arXiv subjects

Niklas Boers

Publications and source records attributed to Niklas Boers.

At least 37 records · Page 2Linked to original sources

arXiv2026

Conditional diffusion models for downscaling and bias correction of Earth system model precipitation

Climate change exacerbates extreme weather events like heavy rainfall and flooding. As these events cause severe socioeconomic damage, accurate high-resolution simulation of precipitation is imperative. However, existing Earth System Models (ESMs) struggle to resolve small-scale dynamics and suffer from biases. Traditional statistical bias correction and downscaling methods fall short in improving spatial structure, while recent deep learning methods lack controllability and suffer from unstable training. Here, we propose a machine learning framework for simultaneous bias correction and downscaling. We first map observational and ESM data to a shared embedding space, where both are unbiased towards each other, and then train a conditional diffusion model to reverse the mapping. Only observational data is used for the training, so that the diffusion model can be employed to correct and downscale any ESM field without need for retraining. Our approach ensures statistical fidelity and preserves spatial patterns larger than a chosen spatial correction scale. We demonstrate that our approach outperforms existing statistical and deep learning methods especially regarding extreme events.

physics.geo-ph↗

arXiv2026

Chaotic Kramers' Law: Hasselmann's Program and AMOC Tipping

In bistable dynamical systems driven by Wiener processes, the widely used Kramers' law relates the strength of the noise forcing to the average time it takes to see a noise-induced transition from one attractor to the other. We extend this law to bistable systems forced by fast chaotic dynamics, which we argue is in some cases a more realistic modeling approach than unbounded noise forcing. Transitions similar to the noise-driven case can only occur if the amplitude of the chaotic forcing is large enough. If this is the case, in our numerical example - a reduced-order model of the Atlantic Meridional Overturning Circulation (AMOC) - we observe the chaotic Kramers' law to hold even when the chaotic forcing is far from the stochastic limit. We discuss the limitations of the chaotic Kramers' law, how to address the numerical issues associated with the timescale separation, and give a possible explanation for the dynamics of recently found AMOC collapses and recoveries in complex climate models.

nlin.CD↗

arXiv2026

Advanced Long-term Earth System Forecasting

Reliable long-term forecasting of Earth system dynamics is fundamentally limited by instabilities in current artificial intelligence (AI) models during extended autoregressive simulations. These failures often originate from inherent spectral bias, leading to inadequate representation of critical high-frequency, small-scale processes and subsequent uncontrolled error amplification. Inspired by the nested grids in numerical models used to resolve small scales, we present TritonCast. At the core of its design is a dedicated latent dynamical core, which ensures the long-term stability of the macro-evolution at a coarse scale. An outer structure then fuses this stable trend with fine-grained local details. This design effectively mitigates the spectral bias caused by cross-scale interactions. In atmospheric science, it achieves state-of-the-art accuracy on the WeatherBench 2 benchmark while demonstrating exceptional long-term stability: executing year-long autoregressive global forecasts and completing multi-year climate simulations that span the entire available $2500$-day test period without drift. In oceanography, it extends skillful eddy forecast to $120$ days and exhibits unprecedented zero-shot cross-resolution generalization. Ablation studies reveal that this performance stems from the synergistic interplay of the architecture's core components. TritonCast thus offers a promising pathway towards a new generation of trustworthy, AI-driven simulations. This significant advance has the potential to accelerate discovery in climate and Earth system science, enabling more reliable long-term forecasting and deeper insights into complex geophysical dynamics.

cs.LG↗

arXiv2025

Physically consistent and uncertainty-aware learning of spatiotemporal dynamics

Accurate long-term forecasting of spatiotemporal dynamics remains a fundamental challenge across scientific and engineering domains. Existing machine learning methods often neglect governing physical laws and fail to quantify inherent uncertainties in spatiotemporal predictions. To address these challenges, we introduce a physics-consistent neural operator (PCNO) that enforces physical constraints by projecting surrogate model outputs onto function spaces satisfying predefined laws. A physics-consistent projection layer within PCNO efficiently computes mass and momentum conservation in Fourier space. Building upon deterministic predictions, we further propose a diffusion model-enhanced PCNO (DiffPCNO), which leverages a consistency model to quantify and mitigate uncertainties, thereby improving the accuracy and reliability of forecasts. PCNO and DiffPCNO achieve high-fidelity spatiotemporal predictions while preserving physical consistency and uncertainty across diverse systems and spatial resolutions, ranging from turbulent flow modeling to real-world flood/atmospheric forecasting. Our two-stage framework provides a robust and versatile approach for accurate, physically grounded, and uncertainty-aware spatiotemporal forecasting.

