Computational Mathematics (CM)
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An implicit symplectic solver for highprecision long term integrations of the Solar System
(2022)We present FCIRK16, a 16thorder implicit symplectic integrator for longterm high precision Solar System simulations. Our integrator takes advantage of the nearKeplerian motion of the planets around the Sun by ... 
Efficient 5axis CNC trochoidal flank milling of 3D cavities using customshaped cutting tools
(202205)A novel method for trochoidal flank milling of 3D cavities bounded by freeform surfaces is proposed. Existing 3D trochoidal milling methods use onmarket milling tools whose shape is typically cylindrical or conical, and ... 
Nonhyperbolic normal moveout stretch correction with deep learning automation
(20220215)Normalmoveout (NMO) correction is a fundamental step in seismic data processing. It consists of mapping seismic data from recorded traveltimes to corresponding zerooffset times. This process produces wavelet stretching ... 
Exploiting the Kronecker product structure of φ−functions in exponential integrators
(20220515)Exponential time integrators are wellestablished discretization methods for time semilinear systems of ordinary differential equations. These methods use (Formula presented.) functions, which are matrix functions related ... 
Supervised Deep Learning with Finite Element simulations for damage identification in bridges
(20220415)This work proposes a supervised Deep Learning approach for damage identification in bridge structures. We employ a hybrid methodology that incorporates Finite Element simulations to enrich the training phase of a Deep ... 
Algebraic equations for constant width curves and Zindler curves
(202203)An explicit method to compute algebraic equations of curves of constant width and Zindler curves generated by a family of middle hedgehogs is given thanks to a property of Chebyshev polynomials. This extends the methodology ... 
Curveguided 5axis CNC flank milling of freeform surfaces using customshaped tools
(202203)A new method for 5axis flank milling of freeform surfaces is proposed. Existing flank milling pathplanning methods typically use onmarket milling tools whose shape is cylindrical or conical, and is therefore not ... 
2.5D Deep Learning Inversion of LWD and DeepSensing em Measurements Across Formations with Dipping Faults
(20220101)Deep learning (DL) inversion of induction logging measurements is used in well geosteering for realtime imaging of the distribution of subsurface electrical conductivity. We develop a DL inversion workflow to solve 2.5D ... 
On quadrature rules for solving Partial Differential Equations using Neural Networks
(20220401)Neural Networks have been widely used to solve Partial Differential Equations. These methods require to approximate definite integrals using quadrature rules. Here, we illustrate via 1D numerical examples the quadrature ... 
Uncertainty Quantification on the Inversion of Geosteering Measurements using Deep Learning
(20211101)We propose the use of a Deep Learning (DL) algorithm for the realtime inversion of electromagnetic measurements acquired during geosteering operations. Moreover, we show that when the DL algorithm is equipped with a ... 
On numerical solution of Fredholm and Hammerstein integral equations via Nystr\"{o}m method and Gaussian quadrature rules for splines
(202201)Nystr\"{o}m method is a standard numerical technique to solve Fredholm integral equations of the second kind where the integration of the kernel is approximated using a quadrature formula. Traditionally, the quadrature ... 
Deep learning enhanced principal component analysis for structural health monitoring
(20220101)This paper proposes a Deep Learning Enhanced Principal Component Analysis (PCA) approach for outlier detection to assess the structural condition of bridges. We employ partially explainable autoencoder architecture to ... 
Error representation of the timemarching DPG scheme
(20220301)In this article, we introduce an error representation function to perform adaptivity in time of the recently developed timemarching Discontinuous Petrov–Galerkin (DPG) scheme. We first provide an analytical expression for ... 
A Finite Element based Deep Learning solver for parametric PDEs
(2021)We introduce a dynamic Deep Learning (DL) architecture based on the Finite Element Method (FEM) to solve linear parametric Partial Differential Equations(PDEs). The connections between neurons in the architecture mimic the ... 
Numerical Approaches for Loads and Motions Assessment of Floating WECs Moored by Means of Catenary Mooring Systems
(2022)Technologies for harvesting offshore renewable energy based on float ing platforms, such as offshore wind, wave and tidal energies, are currently being developed with the purpose of achieving a competitive cost of energy. ... 
Modeling extradeep electromagnetic logs using a deep neural network
(202105)Modern geosteering is heavily dependent on realtime interpretation of deep electromagnetic (EM) measurements. We have developed a methodology to construct a deep neural network (DNN) model trained to reproduce a full set ... 
Motile dislocations knead odd crystals into whorls
(20210101)The competition between thermal fluctuations and potential forces governs the stability of matter in equilibrium, in particular the proliferation and annihilation of topological defects. However, driving matter out of ... 
Majorant series for the Nbody problem
(20210101)As a followup of a previous work of the authors, this work considers uniform global timerenormalization functions for the gravitationalNbody problem. It improves on the estimates of the radii of convergence obtained ... 
Global TimeRenormalization of the Gravitational Nbody Problem
(20210101)This work considers the gravitational Nbody problem and introduces global timerenormalization functions that allow the efficient numerical integration with fixed timesteps. First, a lower bound of the radius of convergence ... 
An Algorithm based on continuation techniques for minimization problems with highly non linear equality constraints
(2021)We present an algorithm based on continuation techniques that can be applied to solve numerically minimization problems with equality constraints. We focus on problems with a great number of local minima which are hard to ...