Stephen J Roberts

Taniya Kapoor, Abhishek Chandra, Anastasios Stamou et al.

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.

Matthew Willetts, Stephen J Roberts, Christopher C Holmes

In semi-supervised learning for classification, it is assumed that every ground truth class of data is present in the small labelled dataset. Many real-world sparsely-labelled datasets are plausibly not of this type. It could easily be the case that some classes of data are found only in the unlabelled dataset -- perhaps the labelling process was biased -- so we do not have any labelled examples to train on for some classes. We call this learning regime $\textit{semi-unsupervised learning}$, an extreme case of semi-supervised learning, where some classes have no labelled exemplars in the training set. First, we outline the pitfalls associated with trying to apply deep generative model (DGM)-based semi-supervised learning algorithms to datasets of this type. We then show how a combination of clustering and semi-supervised learning, using DGMs, can be brought to bear on this problem. We study several different datasets, showing how one can still learn effectively when half of the ground truth classes are entirely unlabelled and the other half are sparsely labelled.