While AI weather models excel at short-to-medium range forecasts (up to 15 days), they frequently suffer from ill-defined "instabilities" when rolled out over longer horizons. This work addresses the lack of a formal taxonomy by categorizing these failures into three distinct regimes: blow-up, drift, and loss of seasonality, through year-long rollouts of nine state-of-the-art AI weather models. Our analysis reveals that stability hinges on the treatment of small spatio-temporal scales: unstable models amplify high-frequency energy, while stable models act as denoisers when noise is added to their inputs. Far from reducing these models to mere stochastic parrots, our findings highlight that stable models generate unique weather trajectories, conditioned on the initial state. We verify our findings through ablation studies on architectural design choices, conducted using state-of-the-art Vision Transformer (ViT) AI weather model architectures.

Abstract Recent advances in AI weather forecasting have led to the emergence of so‐called “foundation models”, typically defined by expensive pretraining and minimal fine‐tuning for downstream tasks. However, in the natural sciences, a desirable foundation model should also encode meaningful statistical relationships between the underlying physical variables. This study evaluates the performance of the state‐of‐the‐art Aurora foundation model in predicting hydrological variables, which were not included during pretraining. We introduce a lightweight approach using shallow decoders trained on the latent representations of the pretrained model to predict these new variables. As a baseline, we compare this to fine‐tuning the full model, which allows further optimization of the latent space while incorporating new variables into both inputs and outputs. The decoder‐based approach requires 43% less training time and 53% less memory, while achieving strong accuracy across various hydrological variables and preserving desirable properties of the foundation model, such as autoregressive stability. Notably, decoder accuracy depends on the physical correlation between the new variables and those used during pretraining, indicating that Aurora's latent space captures meaningful physical relationships. The decoders outperform UNet, climatology, and persistence baselines on variables related to pretraining, showing the benefits of the latent space. In this sense, we argue that an important quality metric for foundation models in Earth sciences is their ability to be extended to new variables without a full fine‐tuning. This provides a new perspective for making foundation models more accessible to communities with limited computational resources, while supporting broader adoption in Earth sciences.

AI weather models and weather-based foundation models have demonstrated impressive skills in short- to medium-range forecasts. While most weather models become unstable on longer time scales, a wide variety of AI climate emulators have been proposed, raising questions about the fundamental differences between these approaches.In this work, we compare state-of-the-art models when producing rollouts on annual time scales. We quantify and characterize different types of instability: smoothing, visual artifacts, drift, and loss of seasonality. This analysis highlights the previously unreported stability of the Aurora foundation model and the Earth System Foundation Model (ESFM) for rollouts longer than 35 years.To encompass more diverse representations of possible states of the Earth, ESFM is pretrained on a variety of CMIP6 datasets from the historical period, in addition to the ERA5 reanalysis commonly used in AI models. ESFM also includes climate forcings for physically driven long rollouts. We demonstrate the benefits of CMIP6 pretraining when finetuning on new CMIP6 datasets, including datasets with higher resolution, unseen physical processes, and climate change scenarios.Overall, this work opens perspectives to adapt large-scale pretrained foundation models to the specific challenges of climate projections.

