Equation-free surrogate modeling of geophysical flows at the intersection of machine learning and data assimilation

Abstract

There is a growing interest in developing data-driven reduced-order models for atmospheric and oceanic flows that are trained on data obtained either from high-resolution simulations or satellite observations. The data-driven models are non-intrusive in nature and offer significant computational savings compared to large-scale numerical models. These low-dimensional models can be utilized to reduce the computational burden of generating forecasts and estimating model uncertainty without losing the key information needed for data assimilation to produce accurate state estimates. This paper aims at exploring an equation-free surrogate modeling approach at the intersection of machine learning and data assimilation in Earth system modeling. With this objective, we introduce an end-to-end non-intrusive reduced-order modeling (NIROM) framework equipped with contributions in modal decomposition, time series prediction, optimal sensor placement, and sequential data assimilation. Specifically, we use proper orthogonal decomposition (POD) to identify the dominant structures of the flow, and a long short-term memory network to model the dynamics of the POD modes. The NIROM is integrated within the deterministic ensemble Kalman filter (DEnKF) to incorporate sparse and noisy observations at optimal sensor locations obtained through QR pivoting. The feasibility and the benefit of the proposed framework are demonstrated for the NOAA Optimum Interpolation Sea Surface Temperature (SST) V2 dataset. Our results indicate that the NIROM is stable for long-term forecasting and can model dynamics of SST with a reasonable level of accuracy. Furthermore, the prediction accuracy of the NIROM gets improved by one order of magnitude by the DEnKF algorithm. This work provides a way forward toward transitioning these methods to fuse information from Earth system models and observations to achieve accurate forecasts.

References in corpus (29)

• Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcasting
• Machine Learning for Fluid Mechanics
• Deep learning to represent sub-grid processes in climate models
• Data-Driven Sparse Sensor Placement for Reconstruction
• WeatherBench: A benchmark dataset for data-driven weather forecasting
• Enforcing Analytic Constraints in Neural-Networks Emulating Physical Systems
• FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators
• Data-Driven Forecasting of High-Dimensional Chaotic Systems with Long Short-Term Memory Networks
• A New Selection Operator for the Discrete Empirical Interpolation Method -- improved a priori error bound and extensions
• Will Artificial Intelligence supersede Earth System and Climate Models?
• Shallow Neural Networks for Fluid Flow Reconstruction with Limited Sensors
• Data-assisted reduced-order modeling of extreme events in complex dynamical systems
• Machine Learning for Stochastic Parameterization: Generative Adversarial Networks in the Lorenz '96 Model
• Combining data assimilation and machine learning to emulate a dynamical model from sparse and noisy observations: a case study with the Lorenz 96 model
• Robust flow field reconstruction from limited measurements via sparse representation
• Enforcing Statistical Constraints in Generative Adversarial Networks for Modeling Chaotic Dynamical Systems
• Data-driven medium-range weather prediction with a Resnet pretrained on climate simulations: A new model for WeatherBench
• On closures for reduced order models $-$ A spectrum of first-principle to machine-learned avenues
• Long-time predictive modeling of nonlinear dynamical systems using neural networks
• A non-intrusive reduced order modeling framework for quasi-geostrophic turbulence
• A stabilized proper orthogonal decomposition reduced-order model for large scale quasigeostrophic ocean circulation
• Latent Space Data Assimilation by using Deep Learning
• Integrating Recurrent Neural Networks with Data Assimilation for Scalable Data-Driven State Estimation
• Nonlinear proper orthogonal decomposition for convection-dominated flows
• Towards physically consistent data-driven weather forecasting: Integrating data assimilation with equivariance-preserving deep spatial transformers
• Data Assimilation in the Latent Space of a Neural Network
• Frame invariant neural network closures for Kraichnan turbulence
• Generalised Latent Assimilation in Heterogeneous Reduced Spaces with Machine Learning Surrogate Models
• Data-driven sensor placement with shallow decoder networks

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