# Imposing Sparsity Within Ensemble Kalman Inversion

@article{Schneider2020ImposingSW, title={Imposing Sparsity Within Ensemble Kalman Inversion}, author={Tapio Schneider and Andrew M. Stuart and Jinlong Wu}, journal={arXiv: Optimization and Control}, year={2020} }

Enforcing sparse structure within learning has led to significant advances in the field of pure data-driven discovery of dynamical systems. However, such methods require access not only to time-series of the state of the dynamical system, but also the time derivative. This poses problems when dealing with data polluted by noise, or when learning stochastic systems with non-differentiable solutions. To overcome such limitations we propose a sparse learning methodology to discover the vector…

## Figures and Tables from this paper

## 6 Citations

Adaptive Tikhonov strategies for stochastic ensemble Kalman inversion

- Computer Science, MathematicsArXiv
- 2021

This work builds upon Tikhonov EKI (TEKI), and presents three adaptive regularization schemes, which are highlighted from both the deterministic and Bayesian approaches for inverse problems, which include bilevel optimization, the MAP formulation and covariance learning.

Iterative Ensemble Kalman Methods: A Unified Perspective with Some New Variants

- Computer Science, MathematicsArXiv
- 2020

This paper aims to demonstrate the efforts towards in-situ applicability of EMMARM, which aims to provide real-time information about the physical and emotional impacts of infectious disease on animals and their care and treatment.

Ensemble-Based Experimental Design for Targeted High-Resolution Simulations to Inform Climate Models

- Mathematics
- 2022

Targeted high-resolution simulations driven by a general circulation model (GCM) can be used to calibrate GCM parameterizations of processes that are globally unresolvable but can be resolved in…

Calibration and Uncertainty Quantification of Convective Parameters in an Idealized GCM

- 2021

Parameters in climate models are usually calibrated manually, exploiting only small subsets of the available data. This precludes an optimal calibration and quantification of uncertainties.…

Ensemble gradient for learning turbulence models from indirect observations

- Mathematics, Physics
- 2021

Training data-driven turbulence models with high fidelity Reynolds stress can be impractical and recently such models have been trained with velocity and pressure measurements. For gradient-based…

lp regularization for ensemble Kalman inversion

- Computer Science, MathematicsSIAM Journal on Scientific Computing
- 2021

This paper proposes a strategy to implement regularization for EKI to recover sparse structures in the solution, and validate the proposed approach's effectiveness and robustness through a suite of numerical experiments, including compressive sensing and subsurface flow inverse problems.

## References

SHOWING 1-10 OF 18 REFERENCES

Tikhonov Regularization within Ensemble Kalman Inversion

- Mathematics, Computer ScienceSIAM J. Numer. Anal.
- 2020

This work demonstrates how further regularization can be imposed, incorporating prior information about the underlying unknown, and studies how to impose Tikhonov-like Sobolev penalties in the ensemble inversion context.

Learning stochastic closures using ensemble Kalman inversion

- Mathematics, PhysicsTransactions of Mathematics and Its Applications
- 2021

The proposed methodology for the fitting of SDE models is demonstrated, first in a simulation study with a noisy Lorenz ’63 model, and then in other applications, including dimension reduction in deterministic chaotic systems arising in the atmospheric sciences, large-scale pattern modeling in climate dynamics and simplified models for key observables arising in molecular dynamics.

On the Incorporation of Box-Constraints for Ensemble Kalman Inversion

- Computer Science, MathematicsFoundations of Data Science
- 2019

This work proposes a new variant of the ensemble Kalman inversion to include box constraints on the unknown parameters motivated by the theory of projected preconditioned gradient flows, and discusses a complete convergence analysis for linear forward problems.

Adding Constraints to Bayesian Inverse Problems

- Mathematics, Computer ScienceAAAI
- 2019

An approach to improve parameter estimation in inverse problems by incorporating constraints in a Bayesian inference framework and extending this framework to an approximate Bayesian inferred framework in terms of the ensemble Kalman filter method, where the constraint is imposed by re-weighing the ensemble members based on the likelihood function.

An introduction to multiple time series analysis.

- MedicineMedical care
- 1993

An expository account of multiple time series analysis is presented, making it possible to ascertain dynamic leading, lagging, and feedback relationships among the series to produce more efficient forecasts and to develop control schemes.

Atmospheric Modeling, Data Assimilation and Predictability

- Environmental Science, Computer Science
- 2002

This work focuses on the post processing of numerical model output to obtain station weather forecasts and the parameterizations of subgrid-scale physical processes.

Stochastic Processes and their Applications

- Computer Science
- 2006

Well, someone can decide by themselves what they want to do and need to do but sometimes, that kind of person will need some stochastic processes and their applications references. People with open…

Inverse Problems

- 2004

The leading international journal on the theory and practice of inverse problems, inverse methods and computerized inversion of data.

Additive Manufacturing Technologies: Rapid Prototyping to Direct Digital Manufacturing

- Engineering
- 2009

Additive Manufacturing Technologies: Rapid Prototyping to Direct Digital Manufacturing deals with various aspects of joining materials to form parts. Additive Manufacturing (AM) is an automated…