Alfredo Garbuno Iñigo

selected publications

1. CES

   

   Calibrate, Emulate, Sample

   Cleary, Emmet, Garbuno-Inigo, Alfredo, Lan, Shiwei, Schneider, Tapio, and Stuart, Andrew M

   Journal of Computational Physics 2021

   Abs arXiv Bib

   Many parameter estimation problems arising in applications can be cast in the framework of Bayesian inversion. This allows not only for an estimate of the parameters, but also for the quantification of uncertainties in the estimates. Often in such problems the parameter-to-data map is very expensive to evaluate, and computing derivatives of the map, or derivative-adjoints, may not be feasible. Additionally, in many applications only noisy evaluations of the map may be available. We propose an approach to Bayesian inversion in such settings that builds on the derivative-free optimization capabilities of ensemble Kalman inversion methods. The overarching approach is to first use ensemble Kalman sampling (EKS) to calibrate the unknown parameters to fit the data; second, to use the output of the EKS to emulate the parameter-to-data map; third, to sample from an approximate Bayesian posterior distribution in which the parameter-to-data map is replaced by its emulator. This results in a principled approach to approximate Bayesian inference that requires only a small number of evaluations of the (possibly noisy approximation of the) parameter-to-data map. It does not require derivatives of this map, but instead leverages the documented power of ensemble Kalman methods. Furthermore, the EKS has the desirable property that it evolves the parameter ensemble towards the regions in which the bulk of the parameter posterior mass is located, thereby locating them well for the emulation phase of the methodology. In essence, the EKS methodology provides a cheap solution to the design problem of where to place points in parameter space to efficiently train an emulator of the parameter-to-data map for the purposes of Bayesian inversion.

   @article{Cleary2021,
     author = {Cleary, Emmet and Garbuno-Inigo, Alfredo and Lan, Shiwei and Schneider, Tapio and Stuart, Andrew M},
     title = {Calibrate, Emulate, Sample},
     journal = {Journal of Computational Physics},
     volume = {424},
     year = {2021},
     image = {/assets/img/pubimg/ces-fmk.png},
     url = {https://doi.org/10.1016/j.jcp.2020.109716},
     abbr = {CES},
     bibtex_show = {true},
     publisher = {Elsevier},
     selected = {true},
     arxiv = {2001.03689}
   }

2. EKS

   

   Interacting Langevin Diffusions: Gradient Structure and Ensemble Kalman Sampler

   Garbuno-Inigo, Alfredo, Hoffmann, Franca, Li, Wuchen, and Stuart, Andrew M

   SIAM Journal on Applied Dynamical Systems 2020

   Abs arXiv Bib

   Solving inverse problems without the use of derivatives or adjoints of the forward model is highly desirable in many applications arising in science and engineering. In this paper we propose a new version of such a methodology, a framework for its analysis, and numerical evidence of the practicality of the method proposed. Our starting point is an ensemble of overdamped Langevin diffusions which interact through a single preconditioner computed as the empirical ensemble covariance. We demonstrate that the nonlinear Fokker–Planck equation arising from the mean-field limit of the associated stochastic differential equation (SDE) has a novel gradient flow structure, built on the Wasserstein metric and the covariance matrix of the noisy flow. Using this structure, we investigate large time properties of the Fokker–Planck equation, showing that its invariant measure coincides with that of a single Langevin diffusion, and demonstrating exponential convergence to the invariant measure in a number of settings. We introduce a new noisy variant on ensemble Kalman inversion (EKI) algorithms found from the original SDE by replacing exact gradients with ensemble differences; this defines the ensemble Kalman sampler (EKS). Numerical results are presented which demonstrate its efficacy as a derivative-free approximate sampler for the Bayesian posterior arising from inverse problems.

   @article{Garbuno-Inigo2021,
     author = {Garbuno-Inigo, Alfredo and Hoffmann, Franca and Li, Wuchen and Stuart, Andrew M},
     title = {Interacting Langevin Diffusions: Gradient Structure
                       and Ensemble Kalman Sampler},
     journal = {SIAM Journal on Applied Dynamical Systems},
     volume = {19},
     number = {1},
     pages = {412--441},
     year = {2020},
     image = {/assets/img/pubimg/numerics00.png},
     url = {https://epubs.siam.org/doi/abs/10.1137/19M1251655},
     abbr = {EKS},
     bibtex_show = {true},
     publisher = {SIAM},
     selected = {true},
     arxiv = {1903.08866}
   }