Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers

TL;DR

This paper introduces EcoL2, a new metric that evaluates neural PDE solvers by balancing accuracy and environmental impact, promoting sustainable scientific machine learning.

Contribution

It proposes EcoL2, a novel metric that incorporates carbon emissions into the evaluation of neural PDE solvers, addressing environmental concerns often overlooked in accuracy-focused assessments.

Findings

EcoL2 effectively balances accuracy and emissions in PDE solvers.

Experiments show EcoL2 provides a holistic performance and sustainability assessment.

The metric encourages development of environmentally sustainable neural PDE methods.

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.