Abstract Natural porous media are highly heterogeneous, with flow and transport controlled by pore‐space morphology and connectivity. Consequently, classical continuum models often fail to describe observed transport under strong heterogeneity. A key challenge is identifying physically interpretable transport models from sparse observational data. We address this using a physics‐informed, data‐driven machine‐learning framework combining symbolic regression with genetic programming system identification, a stochastic optimization approach that discovers candidate partial differential equations (PDEs) directly from data. We apply it to two classical experimental data sets of solute transport. For Scheidegger's (1959) breakthrough‐curve measurements in Berea sandstones, a long‐standing benchmark for anomalous transport, the framework identifies data‐consistent, physically interpretable models using only sparse outlet observations and physical constraints. These include fractional advection–dispersion equations with temporal and spatial fractional operators: the temporal derivative represents memory effects from solute trapping in dead‐end pores, whereas the spatial derivative captures nonlocal transport from preferential flow paths and conductivity heterogeneity. For the Levy and Berkowitz (2003, https://doi.org/10.1016/s0169‐7722(02)00204‐8 ) data, the framework recovers both classical and anomalous transport representations depending on medium heterogeneity, distinguishing Fickian from non‐Fickian regimes from sparse breakthrough curves alone. The identified models are validated against independent data at different injection rates. Both data sets are intentionally sparse (one and four breakthrough curves, respectively), so these results should be read as evidence of feasibility under severe data scarcity, not as a general demonstration across broad classes of porous media. They illustrate the potential of symbolic‐regression‐based PDE discovery as an interpretable, physically constrained framework for transport‐model identification in heterogeneous geologic media.
Abstract Accurate predictions of intensity and structure of tropical cyclones (TCs) are crucial for disaster warning, prevention and mitigation. Traditional dynamical models with coarse horizontal resolutions suffer from systematic underprediction of TC intensity, whereas those with fine horizontal resolutions require intensive computations. Deep learning (DL)‐based models are computationally efficient yet substantially underpredict the TC intensity. To enhance the prediction of DL‐based weather models for TC intensities and structures, a hybrid framework (HybSR‐TC) is proposed here. By integrating a Swin Transformer backbone with multi‐variable processing and meta‐upsampling techniques, HybSR‐TC is trained based on low‐resolution (0.25°) forecasts of Pangu‐Weather and high‐resolution (2 km) weather research and forecasting forecasts with accurate TC tracks and well simulated intensities and structures. For TC predictions, HybSR‐TC maps the 6‐hr Pangu‐Weather forecasts of surface pressure and wind fields at 0.25° resolution to 2‐km resolution fields without the requirement for massive computational costs. HybSR‐TC can better capture the rapid intensification and temporal evolution of TCs than Pangu‐Weather and bilinear interpolation. HybSR‐TC produces significantly smaller errors of TC intensity and structure than Pangu‐Weather and bilinear interpolation, until approximately 10‐day lead times. Thus, the ability of HybSR‐TC to enhance the forecasts of TC intensity and structure based on the low‐resolution forecasts from AI models has been demonstrated.
Abstract Determining earthquake magnitude and location through fast, automated methods is fundamental for seismic monitoring. Recent studies have shown that Large Language Models (LLMs) can operate as pattern‐recognition systems capable of handling novel domains and purely numerical tasks. Here, we assess the utility of LLMs for earthquake characterization and propose a novel approach based on a small LLM called TinyLlama. We adapt the LLM for seismology through fine‐tuning on a subset of Italian earthquakes using the LoRA technique, which involves retraining only about 0.1% of the model parameters. Our method takes station coordinates, P‐wave arrival times, and peak ground velocities in a small window (0.2 s) around the P‐wave and accurately estimates earthquake magnitude, location, and origin time without using a seismic velocity model. To explore the potential for rapid characterization, we consider only stations where the P‐wave arrives within 5 s of the first triggered station. Compared to standard automatic methods currently used by INGV in Italy our model achieves comparable performance in magnitude estimation and superior accuracy in epicenter, hypocenter and origin time estimation. Validation using both P‐ and S‐waves shows only a slight performance improvement that does not justify the additional latency. We explored a range of data splitting strategies and found that the LLM‐based seismic method is robust. Our results highlight the ability of LLMs to function as effective tools in seismology and suggest their potential for advancing data‐driven approaches to rapid earthquake characterization.
Abstract Surface Quasi‐Geostrophic (SQG) theory provides a closed‐form mapping from surface buoyancy to interior stream function under the assumption that interior potential vorticity (PV) vanishes (Q=0). In realistic flows, however, the interior PV is typically nonzero. Here we use machine learning to determine whether surface buoyancy can be used to infer additional information about interior flow when the interior PV is non‐zero and SQG theory is not expected to work well. We perform controlled numerical experiments with a multilayer QG model spanning three regimes: a canonical SQG case (Q=0) and two multilayer quasi‐geostrophic cases (Q≠0) with linear and exponential zonal velocity shear profiles, correspondingly. We then use these data to train a Vision Transformer (ViT) to predict the streamfunction at all levels from the surface buoyancy in each regime, and we compare it with the predictions of SQG theory. In the SQG‐consistent regime, the ViT recovers the SQG analytical predictions to within 2% normalized error. When interior PV is present, the SQG calculation develops systematic depth‐dependent amplitude biases and pattern degradation, as expected; the ViT shows better skill in predicting the interior flow and reduces these errors by approximately 50%–90%, depending on depth and regime. These results demonstrate that learned operators can accurately predict interior structure from surface data alone, even when classical assumptions break down. This suggests a potential for an improved theory in the regime of non‐zero interior PV.
Abstract A wide selection of linear and non‐linear dimensionality reduction techniques is evaluated on synthetic tsunami data that is the basis for tsunami hazard assessment and computational forecasting. The data were computed from earthquake rupture forecasts (ERFs) supplying initial generation conditions and a linear long‐wave Green's function approach to efficiently calculate tsunami propagation. The dimensionality reduction techniques include various forms of principal component analysis, manifold learning, and neural networks. Both external (e.g., mutual information) and internal (silhouette) metrics are used to evaluate clustering in the reduced dimension, focusing on peak‐nearshore tsunami amplitudes (PNTA) along a nearshore isobath and time‐series (marigrams) at specific nearshore locations. This evaluation is intentionally scoped to cluster‐based downsampling to produce probabilistic inundation maps. For our test case along the Nankai subduction zone, manifold learning methods produced the highest clustering metric scores for PNTA profiles among the examined dimensionality reduction techniques. The marigram results are less consistent, owing primarily to uncertainty in defining appropriate clusters in the original high‐dimensional (ambient) space to establish a “ground truth.” A novel application of using the integrative ERF‐tsunami approach is that features extracted in the reduced domain, particularly from manifold learning, can be mapped back to rupture zones along the fault. This yields targeted fault information associated with unique PNTA profiles and marigram characteristics, such as late‐arriving waves. Further testing would be needed for application‐specific workflows and more complex fault systems, but results from this single subduction zone case study support the consideration of non‐linear techniques (e.g., manifold learning) as alternatives to linear methods.
