Discovery of interpretable structural model errors by combining Bayesian sparse regression and data assimilation: A chaotic Kuramoto-Sivashinsky test case

Abstract

Models of many engineering and natural systems are imperfect. The discrepancy between the mathematical representations of a true physical system and its imperfect model is called the model error. These model errors can lead to substantial differences between the numerical solutions of the model and the state of the system, particularly in those involving nonlinear, multi-scale phenomena. Thus, there is increasing interest in reducing model errors, particularly by leveraging the rapidly growing observational data to understand their physics and sources. Here, we introduce a framework named MEDIDA: Model Error Discovery with Interpretability and Data Assimilation. MEDIDA only requires a working numerical solver of the model and a small number of noise-free or noisy sporadic observations of the system. In MEDIDA, first the model error is estimated from differences between the observed states and model-predicted states (the latter are obtained from a number of one-time-step numerical integrations from the previous observed states). If observations are noisy, a data assimilation (DA) technique such as ensemble Kalman filter (EnKF) is employed to provide the analysis state of the system, which is then used to estimate the model error. Finally, an equation-discovery technique, here the relevance vector machine (RVM), a sparsity-promoting Bayesian method, is used to identify an interpretable, parsimonious, and closed-form representation of the model error. Using the chaotic Kuramoto-Sivashinsky (KS) system as the test case, we demonstrate the excellent performance of MEDIDA in discovering different types of structural/parametric model errors, representing different types of missing physics, using noise-free and noisy observations.

9 pages, 2 figures

References in corpus (13)

• FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators
• Perspectives on Machine Learning-augmented Reynolds-averaged and Large Eddy Simulation Models of Turbulence
• Using machine learning to correct model error in data assimilation and forecast applications
• Using Noisy or Incomplete Data to Discover Models of Spatiotemporal Dynamics
• Robust learning from noisy, incomplete, high-dimensional experimental data via physically constrained symbolic regression
• Feature engineering and symbolic regression methods for detecting hidden physics from sparse sensors
• Data-driven subgrid-scale modeling of forced Burgers turbulence using deep learning with generalization to higher Reynolds numbers via transfer learning
• Discovery of Nonlinear Dynamical Systems using a Runge-Kutta Inspired Dictionary-based Sparse Regression Approach
• Long short-term memory embedded nudging schemes for nonlinear data assimilation of geophysical flows
• Combining machine learning and data assimilation to forecast dynamical systems from noisy partial observations
• Using Data Assimilation to Train a Hybrid Forecast System that Combines Machine-Learning and Knowledge-Based Components
• Using Machine Learning to Augment Coarse-Grid Computational Fluid Dynamics Simulations
• BAMCAFE: A Bayesian Machine Learning Advanced Forecast Ensemble Method for Complex Turbulent Systems with Partial Observations

Cited by in corpus (6)

• Deep learning of systematic sea ice model errors from data assimilation increments
• Machine learning for online sea ice bias correction within global ice-ocean simulations
• Learning Closed-form Equations for Subgrid-scale Closures from High-fidelity Data: Promises and Challenges
• CEBoosting: Online Sparse Identification of Dynamical Systems with Regime Switching by Causation Entropy Boosting
• Interpretable structural model error discovery from sparse assimilation increments using spectral bias-reduced neural networks: A quasi-geostrophic turbulence test case
• Remarks on the stabilization of large-scale growth in the 2D Kuramoto-Sivashinsky equation