Physics-informed Neural Networks for Solving Inverse Problems of Nonlinear Biot's Equations: Batch Training

In biomedical engineering, earthquake prediction, and underground energy harvesting, it is crucial to indirectly estimate the physical properties of porous media since the direct measurement of those are usually impractical/prohibitive. Here we apply the physics-informed neural networks to solve the inverse problem with regard to the nonlinear Biot's equations. Specifically, we consider batch training and explore the effect of different batch sizes. The results show that training with small batch sizes, i.e., a few examples per batch, provides better approximations (lower percentage error) of the physical parameters than using large batches or the full batch. The increased accuracy of the physical parameters, comes at the cost of longer training time. Specifically, we find the size should not be too small since a very small batch size requires a very long training time without a corresponding improvement in estimation accuracy. We find that a batch size of 8 or 32 is a good compromise, which is also robust to additive noise in the data. The learning rate also plays an important role and should be used as a hyperparameter.Comment: arXiv admin note: text overlap with arXiv:2002.0823

Real-time simulation of soft tissue deformation for surgical simulation

Surgical simulation plays an important role in the training, planning and evaluation of many surgical procedures. It requires realistic and real-time simulation of soft tissue deformation under interaction with surgical tools. However, it is challenging to satisfy both of these conflicting requirements. On one hand, biological soft tissues are complex in terms of material compositions, structural formations, and mechanical behaviours, resulting in nonlinear deformation characteristics under an external load. Due to the involvement of both material and geometric nonlinearities, the use of nonlinear elasticity causes a highly expensive computational load, leading to the difficulty to achieve the real-time computational performance required by surgical simulation. On the other hand, in order to satisfy the real-time computational requirement, most of the existing methods are mainly based on linear elasticity under the assumptions of small deformation and homogeneity to describe deformation of soft tissues. Such simplifications allow reduced runtime computation; however, they are inadequate for modelling nonlinear material properties such as anisotropy, heterogeneity and large deformation of soft tissues. In general, the two conflicting requirements of surgical simulation raise immense complexity in modelling of soft tissue deformation. This thesis focuses on establishment of new methodologies for modelling of soft tissue deformation for surgical simulation. Due to geometric and material nonlinearities in soft tissue deformation, the existing methods have only limited capabilities in achieving nonlinear soft tissue deformation in real-time. In this thesis, the main focus is devoted to the real-time and realistic modelling of nonlinear soft tissue deformation for surgical simulation. New methodologies, namely new ChainMail algorithms, energy propagation method, and energy balance method, are proposed to address soft tissue deformation. Results demonstrate that the proposed methods can simulate the typical soft tissue mechanical properties, accommodate isotropic and homogeneous, anisotropic and heterogeneous materials, handle incompressibility and viscoelastic behaviours, conserve system energy, and achieve realistic, real-time and stable deformation. In the future, it is projected to extend the proposed methodologies to handle surgical operations, such as cutting, joining and suturing, for topology changes occurred in surgical simulation

Human Pose Estimation from Monocular Images : a Comprehensive Survey

Human pose estimation refers to the estimation of the location of body parts and how they are connected in an image. Human pose estimation from monocular images has wide applications (e.g., image indexing). Several surveys on human pose estimation can be found in the literature, but they focus on a certain category; for example, model-based approaches or human motion analysis, etc. As far as we know, an overall review of this problem domain has yet to be provided. Furthermore, recent advancements based on deep learning have brought novel algorithms for this problem. In this paper, a comprehensive survey of human pose estimation from monocular images is carried out including milestone works and recent advancements. Based on one standard pipeline for the solution of computer vision problems, this survey splits the problema into several modules: feature extraction and description, human body models, and modelin methods. Problem modeling methods are approached based on two means of categorization in this survey. One way to categorize includes top-down and bottom-up methods, and another way includes generative and discriminative methods. Considering the fact that one direct application of human pose estimation is to provide initialization for automatic video surveillance, there are additional sections for motion-related methods in all modules: motion features, motion models, and motion-based methods. Finally, the paper also collects 26 publicly available data sets for validation and provides error measurement methods that are frequently used

Structure and pressure drop of real and virtual metal wire meshes

An efficient mathematical model to virtually generate woven metal wire meshes is presented. The accuracy of this model is verified by the comparison of virtual structures with three-dimensional images of real meshes, which are produced via computer tomography. Virtual structures are generated for three types of metal wire meshes using only easy to measure parameters. For these geometries the velocity-dependent pressure drop is simulated and compared with measurements performed by the GKD - Gebr. Kufferath AG. The simulation results lie within the tolerances of the measurements. The generation of the structures and the numerical simulations were done at GKD using the Fraunhofer GeoDict software

A proof of convergence of a finite volume scheme for modified steady Richards’ equation describing transport processes in the pressing section of a paper machine

