Projecting sea-level change in various climate-change scenarios typically
involves running forward simulations of the Earth's gravitational, rotational
and deformational (GRD) response to ice mass change, which requires high
computational cost and time. Here we build neural-network emulators of
sea-level change at 27 coastal locations, due to the GRD effects associated
with future Antarctic Ice Sheet mass change over the 21st century. The
emulators are based on datasets produced using a numerical solver for the
static sea-level equation and published ISMIP6-2100 ice-sheet model simulations
referenced in the IPCC AR6 report. We show that the neural-network emulators
have an accuracy that is competitive with baseline machine learning emulators.
In order to quantify uncertainty, we derive well-calibrated prediction
intervals for simulated sea-level change via a linear regression postprocessing
technique that uses (nonlinear) machine learning model outputs, a technique
that has previously been applied to numerical climate models. We also
demonstrate substantial gains in computational efficiency: a feedforward
neural-network emulator exhibits on the order of 100 times speedup in
comparison to the numerical sea-level equation solver that is used for
training.

通过基于神经网络的模拟器，本研究在未来的气候变化情景下，建立了海平面变化与地球重力、旋转和形变（GRD）效应之间的关联。通过采用机器学习模型输出的非线性回归后处理技术，我们推导出了对模拟的海平面变化的预测区间，并展示了神经网络模拟器在准确性和计算效率上的优势。

利用不确定性的机器学习模拟南极冰盖引起的区域海平面变化

Uncertainty-enabled machine learning for emulation of regional sea-level  change caused by the Antarctic Ice Sheet

The ice shelves buttressing the Antarctic ice sheet determine the rate of
ice-discharge into the surrounding oceans. The geometry of ice shelves, and
hence their buttressing strength, is determined by ice flow as well as by the
local surface accumulation and basal melt rates, governed by atmospheric and
oceanic conditions. Contemporary methods resolve one of these rates, but
typically not both. Moreover, there is little information of how they changed
in time. We present a new method to simultaneously infer the surface
accumulation and basal melt rates averaged over decadal and centennial
timescales. We infer the spatial dependence of these rates along flow line
transects using internal stratigraphy observed by radars, using a kinematic
forward model of internal stratigraphy. We solve the inverse problem using
simulation-based inference (SBI). SBI performs Bayesian inference by training
neural networks on simulations of the forward model to approximate the
posterior distribution, allowing us to also quantify uncertainties over the
inferred parameters. We demonstrate the validity of our method on a synthetic
example, and apply it to Ekstr\"om Ice Shelf, Antarctica, for which newly
acquired radar measurements are available. We obtain posterior distributions of
surface accumulation and basal melt averaging over 42, 84, 146, and 188 years
before 2022. Our results suggest stable atmospheric and oceanographic
conditions over this period in this catchment of Antarctica. Use of observed
internal stratigraphy can separate the effects of surface accumulation and
basal melt, allowing them to be interpreted in a historical context of the last
centuries and beyond.

通过使用基于模拟的推理 (simulation-based inference) 方法和雷达观测到的内部地层学，我们在南极洲的 Ekstr"om 冰架上推断出过去 42 年、84 年、146 年和 188 年表面积累和底部融化的后分布，结果显示该流域在这段时期内的大气和海洋环境相对稳定。