Monday | Tuesday | Wednesday | Thursday | Friday | |

9:00-9:50 | Tan Bui Thanh | Heikki Haario | Youssef Marzouk |
9:00-13:00 Free discussions and collaboration |
9:00-13:00 Free discussions and collaboration |

10:00-10:40 | Antonio Capella Kort |
Gerardo Hernández Dueñas |
Héctor Juárez Valencia |
||

10:40-11:00 | Coffee break | Coffee break | Coffee break | ||

11:00-11:40 | Miguel Angel Moreles | Andrés Christen | Marcos Capistrán | ||

11:50-12:30 | Hugo Flores | Liliana Guadalupe Salvador | Yury Elena García | ||

12:40-13:20 | Leticia Ramírez | Ursula Iturraran | Nicolas Kuschinski | ||

13:30-15:00 | Lunch | Lunch | Lunch | Lunch | Lunch |

15:00-18:00 | Free discussion and interaction | Free discussion and interaction | Free discussion and interaction | Free discussions and interaction | Free discussions and interaction |

18:00 | Conference dinner |

**Tan Bui Thanh **

Title:**Towards Large-Scale Computational Science and Engineering with Quantifiable Uncertainty**

Abstract:

We present our recent efforts towards uncertainty quantification for large-scale computational mechanics. The talk has three parts.

In the first part we present a systematic FEM-based discretization of function-space Markov chain Monte Carlo (MCMC) methods to obtrain dimension-independent MCMC methods. This class of MCMC methods are important for PDE-constrained Bayesian inverse problems because they ensure the convergence of the computation as the mesh is refined.

In the second part, we present several particle methods to compute (approximate) posterior samples without the need for a Markov chain. We present theory, computational experiments, and comparisons among the methods.

In the last part, we present dimension-reduction techniques to reduce the data, the parameter, and the state for large-scale data-driven inverse problems in high dimensional parameter spaces.

Numerical results for several inverse problems, including inverse electromagnetic scattering and seismici nversions, will be discussed.

**Antonio Capella Kort**

Title:**Bayesian method for an inverse homogenized problem in low contrast conductivity. **

Abstract:

In this work we propose an algorithm to solve an inverse problem in low contrast

conductivity. The approach combine ideas from the homogenized method developed by Allaire and Gutierrez and Gutierrez and Mura for optimal design problems and the Bayes approach to inverse problem. Besides describing the algorithm we show some numerical examples of the proposed algorithm.

**Miguel Angel Moreles**

Title: **A posteriori estimates and HPC for accelerating posterior density sampling in bayesian estimation**

Abstract:

In this talk we pose the problem of parameter estimation in differential equations as a problem of bayesian estimation.

It is illustrated with ultrasound propagation through cancellous bone. Bayesian estimation leads to sampling the

posterior distribution, a computationally costly task. In the second part of the talk, we explore with the audience two possible

strategies for reduction:

1. Solving differential equations to compute the forward map with High Performance Computing (HPC).

2. Using a posteriori estimates in the numerical solution of differential equations for an "adaptive MCMC"

**Hugo Alberto Flores Arguedas**

Title:**A stochastic Quasi-Newton Monte Carlo: Limitations on the full waveform inversion**

Abstract:

Simsekli et al. (2016) presents a Stochastic Gradient Markov Chain Monte Carlo method using a quasi-newton optimization method, the L-BFGS. We describe this article and the application on the full waveform inversion.

**Leticia Ramírez**

Title:**A more efficient error control for the numerical posterior in the bayesian Uncertainty Quantification**

Abstract:

Using the expected Bayes Factors Christen et al. (2016) obtained bounds on the absolute global errors originated from numerical solutions to the forward map (FM). This allows to specify the FM numerical solvers error to be tolerated for a specified global error value. In this work we present an algorithmic procedure that is more efficient, achieves the specified error value and originates the same posterior distribution. The method is illustrated with examples and using synthetic data and applied to the real 2014 outbreak data of chikungunya in Dominican Republic.

**Heikki Haario**

Title:**Uncertianties in epidemiological modelling**

**Gerardo Hernández-Dueñas**

Title:**Minimal models for precipitating turbulent convection**

Abstract:

Simulations of precipitating convection are usually carried out with cloud resolving models, which typically represent all the different phases of water: water vapor, cloud water, rain water and ice. Here we investigate the question: what is the minimal possible representation of water processes that is sufficient for these models? The simplified models that we present use a Boussinesq approximation, assume fast auto conversion and neglect ice. To test the simplified models, we present simulations of squall lines and scattered convection and show that they qualitatively capture observations made in nature and also seen in more comprehensive cloud resolving models, such as propagation of squall lines with tilted profiles, cold pools, and scattered convection.

