Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers
This addresses the problem of excessive carbon emissions in scientific machine learning for researchers and engineers, representing an incremental step toward sustainability.
The paper tackles the environmental impact of neural PDE solvers by introducing the EcoL2 metric, which balances model accuracy with carbon emissions across data collection, training, and deployment, demonstrating its application across physics-informed and operator learning architectures.
Real-world systems, from aerospace to railway engineering, are modeled with partial differential equations (PDEs) describing the physics of the system. Estimating robust solutions for such problems is essential. Deep learning-based architectures, such as neural PDE solvers, have recently gained traction as a reliable solution method. The current state of development of these approaches, however, primarily focuses on improving accuracy. The environmental impact of excessive computation, leading to increased carbon emissions, has largely been overlooked. This paper introduces a carbon emission measure for a range of PDE solvers. Our proposed metric, EcoL2, balances model accuracy with emissions across data collection, model training, and deployment. Experiments across both physics-informed machine learning and operator learning architectures demonstrate that the proposed metric presents a holistic assessment of model performance and emission cost. As such solvers grow in scale and deployment, EcoL2 represents a step toward building performant scientific machine learning systems with lower long-term environmental impact.