Romit Maulik

AAAI Conference 2025 Conference Paper

Semi-Implicit Neural Ordinary Differential Equations

• Hong Zhang
• Ying Liu
• Romit Maulik

Classical neural ODEs trained with explicit methods are intrinsically limited by stability, crippling their efficiency and robustness for stiff learning problems that are common in graph learning and scientific machine learning. We present a semi-implicit neural ODE approach that exploits the partitionable structure of the underlying dynamics. Our technique leads to an implicit neural network with significant computational advantages over existing approaches because of enhanced stability and efficient linear solves during time integration. We show that our approach outperforms existing approaches on a variety of applications including graph classification and learning complex dynamical systems. We also demonstrate that our approach can train challenging neural ODEs where both explicit methods and fully implicit methods are intractable.

NeurIPS Conference 2024 Conference Paper

Scaling transformer neural networks for skillful and reliable medium-range weather forecasting

• Tung Nguyen
• Rohan Shah
• Hritik Bansal
• Troy Arcomano
• Romit Maulik
• Veerabhadra Kotamarthi
• Ian Foster
• Sandeep Madireddy

Weather forecasting is a fundamental problem for anticipating and mitigating the impacts of climate change. Recently, data-driven approaches for weather forecasting based on deep learning have shown great promise, achieving accuracies that are competitive with operational systems. However, those methods often employ complex, customized architectures without sufficient ablation analysis, making it difficult to understand what truly contributes to their success. Here we introduce Stormer, a simple transformer model that achieves state-of-the art performance on weather forecasting with minimal changes to the standard transformer backbone. We identify the key components of Stormer through careful empirical analyses, including weather-specific embedding, randomized dynamics forecast, and pressure-weighted loss. At the core of Stormer is a randomized forecasting objective that trains the model to forecast the weather dynamics over varying time intervals. During inference, this allows us to produce multiple forecasts for a target lead time and combine them to obtain better forecast accuracy. On WeatherBench 2, Stormer performs competitively at short to medium-range forecasts and outperforms current methods beyond 7 days, while requiring orders-of-magnitude less training data and compute. Additionally, we demonstrate Stormer’s favorable scaling properties, showing consistent improvements in forecast accuracy with increases in model size and training tokens. Code and checkpoints are available at https: //github. com/tung-nd/stormer.

EAAI Journal 2023 Journal Article

Physics-informed neural networks for mesh deformation with exact boundary enforcement

• Atakan Aygun
• Romit Maulik
• Ali Karakus