**Andres Christen Gracia**

Title:**Bayesian analysis of ODEs: solver optimal accuracy and Bayes factors**

J Andrés Christen, Marcos Capistrán and Miguel Angel Moreles

Abstract:

In the bayesian analysis of Inverse Problems most relevant cases the forward maps (FM, or regressor function) are defined in terms of a system of (O, P)DE's with intractable solutions. These necessarily involve a numerical method to find approximate versions of such

solutions and lead to a numerical/approximate posterior distribution. Recently several results have been published on the regularity conditions required on such numerical methods to ensure converge of the numerical to the theoretical posterior.

However, more practical guidelines are needed to ensure a suitable working numerical posterior. \citet{Capistran2016} prove for ODE's that the Bayes Factor of the approximate vs the theoretical model tends to 1 in the same order as the numerical method order. In this work we generalize the latter paper in that we consider 1) also PDE's, 2) correlated observations, 3) practical guidelines in a multidimensional setting and 4) explore the use of expected Bayes Factors.

This permits us to obtain bounds on the absolute global errors to be tolerated by the FM numerical solver, which we illustrate with some examples. Since the Bayes Factor is kept above 0.95 we expect that the resulting numerical posterior is basically indistinguishable from the theoretical posterior, even though we are using an approximate numerical FM. The method is illustrated with some examples using synthetic data.

**Liliana Guadalupe Salvador**

Title:**A Bayesian approach for parameter identification in aquifers **

Abstract:

An inverse problem of interest in Geohidrology is to estimate phenomenological parameters in aquifers from piezometric heads data. In this talk, we present a Bayesian approach for parameter identification in isotropic aquifers, for which Darcy’s law hold. Generated data are corrupted with Gaussian additive noise and the prior distribution is non informative. Because of the nature of problem, the direct problem has been solve by finite volume method, considering internodal approximations. We estimate parameters for synthetic groundwater models, both confined and unconfined case.

**Ursula Iturraran**

Title:**Inversion of seismic velocities combining Self-Organized Maps and analytic methods**

Abstact:

We apply Self-Organizing maps to classify seismic reflection data into a set of three different facies. This gives us our starting velocity model. In order to test this initial layered velocity model, the elastodynamic response of the stack of plane-layers upon an incident plane wave is computed by means of the Thomson-Hasekell method. We compare the synthetic response with the measured data. We perform an inversion using non-linear squares to fit the synthetic traces and the real data. We see that the final velocity model has a feasible structure and is correlated with the seismic.

**Youssek Marzouk **

Title:**Variational inference via measure transport, for Bayesian filtering and smoothing**

**Marcos Capistrán**

Title:**An inverse problem that arises in reflection and transmission of waves in layered media**

Abstract:

In this paper we consider the inverse problem of reconstructing the mechanic properties of a functionally graded material (FGM). We use explicit formulae introduced by Pham et al (2015) to compute the reflection and transmission of one-component waves through a stack of homogeneous layers as a surrogate model.

The aim of this paper is to study the role of two different sources of uncertainty, namely model approximation and data measurement, in model prediction.

**Yury Elena García**

Title:**BAYESIAN ANALYSIS IN A MULTIPATHOGEN MODEL**

Abstract:

Influenza and respiratory syncytial virus (RSV) are leading etiologic agents of acute respiratory infections (ARI). They are associated with similar clinical symptoms and frequently co-circulate around the same time causing the yearly outbreaks. During the whole year there are also other cases of ARI caused by different virus. Despite this, health public system records the number of infected people each year without differentia the responsible virus. We are interested in describe the dynamic between Influenza and RSV using a Multi-pathogen model and data from the state of San Luis Potosí, Mex. This data correspond to both virus and also include noise corresponding to the virus in circulation during the year. We consider a particle MCMC method to perform the Bayesian inference of the parameters that govern the system. Each iteration of the scheme requires an estimate of marginal likelihood from the output of a sequential Monte Carlo Scheme (known as a particle filter), following the method proposed by Golightly et al. 2012, we use linear noise approximation (LNA) to estimate this marginal likelihood. To illustrate the method, we simulated some data using Gillespie’s algorithm including only one pathogen as the responsible for the annual outbreak. But also, we include a background to simulate the presences of other virus. We also implement the method with the real data from San Luis Potosí using a multi-pathogen model; in this case we found new challenges.

**Nicolas Elio Kuschinski Kathmann**

Title: **Bayesian experimental design for OGTT diagnosis of diabetes**

Abstract:

OGTT is a common test which checks a patient's blood sugar at various points in time. It is frequently used to diagnose insulin resistance or diabetes. Recent developments in studying OGTT results have framed it as an inverse problem which has been the subject of Bayesian inference. This is a powerful new tool for analyzing the results of an OGTT test, and the question arises as to whether the test itself can be improved. Of particular interest is to discover whether the times at which a patient's glucose is measured can be changed to improve the effectiveness of the test. In order to compare different time sets, we will overview the Bayesian theory of experimental design, and look into a new proposal to quantify the uncertainty in comparisons between these designs