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Register a new userCapturing missing physics in climate model parameterizations using neural differential equations
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Even with todays immense computational resources, climate models cannot resolve every cloud in the atmosphere or eddying swirl in the ocean. However, collectively these small-scale turbulent processes play a key role in setting Earths climate. Climate models attempt to represent unresolved scales via surrogate models known as parameterizations. These have limited fidelity and can exhibit structural deficiencies. Here we demonstrate that neural differential equations (NDEs) may be trained by highly resolved fluid-dynamical models of the scales to be parameterized and those NDEs embedded in an ocean model. They can incorporate conservation laws and are stable in time. We argue that NDEs provide a new route forward to the development of surrogate models for climate science, opening up exciting new opportunities.
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A new framework is proposed for the evaluation of stochastic subgrid-scale parameterizations in the context of MAOOAM, a coupled ocean-atmosphere model of intermediate complexity. Two physically-based parameterizations are investigated, the first one based on the singular perturbation of Markov operator, also known as homogenization. The second one is a recently proposed parameterization based on the Ruelles response theory. The two parameterization are implemented in a rigorous way, assuming however that the unresolved scale relevant statistics are Gaussian. They are extensively tested for a low-order version known to exhibit low-frequency variability, and some preliminary results are obtained for an intermediate-order version. Several different configurations of the resolved-unresolved scale separations are then considered. Both parameterizations show remarkable performances in correcting the impact of model errors, being even able to change the modality of the probability distributions. Their respective limitations are also discussed.
Over the last couple of years, machine learning parameterizations have emerged as a potential way to improve the representation of sub-grid processes in Earth System Models (ESMs). So far, all studies were based on the same three-step approach: first a training dataset was created from a high-resolution simulation, then a machine learning algorithm was fitted to this dataset, before the trained algorithm was implemented in the ESM. The resulting online simulations were frequently plagued by instabilities and biases. Here, coupled online learning is proposed as a way to combat these issues. Coupled learning can be seen as a second training stage in which the pretrained machine learning parameterization, specifically a neural network, is run in parallel with a high-resolution simulation. The high-resolution simulation is kept in sync with the neural network-driven ESM through constant nudging. This enables the neural network to learn from the tendencies that the high-resolution simulation would produce if it experienced the states the neural network creates. The concept is illustrated using the Lorenz 96 model, where coupled learning is able to recover the true parameterizations. Further, detailed algorithms for the implementation of coupled learning in 3D cloud-resolving models and the super parameterization framework are presented. Finally, outstanding challenges and issues not resolved by this approach are discussed.
Artificial neural-networks have the potential to emulate cloud processes with higher accuracy than the semi-empirical emulators currently used in climate models. However, neural-network models do not intrinsically conserve energy and mass, which is an obstacle to using them for long-term climate predictions. Here, we propose two methods to enforce linear conservation laws in neural-network emulators of physical models: Constraining (1) the loss function or (2) the architecture of the network itself. Applied to the emulation of explicitly-resolved cloud processes in a prototype multi-scale climate model, we show that architecture constraints can enforce conservation laws to satisfactory numerical precision, while all constraints help the neural-network better generalize to conditions outside of its training set, such as global warming.
Monitoring the dynamics processes in combustors is crucial for safe and efficient operations. However, in practice, only limited data can be obtained due to limitations in the measurable quantities, visualization window, and temporal resolution. This work proposes an approach based on neural differential equations to approximate the unknown quantities from available sparse measurements. The approach tackles the challenges of nonlinearity and the curse of dimensionality in inverse modeling by representing the dynamic signal using neural network models. In addition, we augment physical models for combustion with neural differential equations to enable learning from sparse measurements. We demonstrated the inverse modeling approach in a model combustor system by simulating the oscillation of an industrial combustor with a perfectly stirred reactor. Given the sparse measurements of the temperature inside the combustor, upstream fluctuations in compositions and/or flow rates can be inferred. Various types of fluctuations in the upstream, as well as the responses in the combustor, were synthesized to train and validate the algorithm. The results demonstrated that the approach can efficiently and accurately infer the dynamics of the unknown inlet boundary conditions, even without assuming the types of fluctuations. Those demonstrations shall open a lot of opportunities in utilizing neural differential equations for fault diagnostics and model-based dynamic control of industrial power systems.
We apply two independent data analysis methodologies to locate stable climate states in an intermediate complexity climate model and analyze their interplay. First, drawing from the theory of quasipotentials, and viewing the state space as an energy landscape with valleys and mountain ridges, we infer the relative likelihood of the identified multistable climate states, and investigate the most likely transition trajectories as well as the expected transition times between them. Second, harnessing techniques from data science, specifically manifold learning, we characterize the data landscape of the simulation output to find climate states and basin boundaries within a fully agnostic and unsupervised framework. Both approaches show remarkable agreement, and reveal, apart from the well known warm and snowball earth states, a third intermediate stable state in one of the two climate models we consider. The combination of our approaches allows to identify how the negative feedback of ocean heat transport and entropy production via the hydrological cycle drastically change the topography of the dynamical landscape of Earths climate.
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