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Cylindrical algebraic decompositions (CADs) are a key tool in real algebraic geometry, used primarily for eliminating quantifiers over the reals and studying semi-algebraic sets. In this paper we introduce cylindrical algebraic…
Consider briefly the equations of fluid dynamics-they describe the enormous wealth of detail in all the interacting physical elements of a fluid flow-whereas in applications we want to deal with a description of just that which is…
A methodology is presented for investigating the dynamics of heterogeneous media using the nonlocal continuum model given by the peridynamic formulation. The approach presented here provides the ability to model the macroscopic dynamics…
A unidirectional reduction of the deep-water surface gravity wave problem is derived in physical space using real variables. By employing a near-identity canonical transformation, cubic interactions are eliminated from the Hamiltonian, with…
A comparison of the displacements of the earth's surface after an earthquake was made, calculating with the analytical expressions coming from an infinite flat slab approximation and compared with these numerically considering the…
In this paper, we combine deep learning concepts and some proper orthogonal decomposition (POD) model reduction methods for predicting flow in heterogeneous porous media. Nonlinear flow dynamics is studied, where the dynamics is regarded as…
As Physics did in previous centuries, there is currently a common dream of extracting generic laws of nature in economics, sociology, neuroscience, by focalising the description of phenomena to a minimal set of variables and parameters,…
The philosophy that a single "monolithic" model can "asymptotically" replace and couple in a simple elegant way several specialized models relevant on various Earth layers is presented and, in special situations, also rigorously justified.…
Simultaneous source seismic acquisition is an efficient method of seismic surveying that can considerably reduce the cost of high density seismic acquisition. The method results in overlapping records, or interference, that must be removed…
We study large deformations of hyperelastic membranes using a purely two-dimensional formulation derived from basic balance principles within a modern geometric setting, ensuring a framework that is independent of an underlying…
In machine learning and neuroscience, certain computational structures and algorithms are known to yield disentangled representations without us understanding why, the most striking examples being perhaps convolutional neural networks and…
We present a new turbulent data reconstruction method with supervised machine learning techniques inspired by super resolution and inbetweening, which can recover high-resolution turbulent flows from grossly coarse flow data in space and…
We present implicit displacement fields, a novel representation for detailed 3D geometry. Inspired by a classic surface deformation technique, displacement mapping, our method represents a complex surface as a smooth base surface plus a…
The three-dimensional reconstruction of scenes from multiple views has made impressive strides in recent years, chiefly by methods correlating isolated feature points, intensities, or curvilinear structure. In the general setting, i.e.,…
The effects of the hydration mechanism on continental crust recycling are analyzed through a 2D finite element thermo-mechanical model. Oceanic slab dehydration and consequent mantle wedge hydration are implemented using a dynamic method.…
This paper introduces a data-driven time embedding method for modeling long-range seasonal dependencies in spatiotemporal forecasting tasks. The proposed approach employs Dynamic Mode Decomposition (DMD) to extract temporal modes directly…
We investigate the performance of fully convolutional networks to simulate the motion and interaction of surface waves in open and closed complex geometries. We focus on a U-Net architecture and analyse how well it generalises to geometric…
Shape constraints enable us to reflect prior knowledge in regression settings. A unimodality constraint, for example, can describe the frequent case of a first increasing and then decreasing intensity. Yet, data shapes often exhibit…
Lifting is an efficient technique to scale up graphical models generalized to relational domains by exploiting the underlying symmetries. Concurrently, neural models are continuously expanding from grid-like tensor data into structured…
Analysing two-dimensional shallow water equations with idealised bottom topographies have many applications in the atmospheric and oceanic sciences; however, restrictive flow pattern assumptions have been made to achieve explicit solutions.…