mlsanityData to 14 Oct 2026

Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers

arXiv 2505.12556 ↗First posted 18 May 2025cs.LG cs.AIcited by 2

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Abstract (arXiv)

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.

Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Builds on 34 of its 67 references that are in the map. First posted on arXiv 18 May 2025.

Builds on

34 of 67 references.

References · 34

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22 more
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Cited by year

Citing papers per year: 2025: 2.

2 papers.

  1. 2025Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systemscited by 0
  2. 2025Performance-Carbon Trade-Offs across Architectural Biases in Shear Flow Forecastingcited by 0