arXiv subjects

Hira Saleem

Publications and source records attributed to Hira Saleem.

8 recordsLinked to original sources

arXiv2026

SGNO: Spectral Generator Neural Operators for Stable Long Horizon PDE Rollouts

Autoregressive neural PDE surrogates predict future states by repeatedly applying a learned one-step operator. This is a simple and widely used method, but small one-step errors can accumulate during long rollouts. The resulting drift often appears as spectral amplitude distortion, phase misalignment, and nonlinear mode-interaction error. These effects are especially important for time-dependent PDEs with clear Fourier structure. We introduce the Spectral Generator Neural Operator (SGNO), a structured autoregressive neural operator for long-horizon PDE forecasting. SGNO organizes each learned one-step map as a structured spectral evolution update. A real-valued nonpositive diagonal generator provides a gain-controlled spectral backbone, while a learned correction pathway with complex-valued spectral mixing completes the residual evolution. This design gives the autoregressive step an evolution-like structure while retaining the flexibility needed for dissipative, dispersive, transport-dominated, and nonlinear PDEs. SGNO is designed for periodic linear and semilinear evolution PDEs with Fourier multiplier linear dynamics. Across ten mechanism-matched APEBench tasks spanning this regime, SGNO consistently outperforms strong single-step autoregressive baselines in long-horizon rollout accuracy, reducing GMean100 by a median of 74.8% relative to the strongest available non-SGNO baseline, with per-task reductions ranging from 13.6% to 92.9%. The gains are strongest on dispersive and transport-dominated tasks, as well as tasks involving nonlinear closure and mode coupling. Spectral diagnostics show lower spectral energy error and improved rollout-level phase fidelity. Ablations show that the constrained generator, the structured update, and the learned correction pathway each contribute to performance. The code is available at https://github.com/cruiseresearchgroup/SGNO.

cs.LG↗

arXiv2026

PINN-Cast: Exploring the Role of Continuous-Depth NODE in Transformers and Physics Informed Loss as Soft Physical Constraints in Short-term Weather Forecasting

Operational weather prediction has long relied on physics-based numerical weather prediction (NWP), whose accuracy comes at the cost of substantial compute and complex simulation workflows. Recent transformer-based forecasters offer efficient data-driven alternatives, however transformers are physics-agnostic models. Additionally, standard transformer encoders evolve representations through discrete layer updates that may be less suited to modeling smooth latent dynamics. In this work, we propose a continuous-depth transformer encoder for weather forecasting that integrates Neural Ordinary Differential Equation (Neural ODE) dynamics within each encoder block. Specifically, we replace discrete residual updates with ODE-based updates solved using adaptive numerical integration. We also introduce a two-branch attention module that combines conventional patch-wise self-attention with an auxiliary branch that applies a derivative operator to attention logits, providing an additional change-sensitive interaction signal. To further align forecasts with governing principles, we propose a customized physics-informed training objective that enforces physical consistency as a soft constraint. We evaluate the proposed method against a standard discrete transformer baseline and an existing continuous-time Neural ODE forecasting variant, demonstrating the importance of PINN-Cast in short term weather forecasting.

cs.LG↗

arXiv2026

A-UTE: Advection Informed, Uncertainty Aware Temperature Emulator

Physics-based Earth system models (ESMs) are essential for attributing climate change and generating scenario projections, yet their reliance on high-resolution numerical integration makes multi-decadal experiments expensive. In parallel, deep learning has delivered strong gains in short-range weather forecasting; however, auto-regressive roll-outs can accumulate error and become unstable when extended to decade-scale climate emulation. We introduce A-UTE: Advection Informed, Uncertainty Aware Temperature Emulator, aimed at stable multi-year emulation across heterogeneous climate models and grid resolutions. A-UTE is trained on various physics-based models at varying spatial resolutions to emulate temperature fields over a 10-year horizon. A-UTE formulates climate emulation as a forward-time stochastic dynamical system. We propose an auto-regressive ODE-SDE surrogate in which transport dynamics are constrained by an advection consistent ODE component, while a learned neural SDE term models coarse-grained variability and cross-model discrepancy at monthly resolution. We train A-UTE under negative log-likelihood objective for principled uncertainty estimates and probabilistic evaluation. Experiments across 20 climate models show that A-UTE improves long roll-out stability and accuracy relative to relevant baselines, advancing data-driven climate emulation with explicit physical structure and uncertainty-aware predictions.

physics.ao-ph↗

arXiv2025

STC-ViT: Spatio Temporal Continuous Vision Transformer for Medium-range Global Weather Forecasting

