Ehsan Zeraatkar

Ehsan Zeraatkar, Rodion Podorozhny, Jelena Tešić

Reconstructing continuous physical fields from sparse, irregular observations is a central challenge in scientific machine learning, particularly for systems governed by partial differential equations (PDEs). Existing physics-informed methods typically enforce governing equations as soft penalty terms during optimization, often leading to gradient imbalance, instability, and degraded physical consistency under limited data. We introduce the Physics-Guided Transformer (PGT), a neural architecture that embeds physical structure directly into the self-attention mechanism. Specifically, PGT incorporates a heat-kernel-derived additive bias into attention logits, encoding diffusion dynamics and temporal causality within the representation. Query coordinates attend to these physics-conditioned context tokens, and the resulting features are decoded using a FiLM-modulated sinusoidal implicit network that adaptively controls spectral response. We evaluate PGT on the one-dimensional heat equation and two-dimensional incompressible Navier-Stokes systems. In sparse 1D reconstruction with 100 observations, PGT achieves a relative L2 error of 5.9e-3, significantly outperforming both PINNs and sinusoidal representations. In the 2D cylinder wake problem, PGT uniquely achieves both low PDE residual (8.3e-4) and competitive relative error (0.034), outperforming methods that optimize only one objective. These results demonstrate that embedding physics within attention improves stability, generalization, and physical fidelity under data-scarce conditions.

Arshia Kermani, Ehsan Zeraatkar, Habib Irani

The increasing computational demands of transformer models in time series classification necessitate effective optimization strategies for energy-efficient deployment. Our study presents a systematic investigation of optimization techniques, focusing on structured pruning and quantization methods for transformer architectures. Through extensive experimentation on three distinct datasets (RefrigerationDevices, ElectricDevices, and PLAID), we quantitatively evaluate model performance and energy efficiency across different transformer configurations. Our experimental results demonstrate that static quantization reduces energy consumption by 29.14% while maintaining classification performance, and L1 pruning achieves a 63% improvement in inference speed with minimal accuracy degradation. Our findings provide valuable insights into the effectiveness of optimization strategies for transformer-based time series classification, establishing a foundation for efficient model deployment in resource-constrained environments.

Ehsan Zeraatkar, Salah A Faroughi, Jelena Tešić

Super-resolution (SR) is crucial for enhancing the spatial fidelity of Earth System Model (ESM) outputs, allowing fine-scale structures vital to climate science to be recovered from coarse simulations. However, traditional deep super-resolution methods, including convolutional and transformer-based models, tend to exhibit spectral bias, reconstructing low-frequency content more readily than valuable high-frequency details. In this work, we introduce two frequency-aware frameworks: the Vision Transformer-Tuned Sinusoidal Implicit Representation (ViSIR), combining Vision Transformers and sinusoidal activations to mitigate spectral bias, and the Vision Transformer Fourier Representation Network (ViFOR), which integrates explicit Fourier-based filtering for independent low- and high-frequency learning. Evaluated on the E3SM-HR Earth system dataset across surface temperature, shortwave, and longwave fluxes, these models outperform leading CNN, GAN, and vanilla transformer baselines, with ViFOR demonstrating up to 2.6~dB improvements in PSNR and significantly higher SSIM. Detailed ablation and scaling studies highlight the benefit of full-field training, the impact of frequency hyperparameters, and the potential for generalization. The results establish ViFOR as a state-of-the-art, scalable solution for climate data downscaling. Future extensions will address temporal super-resolution, multimodal climate variables, automated parameter selection, and integration of physical conservation constraints to broaden scientific applicability.

Ehsan Zeraatkar, Salah Faroughi, Jelena Tešić

Purpose: Earth system models (ESMs) integrate the interactions of the atmosphere, ocean, land, ice, and biosphere to estimate the state of regional and global climate under a wide variety of conditions. The ESMs are highly complex; thus, deep neural network architectures are used to model the complexity and store the down-sampled data. This paper proposes the Vision Transformer Sinusoidal Representation Networks (ViSIR) to improve the ESM data's single image SR (SR) reconstruction task. Methods: ViSIR combines the SR capability of Vision Transformers (ViT) with the high-frequency detail preservation of the Sinusoidal Representation Network (SIREN) to address the spectral bias observed in SR tasks. Results: The ViSIR outperforms SRCNN by 2.16 db, ViT by 6.29 dB, SIREN by 8.34 dB, and SR-Generative Adversarial (SRGANs) by 7.93 dB PSNR on average for three different measurements. Conclusion: The proposed ViSIR is evaluated and compared with state-of-the-art methods. The results show that the proposed algorithm is outperforming other methods in terms of Mean Square Error(MSE), Peak-Signal-to-Noise-Ratio(PSNR), and Structural Similarity Index Measure(SSIM).