cs.LG↗

arXiv2025

Anticipating AMOC transitions via deep learning

Key components of the Earth system can undergo abrupt and potentially irreversible transitions when the magnitude or rate of external forcing exceeds critical thresholds. In this study, we use the example of the Atlantic Meridional Overturning Circulation (AMOC) to demonstrate the challenges associated with anticipating such transitions when the system is susceptible to bifurcation-induced, rate-induced, and noise-induced tipping. Using a calibrated AMOC box model, we conduct large ensemble simulations and show that transition behavior is inherently probabilistic: under identical freshwater forcing scenarios, some ensemble members exhibit transitions while others do not. In this stochastic regime, traditional early warning indicators based on critical slowing down are unreliable in predicting impending transitions. To address this limitation, we develop a convolutional neural network (CNN)-based approach that identifies higher-order statistical differences between transitioning and non-transitioning trajectories within the ensemble realizations. This method enables the real-time prediction of transition probabilities for individual trajectories prior to the onset of tipping. Our results show that the CNN-based indicator provides effective early warnings in a system where transitions can be induced by bifurcations, critical forcing rates, and noise. These findings underscore the potential in identifying safe operating spaces and early warning indicators for abrupt transitions of Earth system components under uncertainty.

cs.CE↗

arXiv2025

Red noise in continuous-time stochastic modelling

The concept of time-correlated noise is important to applied stochastic modelling. Nevertheless, there is no generally agreed-upon definition of the term red noise in continuous-time stochastic modelling settings. We present here a rigorous argumentation for the Ornstein-Uhlenbeck process integrated against time ($U_t \mathrm{d} t$) as a uniquely appropriate red noise implementation. We also identify the term $\mathrm{d}U_t$ as an erroneous formulation of red noise commonly found in the applied literature. To this end, we prove a theorem linking properties of the power spectral density (PSD) to classes of Itô-differentials. The commonly ascribed red noise attribute of a PSD decaying as $S(ω)\simω^{-2}$ restricts the range of possible Itô-differentials $\mathrm{d}Y_t=α_t\mathrm{d} t+β_t\mathrm{d} W_t$. In particular, any such differential with continuous, square-integrable integrands must have a vanishing martingale part, i.e. $\mathrm{d}Y_t=α_t\mathrm{d} t$ for almost all $t\geq 0$. We further point out that taking $(α_t)_{t\geq 0}$ to be an Ornstein-Uhlenbeck process constitutes a uniquely relevant model choice due to its Gauss-Markov property. The erroneous use of the noise term $\mathrm{d} U_t$ as red noise and its consequences are discussed in two examples from the literature.

math.PR↗

arXiv2025

Reconstructing Historical Climate Fields With Deep Learning

Historical records of climate fields are often sparse due to missing measurements, especially before the introduction of large-scale satellite missions. Several statistical and model-based methods have been introduced to fill gaps and reconstruct historical records. Here, we employ a recently introduced deep-learning approach based on Fourier convolutions, trained on numerical climate model output, to reconstruct historical climate fields. Using this approach we are able to realistically reconstruct large and irregular areas of missing data, as well as reconstruct known historical events such as strong El Niño and La Niña with very little given information. Our method outperforms the widely used statistical kriging method as well as other recent machine learning approaches. The model generalizes to higher resolutions than the ones it was trained on and can be used on a variety of climate fields. Moreover, it allows inpainting of masks never seen before during the model training.

