GNSS-FM: A Self-Supervised Foundation Model for Daily GNSS Displacement Time Series

Displacement time series from Global Navigation Satellite Systems (GNSS) are essential for a wide range of applications, including monitoring tectonic crustal deformations and investigating the different stages of the earthquake cycle. Machine learning methods have proven promising for GNSS applications; however, most remain fully supervised. This creates a bottleneck as labeled data are scarce, even though large amounts of unlabeled GNSS data are freely available. We present GNSS-FM, a self-supervised foundation model for daily GNSS time series. The model uses a dual-stream input combining displacement and velocity-like increments, and is pretrained using a masked latent prediction objective with vector-quantized targets adapted from wav2vec 2.0, with several modifications for geodetic data. Pretrained on data from over 17,000 globally distributed GNSS stations, an analysis of the learned codebook suggests that the representations capture the main signal types in GNSS displacement data, including seismic offsets, tectonic drift, and seasonal patterns. The foundation model is later fine-tuned on two downstream tasks, namely 90-day displacement forecasting and seismic step localization, where it outperforms strong task-specific baselines in both cases. These results show that self-supervised pretraining is a promising approach for GNSS time series analysis.

Correcting Neural Operator Spectral Bias via Diffusion Posterior Sampling with Sparse Observations

Neural operator surrogates (NO) approximate PDE solutions orders of magnitude faster than numerical solvers, but suffer from spectral bias: high-frequency content is systematically attenuated, limiting reliability where fine-scale structure matters. Sparse sensor measurements of the field are often available too, offering pointwise accuracy without spectral distortion but covering only a small fraction of the domain. We address this by treating NO predictions as auxiliary observations in a diffusion posterior sampling framework. Our method, FreqNO-DPS (https://github.com/niccoloperrone/FreqNO-DPS), combines an unconditional score-based diffusion prior, trained on high-fidelity simulations, with diffusion posterior sampling (DPS) conditioned on sparse observations and guided by a frozen neural operator. Naive integration reintroduces the surrogate's spectral bias; we resolve this with a closed-form, spectrally shaped guidance score that weights the surrogate by its frequency-dependent accuracy and needs no denoiser backpropagation. A distribution-free analysis bounds the approximation error across the frequency-diffusion-time plane and shows the guidance's frequency dependence is preserved regardless of distributional assumptions. On 3D elastic wavefield prediction at 5% and 2% sensor coverage, the method reaches near-zero spectral bias across all bands, where both the surrogate and sensor-only DPS show systematic high-frequency attenuation. Isotropic guidance, the natural baseline, improves pointwise accuracy but carries the bias into the posterior nearly intact, confirming that frequency-dependent calibration is essential, not merely beneficial. The framework needs only paired surrogate/reference data and exploits no problem-specific structure beyond the residual's approximate spectral diagonality, verifiable for new surrogates via the coherence diagnostic we provide.

Can AI Weather Models Predict Beyond Two Weeks? A Quantitative Benchmark and Analysis of Long Rollouts

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.

Finetuning a Weather Foundation Model with Lightweight Decoders for Unseen Physical Processes

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.

Integrating Fourier Neural Operators with Diffusion Models to improve Spectral Representation of Synthetic Earthquake Ground Motion Response

Nuclear reactor buildings must be designed to withstand the dynamic load induced by strong ground motion earthquakes. For this reason, their structural behavior must be assessed in multiple realistic ground shaking scenarios (e.g., the Maximum Credible Earthquake). However, earthquake catalogs and recorded seismograms may not always be available in the region of interest. Therefore, synthetic earthquake ground motion is progressively being employed, although with some due precautions: earthquake physics is sometimes not well enough understood to be accurately reproduced with numerical tools, and the underlying epistemic uncertainties lead to prohibitive computational costs related to model calibration. In this study, we propose an AI physics-based approach to generate synthetic ground motion, based on the combination of a neural operator that approximates the elastodynamics Green's operator in arbitrary source-geology setups, enhanced by a denoising diffusion probabilistic model. The diffusion model is trained to correct the ground motion time series generated by the neural operator. Our results show that such an approach promisingly enhances the realism of the generated synthetic seismograms, with frequency biases and Goodness-Of-Fit (GOF) scores being improved by the diffusion model. This indicates that the latter is capable to mitigate the mid-frequency spectral falloff observed in the time series generated by the neural operator. Our method showcases fast and cheap inference in different site and source conditions.

Multiple-Input Fourier Neural Operator (MIFNO) for source-dependent 3D elastodynamics

Numerical simulations are essential tools to evaluate the solution of the wave equation in complex settings, such as three-dimensional (3D) domains with heterogeneous properties. However, their application is limited by high computational costs and existing surrogate models lack the flexibility of numerical solvers. This work introduces the Multiple-Input Fourier Neural Operator (MIFNO) to deal with structured 3D fields representing material properties as well as vectors describing the source characteristics. The MIFNO is applied to the problem of elastic wave propagation in the Earth's crust. It is trained on the HEMEW^S-3D database containing 30000 earthquake simulations in different heterogeneous domains with random source positions and orientations. Outputs are time- and space-dependent surface wavefields. The MIFNO predictions are assessed as good to excellent based on Goodness-Of-Fit (GOF) criteria. Wave arrival times and wave fronts' propagation are very accurate since 80% of the predictions have an excellent phase GOF. The fluctuations amplitudes are good for 87% of the predictions. The envelope score is hindered by the small-scale fluctuations that are challenging to capture due to the complex physical phenomena associated with high-frequency features. Nevertheless, the MIFNO can generalize to sources located outside the training domain and it shows good generalization ability to a real complex overthrust geology. When focusing on a region of interest, transfer learning improves the accuracy with limited additional costs, since GOF scores improved by more than 1 GOF unit with only 500 additional specific samples. The MIFNO is the first surrogate model offering the flexibility of an earthquake simulator with varying sources and material properties. Its good accuracy and massive speed-up offer new perspectives to replace numerical simulations in many-query problems.

Fourier Neural Operator Surrogate Model to Predict 3D Seismic Waves Propagation

With the recent rise of neural operators, scientific machine learning offers new solutions to quantify uncertainties associated with high-fidelity numerical simulations. Traditional neural networks, such as Convolutional Neural Networks (CNN) or Physics-Informed Neural Networks (PINN), are restricted to the prediction of solutions in a predefined configuration. With neural operators, one can learn the general solution of Partial Differential Equations, such as the elastic wave equation, with varying parameters. There have been very few applications of neural operators in seismology. All of them were limited to two-dimensional settings, although the importance of three-dimensional (3D) effects is well known. In this work, we apply the Fourier Neural Operator (FNO) to predict ground motion time series from a 3D geological description. We used a high-fidelity simulation code, SEM3D, to build an extensive database of ground motions generated by 30,000 different geologies. With this database, we show that the FNO can produce accurate ground motion even when the underlying geology exhibits large heterogeneities. Intensity measures at moderate and large periods are especially well reproduced. We present the first seismological application of Fourier Neural Operators in 3D. Thanks to the generalizability of our database, we believe that our model can be used to assess the influence of geological features such as sedimentary basins on ground motion, which is paramount to evaluating site effects.