adaptability, as its optimal performance varies with the quantile threshold chosen, demonstrating increased effectiveness for higher extremes prediction.

PnP-DA: Towards Principled Plug-and-Play Integration of Variational Data Assimilation and Generative Models

Earth system modeling presents a fundamental challenge in scientific computing: capturing complex, multiscale nonlinear dynamics in computationally efficient models while minimizing forecast errors caused by necessary simplifications. Even the most powerful AI- or physics-based forecast system suffer from gradual error accumulation. Data assimilation (DA) aims to mitigate these errors by optimally blending (noisy) observations with prior model forecasts, but conventional variational methods often assume Gaussian error statistics that fail to capture the true, non-Gaussian behavior of chaotic dynamical systems. We propose PnP-DA, a Plug-and-Play algorithm that alternates (1) a lightweight, gradient-based analysis update (using a Mahalanobis-distance misfit on new observations) with (2) a single forward pass through a pretrained generative prior conditioned on the background forecast via a conditional Wasserstein coupling. This strategy relaxes restrictive statistical assumptions and leverages rich historical data without requiring an explicit regularization functional, and it also avoids the need to backpropagate gradients through the complex neural network that encodes the prior during assimilation cycles. Experiments on standard chaotic testbeds demonstrate that this strategy consistently reduces forecast errors across a range of observation sparsities and noise levels, outperforming classical variational methods.

Align-DA: Align Score-based Atmospheric Data Assimilation with Multiple Preferences

Data assimilation (DA) aims to estimate the full state of a dynamical system by combining partial and noisy observations with a prior model forecast, commonly referred to as the background. In atmospheric applications, this problem is fundamentally ill-posed due to the sparsity of observations relative to the high-dimensional state space. Traditional methods address this challenge by simplifying background priors to regularize the solution, which are empirical and require continual tuning for application. Inspired by alignment techniques in text-to-image diffusion models, we propose Align-DA, which formulates DA as a generative process and uses reward signals to guide background priors, replacing manual tuning with data-driven alignment. Specifically, we train a score-based model in the latent space to approximate the background-conditioned prior, and align it using three complementary reward signals for DA: (1) assimilation accuracy, (2) forecast skill initialized from the assimilated state, and (3) physical adherence of the analysis fields. Experiments with multiple reward signals demonstrate consistent improvements in analysis quality across different evaluation metrics and observation-guidance strategies. These results show that preference alignment, implemented as a soft constraint, can automatically adapt complex background priors tailored to DA, offering a promising new direction for advancing the field.

Strictly Constrained Generative Modeling via Split Augmented Langevin Sampling

Deep generative models hold great promise for representing complex physical systems, but their deployment is currently limited by the lack of guarantees on the physical plausibility of the generated outputs. Ensuring that known physical constraints are enforced is therefore critical when applying generative models to scientific and engineering problems. We address this limitation by developing a principled framework for sampling from a target distribution while rigorously satisfying physical constraints. Leveraging the variational formulation of Langevin dynamics, we propose Split Augmented Langevin (SAL), a novel primal-dual sampling algorithm that enforces constraints progressively through variable splitting, with convergence guarantees. While the method is developed theoretically for Langevin dynamics, we demonstrate its effective applicability to diffusion models. In particular, we use constrained diffusion models to generate physical fields satisfying energy and mass conservation laws. We apply our method to diffusion-based data assimilation on a complex physical system, where enforcing physical constraints substantially improves both forecast accuracy and the preservation of critical conserved quantities. We also demonstrate the potential of SAL for challenging feasibility problems in optimal control.

CausalDynamics: A large-scale benchmark for structural discovery of dynamical causal models

Causal discovery for dynamical systems poses a major challenge in fields where active interventions are infeasible. Most methods used to investigate these systems and their associated benchmarks are tailored to deterministic, low-dimensional and weakly nonlinear time-series data. To address these limitations, we present CausalDynamics, a large-scale benchmark and extensible data generation framework to advance the structural discovery of dynamical causal models. Our benchmark consists of true causal graphs derived from thousands of coupled ordinary and stochastic differential equations as well as two idealized climate models. We perform a comprehensive evaluation of state-of-the-art causal discovery algorithms for graph reconstruction on systems with noisy, confounded, and lagged dynamics. CausalDynamics consists of a plug-and-play, build-your-own coupling workflow that enables the construction of a hierarchy of physical systems. We anticipate that our framework will facilitate the development of robust causal discovery algorithms that are broadly applicable across domains while addressing their unique challenges. We provide a user-friendly implementation and documentation on https://kausable.github.io/CausalDynamics.

Deep Koopman operator framework for causal discovery in nonlinear dynamical systems

We use a deep Koopman operator-theoretic formalism to develop a novel causal discovery algorithm, Kausal. Causal discovery aims to identify cause-effect mechanisms for better scientific understanding, explainable decision-making, and more accurate modeling. Standard statistical frameworks, such as Granger causality, lack the ability to quantify causal relationships in nonlinear dynamics due to the presence of complex feedback mechanisms, timescale mixing, and nonstationarity. This presents a challenge in studying many real-world systems, such as the Earth's climate. Meanwhile, Koopman operator methods have emerged as a promising tool for approximating nonlinear dynamics in a linear space of observables. In Kausal, we propose to leverage this powerful idea for causal analysis where optimal observables are inferred using deep learning. Causal estimates are then evaluated in a reproducing kernel Hilbert space, and defined as the distance between the marginal dynamics of the effect and the joint dynamics of the cause-effect observables. Our numerical experiments demonstrate Kausal's superior ability in discovering and characterizing causal signals compared to existing approaches of prescribed observables. Lastly, we extend our analysis to observations of El Ni\~no-Southern Oscillation highlighting our algorithm's applicability to real-world phenomena. Our code is available at https://github.com/juannat7/kausal.