  Improving predictive understanding of Earth system variability and change
requires data-model integration. Efficient data-model integration for complex
models requires surrogate modeling to reduce model evaluation time. However,
building a surrogate of a large-scale Earth system model (ESM) with many output
variables is computationally intensive because it involves a large number of
expensive ESM simulations. In this effort, we propose an efficient surrogate
method capable of using a few ESM runs to build an accurate and
fast-to-evaluate surrogate system of model outputs over large spatial and
temporal domains. We first use singular value decomposition to reduce the
output dimensions, and then use Bayesian optimization techniques to generate an
accurate neural network surrogate model based on limited ESM simulation
samples. Our machine learning based surrogate methods can build and evaluate a
large surrogate system of many variables quickly. Thus, whenever the quantities
of interest change such as a different objective function, a new site, and a
longer simulation time, we can simply extract the information of interest from
the surrogate system without rebuilding new surrogates, which significantly
saves computational efforts. We apply the proposed method to a regional
ecosystem model to approximate the relationship between 8 model parameters and
42660 carbon flux outputs. Results indicate that using only 20 model
simulations, we can build an accurate surrogate system of the 42660 variables,
where the consistency between the surrogate prediction and actual model
simulation is 0.93 and the mean squared error is 0.02. This highly-accurate and
fast-to-evaluate surrogate system will greatly enhance the computational
efficiency in data-model integration to improve predictions and advance our
understanding of the Earth system.