With increased availability of high quality diverse weather data, including reanalysis, satellite, surface stations, climate model data, the amount of data-driven foundation models (FM) in the environmental field has increased significantly over the past years with forecasting performances matching and sometimes exceeding physics-based numerical model predictions. However, most FMs are trained with one dataset or a few datasets with similar sampling and/or resolution properties. While the proposed models achieve remarkable results with the datasets and variables they are trained on; it would be hard to anticipate similar performance under partially missing observations across different dimensions at test time. Similarly, typical design considerations risk limiting usage of these FMs to other heterogeneous datasets concerning the broader Earth sciences community.We propose Earth System Foundation Model (ESFM), an FM capable of handling heterogeneous observations (i) across different resolutions, (ii) with spatially gridded and non-gridded nature, and (iii) with little to extreme sparsity. We achieve this through simple architectural design considerations and a masked training protocol. Namely, we bin similar ranges of grid resolutions together, while optimizing a different set of tokenizers for significantly different resolution bins to accommodate a single FM for observations across different resolutions. Similarly, we tokenize non-gridded data (i.e., station) separately with a single pixel patch size. Finally, we use variable specific tokenizers, coupled with learnable missing observation tokens, that allow ESFM to naturally accommodate for various subsets of available variables across different spatiotemporal positions. In this exploratory study, we show that ESFM is a flexible FM that can achieve impressive forecasting performance under different adverse setups with missing test data across any dimension on ERA5; spatio-temporal and inter-variable. We further test forecasting performance of ESFM in very sparse satellite imagery (3% pixel occupancy) data as well as station data. The proposed framework; also compatible for different backbone architectures than the one we experimented with; provides a general approach for integrating diverse Earth system data sources with varying resolutions, sampling patterns, and availability. This makes ESFM particularly relevant for the broader environmental sciences and Earth and space sciences, where challenges related to data heterogeneity and missing observations are central to the development of next-generation data-driven environmental modeling systems.

Foundation models (FMs) for the Earth system learn statistical relationships between physical variables across massive datasets to enable versatile downstream applications through finetuning, separating them from task-specific weather models. Here, we introduce Earth System Foundation Model (ESFM), a fully open model building on the 3D Swin UNet backbone of the pioneering Aurora model. ESFM introduces extensions that increase functionality and foster adoption in climate sciences. First, the encoding scheme and training protocols have been extended to handle diverse datasets, including those containing missing values across all spatio-temporal dimensions such as satellite data, as well as station data, all under one backbone. Axial attention is introduced to capture inter-variable dependencies. As a result ESFM skillfully predicts variables in regions or on pressure levels where no data is present at the initial time, while preserving inter-variable relationships, for example between temperature, pressure, and humidity. Individual variable tokenization enables different sets of variables to be shuffled during training and simplifies the process of building extensions for new downstream tasks. Adaptive layer norm-based ensembles allow for a simple yet effective way to transform deterministic ESFM to a probabilistic FM. We present findings using dense gridded data (ERA5, CMIP6), regionally masked dense data, sparse gridded MODIS satellite data, and station data. Results demonstrate competitive or superior performance relative to state-of-the-art benchmarks. Case studies of Super Typhoon Doksuri (2023) and 2024 sudden stratospheric warming events show accurate positional and magnitude estimations of extreme weather. ESFM retains the strengths of previous foundation models, such as long-term stability, but facilitates application to a variety of downstream tasks.

Cardiac magnetic resonance imaging (CMR) captures rich spatiotemporal information about ventricular structure and motion, but conventional risk models use only a few image-derived indices from selected cardiac phases. We present a latent dynamical model that encodes bi-ventricular anatomy and full-cycle cine motion as a continuous latent trajectory, using heart-rate-aware neural ordinary differential equation (ODE) dynamics and a graph-based mesh autoencoder to reconstruct anatomically consistent 3D+t ventricular motion. A covariate-conditioned prior defines the expected end-diastolic latent state, and a Cox proportional hazards model tests whether deviations from this prior predict incident heart failure. We studied 72,386 UK Biobank participants without baseline cardiovascular disease, including 367 incident heart failure events. In a held-out evaluation subset, adding the latent score to refitted pooled cohort equations improved the stratified C-index from 0.704 to 0.785, compared with 0.764 for seven established cardiac markers. Compared with non-graph and non-ODE approaches, the proposed model gave the best trade-off between reconstruction fidelity, generative realism, and downstream prognostic performance. These results suggest that continuous full-cycle modeling of ventricular motion provides informative cardiac phenotypes beyond conventional CMR summaries, while external validation in more representative patient cohorts is required before clinical risk-prediction use.

