Regularized Ensemble Kalman Methods for Inverse Problems

Abstract

Inverse problems are common and important in many applications in computational physics but are inherently ill-posed with many possible model parameters resulting in satisfactory results in the observation space. When solving the inverse problem with adjoint-based optimization, the problem can be regularized by adding additional constraints in the cost function. However, similar regularizations have not been used in ensemble-based methods, where the same optimization is done implicitly through the analysis step rather than through explicit minimization of the cost function. Ensemble-based methods, and in particular ensemble Kalman methods, have gained popularity in practice where physics models typically do not have readily available adjoint capabilities. While the model outputs can be improved by incorporating observations using these methods, the lack of regularization means the inference of the model parameters remains ill-posed. Here we propose a regularized ensemble Kalman method capable of enforcing regularization constraints. Specifically, we derive a modified analysis scheme that implicitly minimizes a cost function with generalized constraints. We demonstrate the method's ability to regularize the inverse problem with three cases of increasing complexity, starting with inferring scalar model parameters. As a final case, we utilize the proposed method to infer the closure field in the Reynolds-averaged Navier--Stokes equations; a problem of significant importance in fluid dynamics and many engineering applications.

References in corpus (5)

• The Ensemble Kalman Filter for Inverse Problems
• Quantifying and Reducing Model-Form Uncertainties in Reynolds-Averaged Navier-Stokes Simulations: A Data-Driven, Physics-Based Bayesian Approach
• Fighting Sample Degeneracy and Impoverishment in Particle Filters: A Review of Intelligent Approaches
• Ensemble Kalman Methods With Constraints
• Enforcing Boundary Conditions on Physical Fields in Bayesian Inversion

Cited by in corpus (13)

• Onset of wake meandering for a floating offshore wind turbine under side-to-side motion
• Ensemble Kalman method for learning turbulence models from indirect observation data
• A multigrid/ensemble Kalman Filter strategy for assimilation of unsteady flows
• Combining direct and indirect sparse data for learning generalizable turbulence models
• Enforcing Boundary Conditions on Physical Fields in Bayesian Inversion
• Neural Dynamical Operator: Continuous Spatial-Temporal Model with Gradient-Based and Derivative-Free Optimization Methods
• Optimized parametric inference for the inner loop of the Multigrid Ensemble Kalman Filter
• Fourier Series-Based Approximation of Time-Varying Parameters in Ordinary Differential Equations
• Assimilation of disparate data for enhanced reconstruction of turbulent mean flows
• Data-driven detached-eddy simulations based on explicit algebraic stress expressions for turbulent flows
• Preserving linear invariants in ensemble filtering methods
• Ensemble gradient for learning turbulence models from indirect observations
• DAFI: An Open-Source Framework for Ensemble-Based Data Assimilation and Field Inversion