Real-time Inversion using Deep Learning Methods
Objective:DEEPINVERSE project focuses on the numerical real-time inversion of wave propagation problems governed by Partial Differential Equations (PDEs) utilizing Deep Learning (DL) algorithms. First, we shall generate massive databases employing advanced Galerkin methods for computing tens of thousands of solutions of a given PDE with varying coefficients. State-of-the-art methods like Proper Generalized Decomposition (PGD), Reduced Order Modeling, and Dimensionality Reduction methods using Fourier analysis will be employed for this purpose. Then, we shall construct DL algorithms with advanced encoder-decoder neural networks to numerically approximate both the forward and inverse solutions. We will employ different regularization terms to favorize certain inverse solutions over other possibly existing solutions of the inverse problem that may be physically meaningless. Finally, we shall apply the results to: (a) the real-time inversion of borehole resistivity measurements for geosteering purposes (which is the act of adjusting the well-trajectory in real time based on inverted Earth models recovered from the recorded measurements acquired while drilling), and (b) the structural health monitoring of offshore wind platforms employed to produce renewable energy. The proper maintenance of these structures is critical for the economic viability of this source of renewable energy. This inversion process is based on elasto-acoustic measurements. The research group of BCAM-UPV/EHU that will develop DEEPINVERSE collaborates, among others, with the following institutions: (a) various oil-companies including Repsol, from which we have access to databases comprising borehole electromagnetic measurements, and (b) the technological center Tecnalia Research and Innovation, which is one of the European leading experts on renewable offshore energy applications. Moreover, the research group leads the European H2020 MATHROCKS project which focuses on the application of numerical methods to geophysics. The main research work proposed in DEEPINVERSE will allow us to design and implement more efficient inversion algorithms based on the evaluation of different loss functions and novel error control techniques, strongly impacting the revenues provided by this practice. The high-quality inversion methods proposed in DEEPINVERSE aim at establishing a new paradigm in the field of offshore SHM, providing robust real-time solutions for behavior assessment and remaining life estimation of structural components in wind platforms. The knowledge acquired through the development and implementation of the algorithms and techniques proposed by DEEPINVERSE will provide great power to transfer those methodologies to other related areas such as underground water exploration and SHM of bridges and other infrastructures.
Measuring ideals in a singularity
This proposal concerns singularities arising in the solution spaces of systems of polynomial equations.
MATH4SPORTS - Modelización matemática para la industria deportiva: salud y rendimiento
MATH4SPORTS seeks to transfer applied mathematics as a driving technology to the field of the sports industry, with a high potential for technology transfer to start-ups, professional clubs, researchers and other agents in the innovative environment of Bizkaia.
Chemistry informed machine learning in emulsion polymerization processes and products
Spectral theory and PDE: Real and Fourier Analysis