Group on Applied Mathematical Modeling, Statistics, and Optimization



The MathMode group at the University of the Basque Country offers two Postdoctoral Positions

Research Area: Partial Differential Equations (PDEs) govern multiple physical problems arising in the areas of oil and gas exploration, marine energy, and geothermal energy. In these applications, it is essential to properly model both the so-called forward problem (to predict simulated measurements from given material data) as well as the inverse problem (to predict material data from given measurements).

Research Topic 1 (RT1)​: Development of Deep Learning Algorithms for Real-Time Inversion. The postdoctoral fellow working on RT1 will be trained on solving inverse problems using Deep Neural Networks (DNNs). Specifically, he/she will improve an existing encoder-decoder Deep Convolutional Neural Network (DCNN) by adding residual blocks with a boosting strategy. The implementation will be based on TensorFlow 2.0. The results will be applied to the three aforementioned energy applications.

Research Topic 2 (RT2)​: Development of Finite Element Methods for generating a training database for Deep Learning algorithms. The postdoctoral fellow working on RT2 will explore various numerical methods such as Proper Generalized Decomposition (PGD), Fourier based strategies, multiscale methods, and Finite Element Methods. Then, starting from our in-house finite element simulators, the objective is to develop a numerical method that solves one million two-dimensional (2D) forward problems in eight hours on a computer equipped with four quad-core CPUs.

Salary and conditions​: We offer a one or a two-year contract on each of the positions, depending upon the qualifications. The gross annual salary of the Fellowship will be 28.000 - 32.000€. Free access to the Public Health System in Spain is provided to all employees. Starting date: Fall 2019. Location: University of the Basque Country, Leioa, Bizkaia, Spain.

How to apply​: Please, email your CV and a short letter of interest to David Pardo at​ . Deadline: Sep. 7th, 2019.

MATHMODE is recognized as a Research Group of Excellence (A+) by the Basque Government.













Jon Ander











The key objectives of the Group on Applied Mathematical Modeling, Statistics, and Optimization (MATHMODE) are:

1) Develop knowledge on the numerical simulation of ordinary and partial differential equations as well as on optimization problems and statistics.

2) Transfer this mathematical knowledge to the industry.

3) Train new researchers in the area.


The Group on Applied Mathematical Modeling, Statistics, and Optimization (MATHMODE) works on three areas of knowledge:

1) Mathematics, used to develop advanced numerical and statistical methods.

2) Scientific Computing, used to implement efficiently those numerical methods.

3) Engineering, used to understand and solve real-world industry problems.


The main research directions of the group on Applied Mathematical Modeling, Statistics, and Optimization (MATHMODE) are:

1) Development of highly accurate and robust numerical methods for the solution and inversion via computer simulations challenging multiphysics applications. These applications arise in different areas of knowledge, including medicine, bio-technology, nano-technology and a variety of engineering applications such as Petroleum Engineering.

Our main simulation technology is based on a high-order Finite Element method, where we employ self-adaptive goal-oriented grids to obtain superior accuracy and approximate the error in a given (user-prescribed) quantity of interest. Depending upon the application, we also combine the Finite Element method with other numerical techniques, such as a Fourier transform in a non-orthogonal system of coordinates (for borehole simulations in deviated wells), a Dimensionally Adaptive Method (DAM), and a discontinuous Petrov-Galerkin method (for minimizing the dispersion error in acoustic applications). More recently, we have established a research line on solving inverse problems using Monte Carlo methods and Deep Learning techniques.

A Logging-While-Drilling (LWD) device on a borehole environment

2) Advanced numerical methods for time integration of differential equations. This line of research seeks to analyze, design, and implement numerical integration methods for time evolution problems governed by differential equations whose solution cannot be obtained using conventional packages based on multistep methods nor Runge-Kutta schemes. We make an special emphasis on geometric integration methods and, in particular, methods for conservative problems. We are also interested on highly oscillatory problems. Among the application areas, we include classical mechanics, quantum mechanics, astrophysics, and molecular dynamics.

3) Applied optimization problems. The main objective is to carry out projects with companies, making technology transfer in the fields of optimization, simulation, operational research, and statistics.

4) Statistics. Used to validate and efficiently analyze real data and promote the transfer of the research in statistics to biomedical and experimental fields.


Prof. Victor M. Calo, Curtin University, Australia. Topic: Time domain methods and Isogeometric Analysis (IGA).

Prof. Jay Gopalakrishnan, Portland University, USA. Topic: Numerical analysis.

Prof. Carlos Torres-Verdín, The University of Texas at Austin, USA. Topic: Geophysical applications.

Prof. Maciej Paszynski, AGH University of Science and Technology, Poland. Topic: Solvers of linear equations.

Prof. Luis E. García-Castillo, Univ. Carlos III of Madrid, Spain. Topic: hp-adaptivity.

Prof. Ignacio Muga, Pontificia Universidad Católica de Valparaíso, Chile. Topic: Semi-analytical 1.5D solutions.

Prof. Serge Prudhomme, Univ. Polythecnique Montreal, Canada. Topic: goal-oriented adaptivity.

Prof. Elena Akhmastskaya, Basque Center for Applied Mathematics, Spain. Topic: Monte Carlo methods.

Dr. Carlos Santos Molina, CTR Repsol, Madrid, Spain. Topic: Effective velocities of porous rocks.

Other collaborators: Adrián Galdrán (Portugal), Myung Jin Nam (South Korea), Vladimir Puzyrev (Australia), Pawel Matuszyk (USA), Leszek F. Demkowicz (USA), Helene Barucq (France), Julien Diaz (France), Carlos Jerez (Chile), Ignacio Gómez Revuelto (Spain), Josep de la Puenta (Spain), Pedro Diez (Spain), Juan Galvis (Colombia), Otilio Rojas (Venezuela), Juan Carlos Alfonso (Australia), Ricardo Durán (Argentina), Kris Van der Zee (UK), Pilar Queralt (Spain), Javier del Ser (Spain).