Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers

2025-05-18

AI Summary

Current neural PDE solvers prioritize accuracy while neglecting carbon emissions during training and deployment. This work introduces carbon footprint as a core metric in scientific machine learning evaluation, proposing EcoL₂—a unified objective balancing accuracy and environmental cost. Methodologically, we develop a lifecycle carbon quantification framework spanning data acquisition, model training, and inference, integrating L₂ error with comprehensive carbon accounting across mainstream architectures—including PINNs and operator learning. Our contributions are threefold: (1) establishing the first sustainability quantification standard tailored to scientific AI; (2) shifting beyond purely accuracy-driven evaluation paradigms; and (3) empirically demonstrating EcoL₂’s ability to identify spurious “high-accuracy–high-emission” models across diverse PDE benchmarks, thereby providing a reproducible, comparable assessment benchmark for low-carbon, high-performance scientific AI systems.

Technology Category

• Machine Learning: Efficient ML / Green AI
• Search and Optimization: Learning to Search
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Sustainability and carbon-aware systems for Web, mobile, and WoT
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

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.

Problem

• Balancing accuracy and carbon emissions in neural PDE solvers
• Measuring environmental impact of PDE solver computations
• Developing sustainable metrics for scientific machine learning systems

Innovation

• Introduces EcoL2 metric for sustainable PDE solvers
• Balances accuracy and carbon emissions holistically
• Applies to data, training, and deployment phases