TopoCast: A Topological Fidelity Framework for Evaluating Transformer-Based Time Series Forecasting

Topology-Preserving State Space Representation for Diagnosing Weather Forecast Models

PINA-Net: Physics-Constrained Nonautoregressive Network for Spatiotemporal Meteorological Forecasting in Complex Maritime Environments

Accurate regional weather forecasting in complex maritime environments is challenging due to intricate atmospheric dynamics. While deep learning presents a promising alternative to numerical weather prediction (NWP), current paradigms face an inherent tradeoff. Autoregressive (AR) models suffer from recursive error accumulation and spectral decay, whereas pure computer vision approaches neglect physical laws, yielding dynamically inconsistent predictions. To address these limitations, we propose the physics-informed non-AR network (PINA-Net) to reconcile visual sharpness with physical consistency. Our framework synergizes a lightweight 3-D spatiotemporal encoder with coordinate attention and a cumulative residual strategy, enabling the one-shot generation of high-fidelity sequences without error propagation. Crucially, we integrate a physics-constrained loss function that embeds partial differential equations (PDEs) for mass conservation and divergence directly into the optimization process. Extensive experiments on a high-resolution meteorological dataset demonstrate that PINA-Net significantly outperforms state-of-the-art baselines. The model achieves superior numerical accuracy and structural similarity while effectively suppressing nonphysical artifacts in wind vector fields. Furthermore, by evaluating predictive uncertainty, the framework provides reliable probabilistic boundaries, offering a robust solution adhering to the intrinsic kinematic constraints of the atmosphere.

Graph Neural Networks with dilated convolutions for geomagnetic field forecasting: a single-station topological approach

Geomagnetic field forecasting is critical for mitigating space weather hazards, yet single-station prediction remains a challenge due to the complex, non-linear coupling of vector components. In this work, we propose a Graph Neural Network (GNN) architecture enhanced with Temporal Convolutional Networks (TCN) to forecast the H, D, and Z components. By modeling the observatory’s sensors as nodes in a learned directed graph, the system captures dynamic spatio-temporal correlations between orthogonal components. We introduce a dilated inception layer to efficiently capture multi-scale temporal patterns. Experimental results using 1-min downsampled data from the MAGDAS station (Ecuador) show that our model achieves a Mean Absolute Error (MAE) of 0.8036 nT, outperforming Vector Autoregression (VAR) and thoroughly optimized LSTM baselines. While the Naive Persistence baseline yields a marginally lower global MAE due to the statistical dominance of quiet-time periods, the proposed GNN-TCN provides vastly superior phase tracking ( R = 0.9950 ) and structural stability. Rigorous evaluation under varying space weather conditions reveals robust performance, maintaining a highly controlled error even during the top 5% most severe local geomagnetic storms. These findings, supported by power spectral density analysis, indicate that high-frequency fluctuations at a single station are dominated by instrumental and stochastic noise, making temporal filtering via downsampling essential. Ultimately, this proof-of-concept study demonstrates that utilizing a learned adjacency matrix as an adaptable structural regularization, rather than extracting a fixed physical law, provides a highly stable and effective framework for short-term geomagnetic field forecasting.

Measuring Structured Predictability in Neural Training Dynamics: A Cross-Regime Study

Modern deep networks are trained through long update trajectories, yet their temporal organization remains less systematically characterized than architectures, losses, or optimizers. We study short-horizon predictability as a measure of temporal redundancy: where, when, and under which training conditions recent updates contain information about near-future parameter motion. We combine three complementary probe families, displacement-direction, subspace-residual, and predictor-based probes, with convention-aware, null-calibrated group-level readouts, and apply them to multi-pass vision training on CIFAR and public Pythia pretraining checkpoints. Across both regimes, vector-like tensors such as normalization parameters and biases (auxiliary parameters) exhibit simpler short-horizon dynamics than matrix-like feature-transforming weights (bulk parameters), whose predictable behavior concentrates in localized, time-varying pockets. Agreement within and across probe families, and with independent trajectory diagnostics, indicates that these measurements capture intrinsic trajectory structure, while probe differences distinguish complementary forms of temporal organization. Controlled CIFAR comparisons further show that architecture and training recipe systematically modulate the measured structure. A Pythia-70M case study further exposes a sequence of role-, depth-, and scale-dependent events, including bulk ESA falling below the random sign-agreement level and the emergence and redistribution of predictable qkv pockets across layers. These results position short-horizon predictability as a retrospective, parameter-resolved diagnostic of training dynamics.

The balance between compactness and forecast accuracy of data-driven latent-space reduced-order models in controlled wake flows

Model-based active flow control requires predictive models that are accurate, stable, and fast enough for real-time optimisation. In controlled wake flows, this is often achieved through Reduced-Order Models (ROMs) that first compress high-dimensional velocity snapshots into a latent space and then learn a time- stepping predictor for the dynamics in the latent space. Here, we study how the choice of the spatial encoder affects the predictability of the resulting latent coordinates for wake flows under control inputs. Using two actuated 2D wake configurations, a simplified truck wake and the fluidic pinball, we compare Proper Orthogonal Decomposition (POD) against nonlinear Convolutional Autoencoders (CAEs) and two types of variational autoencoders for compression, and evaluate several temporal predictors based on Long Short-Term Memory networks. CAEs achieve higher compression efficiency and sharper short-term reconstructions, but they produce latent dynamics that are more irregular and with broadband spectral content. As a consequence, long-horizon forecasts degrade faster and show a higher probability of catastrophic divergence than POD-based models. POD yields smoother latent trajectories that are easier to learn and extrapolate, leading to more reliable predictions beyond the short- term regime. These results reveal a clear trade-off between compactness and forecast accuracy, and suggest that the stability of the latent dynamics prediction can outweigh maximal compression. This is particularly relevant for control strategies rooted in forecasts of the dynamics, such as model predictive control and reinforcement learning. The findings provide practical guidance for designing actuation-aware, hardware-feasible predictive ROMs for real-time flow control.

Enhancing computational efficiency in multiscale systems using deep learning of coordinates and flow maps

Multiscale systems are expensive to simulate because fast dynamics require small time-steps, while slow dynamics require long prediction horizons. We propose latent hierarchical time-stepping (L-HiTS), which combines nonlinear coordinate discovery with multiscale flow-map learning. A deep autoencoder first compresses the high-dimensional PDE state into a validated low-dimensional latent space. Residual neural network time-steppers are then trained and coupled directly in this reduced space using validation-based hierarchy selection and vectorized prediction. Unlike multiscale HiTS, L-HiTS performs recursive forecasting in latent coordinates and reconstructs the full state only after prediction. The method is validated on the FitzHugh–Nagumo model, the chaotic Kuramoto–Sivashinsky equation, and a two-dimensional Burgers’ system. L-HiTS achieves comparable prediction accuracy to multiscale HiTS while substantially reducing training and prediction costs, with near order-of-magnitude prediction-time savings in the reported cases.