Foundation models for the Earth system have gained popularity, as they are starting to surpass numerical solvers in the accuracy of predicting Earth’s condition while requiring fewer computational resources. The Earth System Foundation Model (ESFM) contributes to this research direction by further extending the foundation models' flexibility.The forecasting capabilities of ESFM are achieved in an autoregressive manner, using data from the t0 - Δt and t0 timesteps to produce a prediction for t0 + Δt. This approach is effective on weather timescales. Moreover, we find that it also delivers encouraging results for long-term forecasts, showing reasonable zero-shot subseasonal-to-seasonal (S2S) predictions (15–40 days). However, S2S predictions can be further improved while preserving weather skills. This work investigates strategies for this purpose. On such timescales, it is crucial to produce probabilistic predictions to better represent inherent uncertainty. Probabilistic predictions are realised with the introduction of multiple decoder heads (tails) for each variable. Each tail is intended to simulate a different possible trajectory, which, when combined, provides an estimate of the most probable outcome together with the spread of feasible values. To better estimate the distribution of possible values on the S2S timescale, additional trajectories are generated by running multiple predictive rollouts with different initial conditions.Another strategy to improve S2S rollouts is to fine-tune the model to produce outputs for more distant steps. To this end, we leverage LoRA adapters (Hu et al., 2022), which are trained for each subsequent rollout step. This approach effectively improves predictive performance on long horizons, without significantly affecting training complexity or inference cost.We also observe that some predictive variables of the model, such as climate forcings, are slowly evolving and can benefit from incorporating inputs from a more distant past than the t0 - Δt and t0 timesteps commonly used. To investigate this, we introduce an Attention Temporal Aggregator in the encoder, which leverages learned patch embeddings from an arbitrary number of previous timesteps and attends to those that are most informative for a given variable. In this way, for rapidly changing variables such as wind speed, the model focuses on the most recent data, whereas for slowly evolving variables such as sea surface temperature, it can utilise a broader range of inputs.Overall, our experiments provide new insights into the development of foundation models for the Earth system, enabling improved predictions on S2S timescales, while conserving performance for weather forecasts.References:E. J. Hu, Y. Shen, P. Wallis, Z. Allen-Zhu, Y. Li, S. Wang, L. Wang, W. Chen, et al. Lora: Low-rank adaptation of large language models. ICLR, 1(2):3, 2022

Weather foundation models are increasingly expected to operate under heterogeneous and imperfect observation settings while remaining computationally scalable. Building on the Earth System Foundation Model (ESFM) setting for heterogeneous data integration, we explore how Mixture-of-Experts (MoE) can support robust and efficient learning in multi-modal weather foundation models.We introduce ESFM-MoE, an exploratory direction that combines conditional computation with climate-semantic routing, a routing principle that encourages expert specialization aligned with meaningful geophysical structure, rather than treating expert selection as a purely generic scaling mechanism. The motivation is that Earth-system data exhibit strong spatial organization, regime-like variability, and modality-dependent uncertainties; MoE offers a natural way to allocate capacity adaptively and promote structured specialization under such heterogeneity.In this work, we discuss the design space and practical considerations of integrating MoE into Earth-system foundation models, focusing on how routing objectives and inductive biases can shape expert behavior and improve utilization. We highlight potential benefits for robustness to missing observations, scalable training and inference, and outline promising directions for climate-aware expert specialization in next-generation weather foundation models.

This paper continues the exploration of Machine Learning (ML) parameterization for radiative transfer for the ICOsahedral Nonhydrostatic weather and climate model (ICON). Three ML models, developed in Part I of this study, are coupled to ICON. More specifically, a UNet model and a bidirectional recurrent neural network (RNN) with long short-term memory (LSTM) are compared against a random forest. The ML parameterizations are coupled to the ICON code that includes OpenACC compiler directives to enable GPUs support. The coupling is done through Infero, developed by ECMWF, and PyTorch-Fortran. The most accurate model is the bidirectional RNN with physics-informed normalization strategy and heating rate penalty, but the fluxes above 15 km height are computed with a simplified formula for numerical stability reasons. The presented setup enables stable aquaplanet simulations with ICON for several weeks at a resolution of about 80 km and compare well with the physics-based radiative transfer solver ecRad. However, the achieved speed up when using the emulators and the minimum required memory usage relative to the GPU-enabled ecRad depend strongly on the Neural Network (NN) architecture. Future studies may explore physics-constraint emulators that predict heating rates inside the atmospheric model and fluxes at the top.

