34 research outputs found
High-Dimensional Dependency Structure Learning for Physical Processes
In this paper, we consider the use of structure learning methods for
probabilistic graphical models to identify statistical dependencies in
high-dimensional physical processes. Such processes are often synthetically
characterized using PDEs (partial differential equations) and are observed in a
variety of natural phenomena, including geoscience data capturing atmospheric
and hydrological phenomena. Classical structure learning approaches such as the
PC algorithm and variants are challenging to apply due to their high
computational and sample requirements. Modern approaches, often based on sparse
regression and variants, do come with finite sample guarantees, but are usually
highly sensitive to the choice of hyper-parameters, e.g., parameter
for sparsity inducing constraint or regularization. In this paper, we present
ACLIME-ADMM, an efficient two-step algorithm for adaptive structure learning,
which estimates an edge specific parameter in the first step,
and uses these parameters to learn the structure in the second step. Both steps
of our algorithm use (inexact) ADMM to solve suitable linear programs, and all
iterations can be done in closed form in an efficient block parallel manner. We
compare ACLIME-ADMM with baselines on both synthetic data simulated by partial
differential equations (PDEs) that model advection-diffusion processes, and
real data (50 years) of daily global geopotential heights to study information
flow in the atmosphere. ACLIME-ADMM is shown to be efficient, stable, and
competitive, usually better than the baselines especially on difficult
problems. On real data, ACLIME-ADMM recovers the underlying structure of global
atmospheric circulation, including switches in wind directions at the equator
and tropics entirely from the data.Comment: 21 pages, 8 figures, International Conference on Data Mining 201
Indicator patterns of forced change learned by an artificial neural network
Many problems in climate science require the identification of signals
obscured by both the "noise" of internal climate variability and differences
across models. Following previous work, we train an artificial neural network
(ANN) to identify the year of input maps of temperature and precipitation from
forced climate model simulations. This prediction task requires the ANN to
learn forced patterns of change amidst a background of climate noise and model
differences. We then apply a neural network visualization technique (layerwise
relevance propagation) to visualize the spatial patterns that lead the ANN to
successfully predict the year. These spatial patterns thus serve as "reliable
indicators" of the forced change. The architecture of the ANN is chosen such
that these indicators vary in time, thus capturing the evolving nature of
regional signals of change. Results are compared to those of more standard
approaches like signal-to-noise ratios and multi-linear regression in order to
gain intuition about the reliable indicators identified by the ANN. We then
apply an additional visualization tool (backward optimization) to highlight
where disagreements in simulated and observed patterns of change are most
important for the prediction of the year. This work demonstrates that ANNs and
their visualization tools make a powerful pair for extracting climate patterns
of forced change.Comment: The first version of this manuscript has been submitted to the
Journal of Advances in Modeling Earth Systems (JAMES), 202