physics.geo-ph↗

arXiv2025

Predicting Instabilities in Transient Landforms and Interconnected Ecosystems

Many parts of the Earth system are thought to have multiple stable equilibrium states, with the potential for rapid and sometimes catastrophic shifts between them. The most common frameworks for analyzing stability changes, however, require stationary (trend- and seasonality-free) data, which necessitates error-prone data pre-processing. Here we propose a novel method of quantifying system stability based on eigenvalue tracking and Floquet Multipliers, which can be applied directly to diverse data without first removing trend and seasonality, and is robust to changing noise levels, as can be caused by merging signals from different sensors. We first demonstrate this approach with synthetic data and further show how glacier surge onset can be predicted from observed surface velocity time series. We then show that our method can be extended to analyze spatio-temporal data and illustrate this flexibility with remotely sensed Amazon rainforest vegetation productivity, highlighting the spatial patterns of whole-ecosystem destabilization. Our work applies critical slowing down theory to glacier dynamics for the first time, and provides a novel and flexible method to quantify the stability or resilience of a wide range of spatiotemporal systems, including climate subsystems, ecosystems, and transient landforms.

nlin.CD↗

arXiv2025

Improving the Noise Estimation of Latent Neural Stochastic Differential Equations

Latent neural stochastic differential equations (SDEs) have recently emerged as a promising approach for learning generative models from stochastic time series data. However, they systematically underestimate the noise level inherent in such data, limiting their ability to capture stochastic dynamics accurately. We investigate this underestimation in detail and propose a straightforward solution: by including an explicit additional noise regularization in the loss function, we are able to learn a model that accurately captures the diffusion component of the data. We demonstrate our results on a conceptual model system that highlights the improved latent neural SDE's capability to model stochastic bistable dynamics.

cs.LG↗

arXiv2025

The influence of data gaps and outliers on resilience indicators

The resilience, or stability, of major Earth system components is increasingly threatened by anthropogenic pressures, demanding reliable early warning signals for abrupt and irreversible regime shifts. Widely used data-driven resilience indicators based on variance and autocorrelation detect `critical slowing down', a signature of decreasing stability. However, the interpretation of these indicators is hampered by poorly understood interdependencies and their susceptibility to common data issues such as missing values and outliers. Here, we establish a rigorous mathematical analysis of the statistical dependency between variance- and autocorrelation-based resilience indicators, revealing that their agreement is fundamentally driven by the time series' initial data point. Using synthetic and empirical data, we demonstrate that missing values substantially weaken indicator agreement, while outliers introduce systematic biases that lead to overestimation of resilience based on temporal autocorrelation. Our results provide a necessary and rigorous foundation for preprocessing strategies and accuracy assessments across the growing number of disciplines that use real-world data to infer changes in system resilience.

nlin.AO↗

arXiv2025

Generating time-consistent dynamics with discriminator-guided image diffusion models

Realistic temporal dynamics are crucial for many video generation, processing and modelling applications, e.g. in computational fluid dynamics, weather prediction, or long-term climate simulations. Video diffusion models (VDMs) are the current state-of-the-art method for generating highly realistic dynamics. However, training VDMs from scratch can be challenging and requires large computational resources, limiting their wider application. Here, we propose a time-consistency discriminator that enables pretrained image diffusion models to generate realistic spatiotemporal dynamics. The discriminator guides the sampling inference process and does not require extensions or finetuning of the image diffusion model. We compare our approach against a VDM trained from scratch on an idealized turbulence simulation and a real-world global precipitation dataset. Our approach performs equally well in terms of temporal consistency, shows improved uncertainty calibration and lower biases compared to the VDM, and achieves stable centennial-scale climate simulations at daily time steps.

cs.LG↗

arXiv2025

Reconciled warning signals in observations and models imply approaching AMOC tipping point

