Accurate representations of unknown and sub-grid physical processes through
parameterizations (or closure) in numerical simulations with quantified
uncertainty are critical for resolving the coarse-grained partial differential
equations that govern many problems ranging from weather and climate prediction
to turbulence simulations. Recent advances have seen machine learning (ML)
increasingly applied to model these subgrid processes, resulting in the
development of hybrid physics-ML models through the integration with numerical
solvers. In this work, we introduce a novel framework for the joint estimation
and uncertainty quantification of physical parameters and machine learning
parameterizations in tandem, leveraging differentiable programming. Achieved
through online training and efficient Bayesian inference within a
high-dimensional parameter space, this approach is enabled by the capabilities
of differentiable programming. This proof of concept underscores the
substantial potential of differentiable programming in synergistically
combining machine learning with differential equations, thereby enhancing the
capabilities of hybrid physics-ML modeling.

本研究介绍一种新的框架，通过可微编程实现联合估计和不确定性量化，用于同时估计物理参数和机器学习参数化，以增强混合物理 - 机器学习建模的能力。

利用可微编程的不确定性量化进行联合参数和参数化推断

Joint Parameter and Parameterization Inference with Uncertainty  Quantification through Differentiable Programming

The representation of nonlinear sub-grid processes, especially clouds, has
been a major source of uncertainty in climate models for decades.
Cloud-resolving models better represent many of these processes and can now be
run globally but only for short-term simulations of at most a few years because
of computational limitations. Here we demonstrate that deep learning can be
used to capture many advantages of cloud-resolving modeling at a fraction of
the computational cost. We train a deep neural network to represent all
atmospheric sub-grid processes in a climate model by learning from a
multi-scale model in which convection is treated explicitly. The trained neural
network then replaces the traditional sub-grid parameterizations in a global
general circulation model in which it freely interacts with the resolved
dynamics and the surface-flux scheme. The prognostic multi-year simulations are
stable and closely reproduce not only the mean climate of the cloud-resolving
simulation but also key aspects of variability, including precipitation
extremes and the equatorial wave spectrum. Furthermore, the neural network
approximately conserves energy despite not being explicitly instructed to.
Finally, we show that the neural network parameterization generalizes to new
surface forcing patterns but struggles to cope with temperatures far outside
its training manifold. Our results show the feasibility of using deep learning
for climate model parameterization. In a broader context, we anticipate that
data-driven Earth System Model development could play a key role in reducing
climate prediction uncertainty in the coming decade.

利用深度学习可以以极小的计算代价代替传统的云细度建模的层状参数化方法，实现全球多年的气候预测。