Parallelized Adaptive Importance Sampling for Solving Inverse Problems

In the field of groundwater hydrology and more generally geophysics, solving inverse problems in a complex, geologically realistic, and discrete model space often requires the usage of Monte Carlo methods. In a previous paper we introduced PoPEx, a sampling strategy, able to handle such constraints efficiently. Unfortunately, the predictions suffered from a slight bias. In the present work, we propose a series of major modifications of PoPEx. The computational cost of the algorithm is reduced and the underlying uncertainty quantification is improved. Advanced machine learning techniques are combined with an adaptive importance sampling strategy to define a highly efficient and ergodic method that produces unbiased and rapidly convergent predictions. The proposed algorithm may be used for solving a broad range of inverse problems in many different fields. It only requires to obtain a forward problem solver, an inverse problem description and a conditional simulation tool that samples from the prior distribution. Furthermore, its parallel implementation scales perfectly. This means that the required computational time can be decreased almost arbitrarily, such that it is only limited by the available computing resources. The performance of the method is demonstrated using the inversion of a synthetic tracer test problem in an alluvial aquifer. The prior geological knowledge is modeled using multiple-point statistics. The problem consists of the identification of 2 · 104 parameters corresponding to 4 geological facies values. It is used to show empirically the convergence of the PoPEx method

Multilingual RECIST classification of radiology reports using supervised learning.

OBJECTIVES The objective of this study is the exploration of Artificial Intelligence and Natural Language Processing techniques to support the automatic assignment of the four Response Evaluation Criteria in Solid Tumors (RECIST) scales based on radiology reports. We also aim at evaluating how languages and institutional specificities of Swiss teaching hospitals are likely to affect the quality of the classification in French and German languages. METHODS In our approach, 7 machine learning methods were evaluated to establish a strong baseline. Then, robust models were built, fine-tuned according to the language (French and German), and compared with the expert annotation. RESULTS The best strategies yield average F1-scores of 90% and 86% respectively for the 2-classes (Progressive/Non-progressive) and the 4-classes (Progressive Disease, Stable Disease, Partial Response, Complete Response) RECIST classification tasks. CONCLUSIONS These results are competitive with the manual labeling as measured by Matthew's correlation coefficient and Cohen's Kappa (79% and 76%). On this basis, we confirm the capacity of specific models to generalize on new unseen data and we assess the impact of using Pre-trained Language Models (PLMs) on the accuracy of the classifiers

Applications of the Transfinite Map for Parametrized Domain Decomposition

A big challenge in the last few years is to perform simulations of cardiovascular systems. Since it would be too computational expensive and complicated to simulate an entire blood circuit, an idea is to use a Domain Decomposition (DD) technique and to split it into many little parts. But these basic geometrical shapes can still differ quite a lot in forms and size. Therefore for each type of geometry we can define some very few reference geometries. Those reference geometries can then be deformed by a proper suitable map to any needed geometry. The aim of this report is to analyze the Transfinite Map (TM) and we introduce a possible extension of it. This deformations from the reference geometry to the computational one lead in general to a not affine map and affects strongly the complexity of the problem. In order to recover the affine decomposition we use the Empirical Interpolation Method that allows to approximate a not affine function with an affine one

Isogeometric Analysis for the Elastic Wave Equation

In everyday life of an engineer, CAD (Computer Aided Design) and FE (Finite Element) programs play an important role. The two different structures, CAD and FE programs, use different mathematical functions. In CAD programs, so called NURBS find their applications while the standard functions used in FE programs are Lagrange polynomials. This differences in the structure of the two programs result in a significant effort of translation. The concept of Isogeometric Analysis tries to extend the FE method by using NURBS as basis for the analysis. In this report we give first an introduction to NURBS. We will see that, compared to a standard FE analysis, we have a richer repertory for refining a given NURBS basis. Then we will use NURBS as basis for analysis to solve numerically two problems of linear elasticity; an equilibrium problem and a simulation of an earthquake

Isogeometric Analysis for an earthquake simulation

We consider Isogeometric Analysis to simulate an earthquake in a two dimensional model of a sinusoidal shaped valley. We analyze two different time integration schemes, namely the Generalized- and the Leap-Frog methods. Solving a wave propagation problem leads to a numerical dispersion of the wave velocities which depends on the discrete function space, as well as on the direction of propagation. In this work we also analyze the numerical dispersion with respect to the number of quadrature nodes per wavelength and the direction of wave propagation

An improvement on geometrical parameterizations by transfinite maps

We present a method to generate a non-affine transfinite map from a given reference domain to a family of deformed domains. The map is a generalization of the Gordon-Hall transfinite interpolation approach. It is defined globally over the reference domain. Once we have computed some functions over the reference domain, the map can be generated by knowing the parametric expressions of the boundaries of the deformed domain. Being able to define a suitable map from a reference domain to a desired deformation is useful for the management of parameterized geometries. \ua9 2013 Acad\ue9mie des sciences.Nous pr\ue9sentons une m\ue9thode pour g\ue9n\ue9rer une transformation param\ue9tris\ue9e d'une g\ue9om\ue9trie de r\ue9f\ue9rence vers une famille de g\ue9om\ue9tries d\ue9form\ue9es. La transformation est une g\ue9n\ue9ralisation de l'approche d'interpolation transfinie de Gordon\u2013Hall et est d\ue9finie globalement sur le domaine de r\ue9f\ue9rence. Une fois qu'on a calcul\ue9 certaines fonctions sur le domaine de r\ue9f\ue9rence, la transformation peut \ueatre g\ue9n\ue9r\ue9e \ue0 partir des param\ue9trisations des bords du domaine d\ue9form\ue9. Il est utile pour le maniement des g\ue9om\ue9tries d\ue9form\ue9es d'\ueatre capable de d\ue9finir une transformation appropri\ue9e d'un domaine de r\ue9f\ue9rence vers une d\ue9formation souhait\ue9e. \ua9 2013 Acad\ue9mie des sciences