Recent advances in AI weather forecasting have led to the emergence of so-called "foundation models", typically defined by expensive pretraining and minimal fine-tuning for downstream tasks. However, in the natural sciences, a desirable foundation model should also encode meaningful statistical relationships between the underlying physical variables. This study evaluates the performance of the state-of-the-art Aurora foundation model in predicting hydrological variables, which were not considered during pretraining. We introduce a lightweight approach using shallow decoders trained on the latent representations of the pretrained model to predict these new variables. As a baseline, we compare this to fine-tuning the full model, which allows further optimization of the latent space while incorporating new variables into both inputs and outputs. The decoder-based approach requires 50% less training time and 35% less memory, while achieving strong accuracy across various hydrological variables and preserving desirable properties of the foundation model, such as autoregressive stability. Notably, decoder accuracy depends on the physical correlation between the new variables and those used during pretraining, indicating that Aurora's latent space captures meaningful physical relationships. In this sense, we argue that an important quality metric for foundation models in Earth sciences is their ability to be extended to new variables without a full fine-tuning. This provides a new perspective for making foundation models more accessible to communities with limited computational resources, while supporting broader adoption in Earth sciences.

Optoacoustic (OA) imaging is based on excitation of biological tissues with nanosecond-duration laser pulses followed by subsequent detection of ultrasound waves generated via light-absorption-mediated thermoelastic expansion. OA imaging features a powerful combination between rich optical contrast and high resolution in deep tissues. This enabled the exploration of a number of attractive new applications both in clinical and laboratory settings. However, no standardized datasets generated with different types of experimental set-up and associated processing methods are available to facilitate advances in broader applications of OA in clinical settings. This complicates an objective comparison between new and established data processing methods, often leading to qualitative results and arbitrary interpretations of the data. In this paper, we provide both experimental and synthetic OA raw signals and reconstructed image domain datasets rendered with different experimental parameters and tomographic acquisition geometries. We further provide trained neural networks to tackle three important challenges related to OA image processing, namely accurate reconstruction under limited view tomographic conditions, removal of spatial undersampling artifacts and anatomical segmentation for improved image reconstruction. Specifically, we define 44 experiments corresponding to the aforementioned challenges as benchmarks to be used as a reference for the development of more advanced processing methods.

A data-driven inverse design method based on neural networks is proposed for turbomachinery. In the devised methodology, design parameters are provided as input to the neural network, and performance attributes, e.g. efficiency, as output. Once trained, the network is used for inverse design, i.e. target performance values are prescribed to generate various design parameter sets. Through empirical experiments, it is observed that the true efficiency of the network-generated radial turbine and thrust bearing designs are in good agreement with the prescribed target efficiencies. Furthermore, the proposed model can be used to accurately generate designs beyond the range of the training data set, showing strong generalization properties. The proposed approach offers the additional benefit of easy implementation, being fully data-driven and not requiring any modifications to the data generation process. As long as data is available, the method can readily be extended to account for multi-component and multi-physics aspects. After a model is trained using a set of design parameters, the proposed method can also be used to generate a subset of design parameters for prescribed target attributes with ease. The data-driven inverse design method represents a novel design approach in the age of big data, and is highly relevant and applicable for turbomachinery designs where an abundance of design data, pairing design parameters and target attributes is available. Notably, through generating a large variety of accurate designs with improved performance, the proposed method effectively indicates trust regions in the design space where further design explorations could be carried out, showing a significant impact on optimisation strategies.

