15 research outputs found
Postprocessing of Ensemble Weather Forecasts Using Permutation-invariant Neural Networks
Statistical postprocessing is used to translate ensembles of raw numerical
weather forecasts into reliable probabilistic forecast distributions. In this
study, we examine the use of permutation-invariant neural networks for this
task. In contrast to previous approaches, which often operate on ensemble
summary statistics and dismiss details of the ensemble distribution, we propose
networks which treat forecast ensembles as a set of unordered member forecasts
and learn link functions that are by design invariant to permutations of the
member ordering. We evaluate the quality of the obtained forecast distributions
in terms of calibration and sharpness, and compare the models against classical
and neural network-based benchmark methods. In case studies addressing the
postprocessing of surface temperature and wind gust forecasts, we demonstrate
state-of-the-art prediction quality. To deepen the understanding of the learned
inference process, we further propose a permutation-based importance analysis
for ensemble-valued predictors, which highlights specific aspects of the
ensemble forecast that are considered important by the trained postprocessing
models. Our results suggest that most of the relevant information is contained
in few ensemble-internal degrees of freedom, which may impact the design of
future ensemble forecasting and postprocessing systems.Comment: Submitted to Artificial Intelligence for the Earth System
Approximation-Generalization Trade-offs under (Approximate) Group Equivariance
The explicit incorporation of task-specific inductive biases through symmetry
has emerged as a general design precept in the development of high-performance
machine learning models. For example, group equivariant neural networks have
demonstrated impressive performance across various domains and applications
such as protein and drug design. A prevalent intuition about such models is
that the integration of relevant symmetry results in enhanced generalization.
Moreover, it is posited that when the data and/or the model may only exhibit
or symmetry, the optimal or
best-performing model is one where the model symmetry aligns with the data
symmetry. In this paper, we conduct a formal unified investigation of these
intuitions. To begin, we present general quantitative bounds that demonstrate
how models capturing task-specific symmetries lead to improved generalization.
In fact, our results do not require the transformations to be finite or even
form a group and can work with partial or approximate equivariance. Utilizing
this quantification, we examine the more general question of model
mis-specification i.e. when the model symmetries don't align with the data
symmetries. We establish, for a given symmetry group, a quantitative comparison
between the approximate/partial equivariance of the model and that of the data
distribution, precisely connecting model equivariance error and data
equivariance error. Our result delineates conditions under which the model
equivariance error is optimal, thereby yielding the best-performing model for
the given task and data