Paleoclimate proxy records and models suggest that the Atlantic Meridional Overturning Circulation (AMOC) can transition abruptly between a strong and a weak state. Empirical warning signals in observational fingerprints indeed suggest a stability decline and raise concerns that the system may be approaching a tipping point. However, state-of-the-art Earth System Models (ESMs) do not consistently show such a stability loss, hence inconclusive in their projections of AMOC collapse under global warming. It remains unclear whether warning signals of AMOC tipping are overlooked in ESMs or overinterpreted in observations, calling for further investigations of AMOC stability. Here, based on the concept of critical slowing down, AMOC stability decline that can be interpreted as a warning signal of AMOC tipping is identified in the eastern SPNA in both observations and ESMs. This warning signal is in accordance with a physical indicator of AMOC stability, AMOC-induced freshwater convergence into the Atlantic basin. The observed signal can be reconciled with the modeled one only under warming exceeding the Paris Agreement goal, suggesting that AMOC stability is overestimated in ESMs. Our results suggest that the observed AMOC may indeed be losing stability and could thus reach a tipping point much earlier than state-of-the-art ESMs suggest.

physics.ao-ph↗

arXiv2025

Machine Learning for Predicting Chaotic Systems

Predicting chaotic dynamical systems is critical in many scientific fields, such as weather forecasting, but challenging due to the characteristic sensitive dependence on initial conditions. Traditional modeling approaches require extensive domain knowledge, often leading to a shift towards data-driven methods using machine learning. However, existing research provides inconclusive results on which machine learning methods are best suited for predicting chaotic systems. In this paper, we compare different lightweight and heavyweight machine learning architectures using extensive existing benchmark databases, as well as a newly introduced database that allows for uncertainty quantification in the benchmark results. In addition to state-of-the-art methods from the literature, we also present new advantageous variants of established methods. Hyperparameter tuning is adjusted based on computational cost, with more tuning allocated to less costly methods. Furthermore, we introduce the cumulative maximum error, a novel metric that combines desirable properties of traditional metrics and is tailored for chaotic systems. Our results show that well-tuned simple methods, as well as untuned baseline methods, often outperform state-of-the-art deep learning models, but their performance can vary significantly with different experimental setups. These findings highlight the importance of aligning prediction methods with data characteristics and caution against the indiscriminate use of overly complex models.

cs.LG↗

arXiv2025

Generative assimilation and prediction for weather and climate

Machine learning models have shown great success in predicting weather up to two weeks ahead, outperforming process-based benchmarks. However, existing approaches mostly focus on the prediction task, and do not incorporate the necessary data assimilation. Moreover, these models suffer from error accumulation in long roll-outs, limiting their applicability to seasonal predictions or climate projections. Here, we introduce Generative Assimilation and Prediction (GAP), a unified deep generative framework for assimilation and prediction of both weather and climate. By learning to quantify the probabilistic distribution of atmospheric states under observational, predictive, and external forcing constraints, GAP excels in a broad range of weather-climate related tasks, including data assimilation, seamless prediction, and climate simulation. In particular, GAP is competitive with state-of-the-art ensemble assimilation, probabilistic weather forecast and seasonal prediction, yields stable millennial simulations, and reproduces climate variability from daily to decadal time scales.

cs.LG↗

arXiv2025

Fast, Scale-Adaptive, and Uncertainty-Aware Downscaling of Earth System Model Fields with Generative Machine Learning

Accurate and high-resolution Earth system model (ESM) simulations are essential to assess the ecological and socio-economic impacts of anthropogenic climate change, but are computationally too expensive to be run at sufficiently high spatial resolution. Recent machine learning approaches have shown promising results in downscaling ESM simulations, outperforming state-of-the-art statistical approaches. However, existing methods require computationally costly retraining for each ESM and extrapolate poorly to climates unseen during training. We address these shortcomings by learning a consistency model (CM) that efficiently and accurately downscales arbitrary ESM simulations without retraining in a zero-shot manner. Our approach yields probabilistic downscaled fields at a resolution only limited by the observational reference data. We show that the CM outperforms state-of-the-art diffusion models at a fraction of computational cost while maintaining high controllability on the downscaling task. Further, our method generalizes to climate states unseen during training without explicitly formulated physical constraints.