Multiple sclerosis (MS) is a neurological disease of the central nervous system that is the leading cause of non-traumatic disability in young adults. Clinical laboratory tests and neuroimaging studies are the standard methods to diagnose and monitor MS. However, due to infrequent clinic visits, it is fundamental to identify remote and frequent approaches for monitoring MS, which enable timely diagnosis, early access to treatment, and slowing down disease progression. In this work, we investigate the most reliable, clinically useful, and available features derived from mobile and wearable devices as well as their ability to distinguish people with MS (PwMS) from healthy controls, recognize MS disability and fatigue levels. To this end, we formalize clinical knowledge and derive behavioral markers to characterize MS. We evaluate our approach on a dataset we collected from 55 PwMS and 24 healthy controls for a total of 489 days conducted in free-living conditions. The dataset contains wearable sensor data – e.g., heart rate – collected using an arm-worn device, smartphone data – e.g., phone locks – collected through a mobile application, patient health records – e.g., MS type – obtained from the hospital, and self-reports – e.g., fatigue level – collected using validated questionnaires administered via the mobile application. Our results demonstrate the feasibility of using features derived from mobile and wearable sensors to monitor MS. Our findings open up opportunities for continuous monitoring of MS in free-living conditions and can be used to evaluate and guide the effectiveness of treatments, manage the disease, and identify participants for clinical trials.

Modelling the transfer of radiation through the atmosphere is a key component of weather and climate models. The operational radiation scheme in the Icosahedral Nonhydrostatic Weather and Climate Model (ICON) is ecRad. The radiation scheme ecRad is accurate but computationally expensive. It is operationally run in ICON on a grid coarser than the dynamical grid and the time step interval between two calls is significantly larger. This is known to reduce the quality of the climate prediction. A possible approach to accelerate the computation of the radiation fluxes is to use machine learning methods. Machine learning methods can significantly speed up computation of radiation, but they may cause climate drifts if they do not respect essential physical laws. In this work, we study random forest and neural network emulations of ecRad. We study different strategies to compare the stability of the emulations. Concerning the neural network, we compare loss functions with an additional energy penalty term and we observe that modifying the loss function is essential to predict accurately the heating rates. The random forest emulator, which is significantly faster to train than the neural network is used as a reference model that the neural network must outperform. The random forest emulator can become extremely accurate but the memory requirement quickly become prohibitive. Various numerical experiments are performed to illustrate the properties of the machine learning emulators.

Despite the major progress of deep models as learning machines, uncertainty estimation remains a major challenge. Existing solutions rely on modified loss functions or architectural changes. We propose to compensate for the lack of built-in uncertainty estimates by supplementing any network, retrospectively, with a subsequent vine copula model, in an overall compound we call Vine-Copula Neural Network (VCNN). Through synthetic and real-data experiments, we show that VCNNs could be task (regression/classification) and architecture (recurrent, fully connected) agnostic while providing reliable and better-calibrated uncertainty estimates, comparable to state-of-the-art built-in uncertainty solutions.

As climate modellers prepare their code for kilometre-scale global simulations, the computationally demanding radiative transfer parameterization is a prime candidate for machine learning (ML) emulation. Because of the computational demands, many weather centres use a reduced spatial grid and reduced temporal frequency for radiative transfer calculations in their forecast models. This strategy is known to affect forecast quality, which further motivates the use of ML-based radiative transfer parameterizations. This paper contributes to the discussion on how to incorporate physical constraints into an ML-based radiative parameterization, and how different neural network (NN) designs and output normalisation affect prediction performance. A random forest (RF) is used as a baseline method, with the European Centre for Medium-Range Weather Forecasts (ECMWF) model ecRad, the operational radiation scheme in the Icosahedral Nonhydrostatic Weather and Climate Model (ICON), used for training. Surprisingly, the RF is not affected by the top-of-atmosphere (TOA) bias found in all NNs tested (e.g., MLP, CNN, UNet, RNN) in this and previously published studies. At lower atmospheric levels, the RF is able to compete with all NNs tested, but its memory requirements quickly become prohibitive. For a fixed memory size, most NNs outperform the RF except at TOA. For the best emulator, we use a recurrent neural network architecture which closely imitates the physical process it emulates. We additionally normalize the shortwave and longwave fluxes to reduce their dependence from the solar angle and surface temperature respectively. Finally, we train the model with an additional heating rates penalty in the loss function.