A number of water flow problems in porous media are modelled by Richards’ equation [1]. There exist a lot of different applications of this model. We are concerned with the simulation of the pressing section of a paper machine. This part of the industrial process provides the dewatering of the paper layer by the use of clothings, i.e. press felts, which absorb the water during pressing [2]. A system of nips are formed in the simplest case by rolls, which increase sheet dryness by pressing against each other (see Figure 1). A lot of theoretical studies were done for Richards’ equation (see [3], [4] and references therein). Most articles consider the case of x-independent coefficients. This simplifies the system considerably since, after Kirchhoff’s transformation of the problem, the elliptic operator becomes linear. In our case this condition is not satisfied and we have to consider nonlinear operator of second order. Moreover, all these articles are concerned with the nonstationary problem, while we are interested in the stationary case. Due to complexity of the physical process our problem has a specific feature. An additional convective term appears in our model because the porous media moves with the constant velocity through the pressing rolls. This term is zero in immobile porous media. We are not aware of papers, which deal with such kind of modified steady Richards’ problem. The goal of this paper is to obtain the stability results, to show the existence of a solution to the discrete problem, to prove the convergence of the approximate solution to the weak solution of the modified steady Richards’ equation, which describes the transport processes in the pressing section. In Section 2 we present the model which we consider. In Section 3 a numerical scheme obtained by the finite volume method is given. The main part of this paper is theoretical studies, which are given in Section 4. Section 5 presents a numerical experiment. The conclusion of this work is given in Section 6

Lattice Element Method and its application to Multiphysics

In this thesis, a Lattice element modelling method is developed and is applied to model the loose and cemented, natural and artificial, granular matters subject to thermo-hydro-mechanical coupled loading conditions. In lattice element method, the lattice nodes which can be considered as the centres of the unit cells, are connected by cohesive links, such as spring beams that can carry normal and shear forces, bending and torsion moment. For the heat transfer due to conduction, the cohesive links are also used to carry heat as 1D pipes, and the physical properties of these rods are computed based on the Hertz contact model. The hydro part is included with the pore network modelling scheme. The voids are inscribed with the pore nodes and connected with throats, and then the meso level flow equation is solved. The Euler-Bernoulli and Timoshenko beams are chosen as the cohesive links or the lattice elements, while the latter should be used when beam elements are short and deep. This property becomes interesting in modelling auxetic materials. The model is applied to study benchmarks in geotechnical engineering. For heat transfer in the dry and full range of saturation, and fractures in the cemented granular media.How through porous media failure behaviours of rocks at high temperature and pressure and granular composites subjected to coupled Thermo hydro Mechanical loads. The model is further extended to capture the wave motion in the heterogeneous granular matter, and a few case studies for the wavefield modification with existing cracks are presented. The developed method is capable of capturing the complex interaction of crack wave interaction with relative ease and at a substantially less computational cost

Parallel software tool for decomposing and meshing of 3d structures

An algorithm for automatic parallel generation of three-dimensional unstructured computational meshes based on geometrical domain decomposition is proposed in this paper. Software package build upon proposed algorithm is described. Several practical examples of mesh generation on multiprocessor computational systems are given. It is shown that developed parallel algorithm enables us to reduce mesh generation time significantly (dozens of times). Moreover, it easily produces meshes with number of elements of order 5 · 107, construction of those on a single CPU is problematic. Questions of time consumption, efficiency of computations and quality of generated meshes are also considered

Using the Sharp Operator for edge detection and nonlinear diffusion

In this paper we investigate the use of the sharp function known from functional analysis in image processing. The sharp function gives a measure of the variations of a function and can be used as an edge detector. We extend the classical notion of the sharp function for measuring anisotropic behaviour and give a fast anisotropic edge detection variant inspired by the sharp function. We show that these edge detection results are useful to steer isotropic and anisotropic nonlinear diffusion filters for image enhancement

Optimal control for studying wave energy in hydraulic systems

A class of novel models for water waves induced by elastic deformation in the topography is developed and analyzed. The depth-averaged shallow water equations including friction terms for the water free-surface and the well-known second-order elastostatic formulation for the bed deformation have been implemented. Friction forces and water hydrostatic pressure distribution are also accounted for in this model. At the interface between the water ow and the bed topography, transfer conditions are implemented. Furthermore, a hybrid nite element/nite volume method for solving free-surface run-up ow problems over deformable beds has been proposed. The deformations in the topography have been generated by a localized force which causes propagations of the water waves with dierent amplitudes and frequencies. Two dierent methods have been proposed for the transfer of informations through the interface. The rst one is the two-mesh procedure; in this method a proper interpolation has been implemented to transfer the data between the surface nodes and the control volumes using uniform nite volume meshes. In the second method, and to avoid the interpolation at the interface, a nite volume method using non-uniform meshes has been implemented. When the shallow water waves approach the coastline they begin to transform as they enter shallow water regime. As each wave begins to experience the seabed, both run-up and overtopping occur. To solve for this, a class of stable, accurate and simple numerical model for moving wet/dry fronts in shallow water equations using the parametrization concept and the point-wise Riemann solver has been proposed. Many parameters of shallow water equations are subject to uncertainties to the inherit randomness of natural processes. To incorporate uncertain parameters into the stochastic shallow water equations, the stochastic properties of dierent parameters that are considered uncertain, namely in ow boundary condition, the bed friction coecients and the domain topography are added to the system. Development of accurate and ecient tools for uncertainty quantication in shallow water ows has been proposed and carefully examined for single-layer, two-layer - nite volume models. To further quantify the uncertainty in shallow water ows the proposed methods have been extended to multi-layer shallow water ows with mass exchange terms subject to stochastic topography, uncertain friction and viscosity coecients. Several test examples and well-established benchmark problems have been used to assess the numerical performance of the proposed models and methods. Comparisons to experimental measurements have also been carried out in this thesis. Finally, an optimal control technique for bed reconstruction has been presented as in many engineering applications this information is not entirely provided