physics.ao-ph↗

arXiv2025

Discontinuous stochastic forcing in Greenland ice core data

Paleoclimate proxy records from Greenland ice cores, archiving e.g. $δ^{18}$O as a proxy for surface temperature, show that sudden climatic shifts called Dansgaard-Oeschger events (DO) occurred repeatedly during the last glacial interval. They comprised substantial warming of the Arctic region from cold to milder conditions. Concomitant abrupt changes in the dust concentrations of the same ice cores suggest that sudden reorganisations of the hemispheric-scale atmospheric circulation have accompanied the warming events. Genuine bistability of the North Atlantic climate system is commonly hypothesised to explain the existence of stadial (cold) and interstadial (milder) periods in Greenland. However, the physical mechanisms that drove abrupt transitions from the stadial to the interstadial state, and more gradual yet still abrupt reverse transitions, remain debated. Here, we conduct a one-dimensional data-driven analysis of the Greenland temperature and atmospheric circulation proxies under the purview of stochastic processes. We take the Kramers-Moyal equation to estimate each proxy's drift and diffusion terms within a Markovian model framework. We then assess noise contributions beyond Gaussian white noise. The resulting stochastic differential equation (SDE) models feature a monostable drift for the Greenland temperature proxy and a bistable one for the atmospheric circulation proxy. Indicators of discontinuity in stochastic processes suggest to include higher-order terms of the Kramers-Moyal equation when modelling the Greenland temperature proxy's evolution. This constitutes a qualitative difference in the characteristics of the two time series, which should be further investigated from the standpoint of climate dynamics.

physics.ao-ph↗

arXiv2025

Physically Constrained Generative Adversarial Networks for Improving Precipitation Fields from Earth System Models

Precipitation results from complex processes across many scales, making its accurate simulation in Earth system models (ESMs) challenging. Existing post-processing methods can improve ESM simulations locally, but cannot correct errors in modelled spatial patterns. Here we propose a framework based on physically constrained generative adversarial networks (GANs) to improve local distributions and spatial structure simultaneously. We apply our approach to the computationally efficient ESM CM2Mc-LPJmL. Our method outperforms existing ones in correcting local distributions, and leads to strongly improved spatial patterns especially regarding the intermittency of daily precipitation. Notably, a double-peaked Intertropical Convergence Zone, a common problem in ESMs, is removed. Enforcing a physical constraint to preserve global precipitation sums, the GAN can generalize to future climate scenarios unseen during training. Feature attribution shows that the GAN identifies regions where the ESM exhibits strong biases. Our method constitutes a general framework for correcting ESM variables and enables realistic simulations at a fraction of the computational costs.

physics.ao-ph↗

arXiv2024

When Geoscience Meets Foundation Models: Towards General Geoscience Artificial Intelligence System

Artificial intelligence (AI) has significantly advanced Earth sciences, yet its full potential in to comprehensively modeling Earth's complex dynamics remains unrealized. Geoscience foundation models (GFMs) emerge as a paradigm-shifting solution, integrating extensive cross-disciplinary data to enhance the simulation and understanding of Earth system dynamics. These data-centric AI models extract insights from petabytes of structured and unstructured data, effectively addressing the complexities of Earth systems that traditional models struggle to capture. The unique strengths of GFMs include flexible task specification, diverse input-output capabilities, and multi-modal knowledge representation, enabling analyses that surpass those of individual data sources or traditional AI methods. This review not only highlights the key advantages of GFMs, but also presents essential techniques for their construction, with a focus on transformers, pre-training, and adaptation strategies. Subsequently, we examine recent advancements in GFMs, including large language models, vision models, and vision-language models, particularly emphasizing the potential applications in remote sensing. Additionally, the review concludes with a comprehensive analysis of the challenges and future trends in GFMs, addressing five critical aspects: data integration, model complexity, uncertainty quantification, interdisciplinary collaboration, and concerns related to privacy, trust, and security. This review offers a comprehensive overview of emerging geoscientific research paradigms, emphasizing the untapped opportunities at the intersection of advanced AI techniques and geoscience. It examines major methodologies, showcases advances in large-scale models, and discusses the challenges and prospects that will shape the future landscape of GFMs.

cs.AI↗