Data and code working together is fundamental to machine learning (ML), but the context around datasets and interactions between datasets and code are in general captured only rudimentarily. Context such as how the dataset was prepared and created, what source data were used, what code was used in processing, how the dataset evolved, and where it has been used and reused can provide much insight, but this information is often poorly documented. That is unfortunate since it makes datasets into black-boxes with potentially hidden characteristics that have downstream consequences. We argue that making dataset preparation more accessible and dataset usage easier to record and document would have significant benefits for the ML community: it would allow for greater diversity in datasets by inviting modification to published sources, simplify use of alternative datasets and, in doing so, make results more transparent and robust, while allowing for all contributions to be adequately credited. We present a platform, Renku, designed to support and encourage such sustainable development and use of data, datasets, and code, and we demonstrate its benefits through a few illustrative projects which span the spectrum from dataset creation to dataset consumption and showcasing.

Optoacoustic (OA) imaging is based on optical excitation of biological tissues with nanosecond-duration laser pulses and detection of ultrasound (US) waves generated by thermoelastic expansion following light absorption. The image quality and fidelity of OA images critically depend on the extent of tomographic coverage provided by the US detector arrays. However, full tomographic coverage is not always possible due to experimental constraints. One major challenge concerns an efficient integration between OA and pulse-echo US measurements using the same transducer array. A common approach toward the hybridization consists in using standard linear transducer arrays, which readily results in arc-type artifacts and distorted shapes in OA images due to the limited angular coverage. Deep learning methods have been proposed to mitigate limited-view artifacts in OA reconstructions by mapping artifactual to artifact-free (ground truth) images. However, acquisition of ground truth data with full angular coverage is not always possible, particularly when using handheld probes in a clinical setting. Deep learning methods operating in the image domain are then commonly based on networks trained on simulated data. This approach is yet incapable of transferring the learned features between two domains, which results in poor performance on experimental data. Here, we propose a signal domain adaptation network (SDAN) consisting of i) a domain adaptation network to reduce the domain gap between simulated and experimental signals and ii) a sides prediction network to complement the missing signals in limited-view OA datasets acquired from a human forearm by means of a handheld linear transducer array. The proposed method showed improved performance in reducing limited-view artifacts without the need for ground truth signals from full tomographic acquisitions.

We present a Bayesian inference for a three-dimensional hydrodynamic model of Lake Geneva with stochastic weather forcing and high-frequency observational datasets. This is achieved by coupling a Bayesian inference package, SPUX, with a hydrodynamics package, MITgcm, into a single framework, SPUX-MITgcm. To mitigate uncertainty in the atmospheric forcing, we use a smoothed particle Markov chain Monte Carlo method, where the intermediate model state posteriors are resampled in accordance with their respective observational likelihoods. To improve the uncertainty quantification in the particle filter, we develop a bi-directional long short-term memory (BiLSTM) neural network to estimate lake skin temperature from a history of hydrodynamic bulk temperature predictions and atmospheric data. This study analyzes the benefit and costs of such a state-of-the-art computationally expensive calibration and assimilation method for lakes.

For stochastic models with intractable likelihood functions, approximate Bayesian computation offers a way of approximating the true posterior through repeated comparisons of observations with simulated model outputs in terms of a small set of summary statistics. These statistics need to retain the information that is relevant for constraining the parameters but cancel out the noise. They can thus be seen as thermodynamic state variables, for general stochastic models. For many scientific applications, we need strictly more summary statistics than model parameters to reach a satisfactory approximation of the posterior. Therefore, we propose to use a latent representation of deep neural networks based on Autoencoders as summary statistics. To create an incentive for the encoder to encode all the parameter-related information but not the noise, we give the decoder access to explicit or implicit information on the noise that has been used to generate the training data. We validate the approach empirically on two types of stochastic models.