Operational Numerical Weather Prediction (NWP) system relies on computationally expensive physics-based models. Recently, transformer models have shown remarkable potential in weather forecasting achieving state-of-the-art results. However, traditional transformers discretize spatio-temporal dimensions, limiting their ability to model continuous dynamical weather processes. Moreover, their reliance on increased depth to capture complex dependencies results in higher computational cost and parameter redundancy. We address these issues with STC-ViT, a Spatio-Temporal Continuous Vision Transformer for weather forecasting. STC-ViT integrates a Fourier Neural Operator (FNO) for global spatial operators with a transformer parameterised Neural ODE for continuous-time dynamics, yielding a space-time continuous model for weather forecasting. Our proposed method achieves competitive forecasting performance even with a shallow, single-layer transformer encoder mitigating the reliance on deeper networks. STC-ViT generates complete forecast trajectories with an inference speed of only 0.125 seconds and achieves strong medium-range forecasting skill on 1.5-degree WeatherBench 2 as compared to state-of-the-art data-driven and NWP models trained on higher-resolution data, with substantially lower data and compute costs. We also provide detailed empirical analysis on model's performance with respect to denser time grids, higher-accuracy ODE solvers, and deeper transformer stacks.

cs.LG↗

arXiv2025

Generate the Forest before the Trees -- A Hierarchical Diffusion model for Climate Downscaling

Downscaling is essential for generating the high-resolution climate data needed for local planning, but traditional methods remain computationally demanding. Recent years have seen impressive results from AI downscaling models, particularly diffusion models, which have attracted attention due to their ability to generate ensembles and overcome the smoothing problem common in other AI methods. However, these models typically remain computationally intensive. We introduce a Hierarchical Diffusion Downscaling (HDD) model, which introduces an easily-extensible hierarchical sampling process to the diffusion framework. A coarse-to-fine hierarchy is imposed via a simple downsampling scheme. HDD achieves competitive accuracy on ERA5 reanalysis datasets and CMIP6 models, significantly reducing computational load by running on up to half as many pixels with competitive results. Additionally, a single model trained at 0.25° resolution transfers seamlessly across multiple CMIP6 models with much coarser resolution. HDD thus offers a lightweight alternative for probabilistic climate downscaling, facilitating affordable large-ensemble high-resolution climate projections. See a full code implementation at: https://github.com/HDD-Hierarchical-Diffusion-Downscaling/HDD-Hierarchical-Diffusion-Downscaling.

cs.CV↗

arXiv2025

Information Retrieval for Climate Impact

The purpose of the MANILA24 Workshop on information retrieval for climate impact was to bring together researchers from academia, industry, governments, and NGOs to identify and discuss core research problems in information retrieval to assess climate change impacts. The workshop aimed to foster collaboration by bringing communities together that have so far not been very well connected -- information retrieval, natural language processing, systematic reviews, impact assessments, and climate science. The workshop brought together a diverse set of researchers and practitioners interested in contributing to the development of a technical research agenda for information retrieval to assess climate change impacts.

cs.IR↗

arXiv2024

Resolution-Agnostic Transformer-based Climate Downscaling

Understanding future weather changes at regional and local scales is crucial for planning and decision-making, particularly in the context of extreme weather events, as well as for broader applications in agriculture, insurance, and infrastructure development. However, the computational cost of downscaling Global Climate Models (GCMs) to the fine resolutions needed for such applications presents a significant barrier. Drawing on advancements in weather forecasting models, this study introduces a cost-efficient downscaling method using a pretrained Earth Vision Transformer (Earth ViT) model. Initially trained on ERA5 data to downscale from 50 km to 25 km resolution, the model is then tested on the higher resolution BARRA-SY dataset at a 3 km resolution. Remarkably, it performs well without additional training, demonstrating its ability to generalize across different resolutions. This approach holds promise for generating large ensembles of regional climate simulations by downscaling GCMs with varying input resolutions without incurring additional training costs. Ultimately, this method could provide more comprehensive estimates of potential future changes in key climate variables, aiding in effective planning for extreme weather events and climate change adaptation strategies.

cs.CV↗

arXiv2024

Identifying high resolution benchmark data needs and Novel data-driven methodologies for Climate Downscaling

We address the essential role of information retrieval in enhancing climate downscaling, focusing on the need for high-resolution datasets and the application of deep learning models. We explore the requirements for acquiring detailed spatial and temporal climate data, crucial for accurate local forecasts, and discuss how deep learning (DL) techniques can significantly improve downscaling precision by modelling the complex relationships between climate variables. Additionally, we examine the specific challenges related to the retrieval of relevant climatic data, emphasizing methods for efficient data extraction and utilization to support advanced model training. This research underscores an integrated approach, combining information retrieval, deep learning, and climate science to refine the process of climate downscaling, aiming to produce more accurate and actionable local climate projections.

physics.ao-ph↗