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The nonlinear response of Cattaneo-type thermal loading of a laser pulse on a medium using the generalized thermoelastic model

Farshad Shakeriaski, Maryam Ghodrat

Accepted Manuscript , doi: 10.1016/j.taml.2020.01.030

[Abstract] (144) [FullText HTML] (89) [PDF 3211KB] (5)

Abstract:
The nonlinear thermoelastic responses of an elastic medium exposed to laser generated short-pulse heating are investigated in this article. The thermal wave propagation of generalized thermoelastic medium under the impact of thermal loading with energy dissipation is the focus of this research. To model the thermal boundary condition (in the form of thermal conduction), generalized Cattaneo model (GCM) is employed. In the reference configuration, a nonlinear coupled Lord-Shulman-type generalized thermoelasticity formulation using finite strain theory (FST) is developed and the temperature dependency of the thermal conductivity is considered to derive the equations. In order to solve the time-dependent and nonlinear equations, Newmark's numerical time integration technique and an updated finite element algorithm is applied and to ensure achieving accurate continuity of the results, the Hermitian elements are used instead of Lagrangian's. The numerical responses for different factors such as input heat flux and nonlinear terms are expressed graphically and their impacts on the system's reaction are discussed in detail. The results of the study are presented for Green–Lindsay model and the findings are compared with Lord-Shulman model especially with regards to heat wave propagation. It is shown that the nature of the laser's thermal shock and its geometry are particularly determinative in the final stage of deformation. The research also concluded that employing FST leads to achieving more accuracy in terms of elastic deformations; however, the thermally nonlinear analysis does not change the results markedly. For this reason, the nonlinear theory of deformation is required in laser related reviews, while it is reasonable to ignore the temperature changes compared to the reference temperature in deriving governing equations.

Constructal design method dealing with stiffened plates and symmetry boundaries

Rodrigo R. Amaral, Grégori S. Troina, Cristiano Fragassa, Ana Pavlovic, Marcelo L. Cunha, Luiz A. O. Rocha, Elizaldo D. dos Santos, Liércio A. Isoldi

Accepted Manuscript , doi: 10.1016/j.taml.2020.01.042

[Abstract] (129) [FullText HTML] (77) [PDF 3184KB] (7)

Abstract:
A new computational procedure for modelling the structural behavior of stiffened plates with symmetry boundary conditions is here presented. It uses two-dimensional finite elements as a way to decrease computational time without losing precision thanks to a relatively small number of elements applied for analyzing out-of-plane displacements (deflections) and stresses. Adding, the constructal design method was included in the procedure, together with the Exhaustive Search technique, with the scope to optimize the stress/strain status of stiffened plates by design changes. For the purpose, a reference plate without stiffeners was initially design and used as starting point. Part of the volume was reshaped into stiffeners: thickness was reduced maintaining unchanged weight, length and width. The main goal was to minimize strains and stresses by geometric changes. Results demonstrated that, thanks to this design procedure, it is always possible to find an adequate geometry transformation from reference plate into stiffeners, allowing significant improvements in mechanical behavior.

A novel method for investigation of acoustic and elastic wave phenomena using numerical experiments

Alena Favorskaya, Igor Petrov

Accepted Manuscript , doi: 10.1016/j.taml.2020.01.040

[Abstract] (109) [FullText HTML] (68) [PDF 774KB] (1)

Abstract:
The emergence of new types of composite materials, the depletion of existing hydrocarbon deposits, and the increase in the speed of trains require the development of new research methods based on wave scattering. Therefore, it is necessary to determine the laws of wave scattering in inhomogeneous media. We propose a method that combines the advantages of a numerical simulation with an analytical study of the boundary value problem of elastic and acoustic wave equations. In this letter we present the results of the study using the proposed method: the formation of a response from a shear wave in an acoustic medium and the formation of shear waves when a vertically incident longitudinal wave is scattered by a vertical gas-filled fracture. We have obtained a number of analytical expressions characterising the scattering of these wave types.

A note on a family of proximal gradient methods for quasi-static incremental problems in elastoplastic analysis

Yoshihiro Kanno

Accepted Manuscript , doi: 10.1016/j.taml.2020.01.044

[Abstract] (67) [FullText HTML] (46) [PDF 2598KB] (0)

Abstract:
Accelerated proximal gradient methods have recently been developed for solving quasi-static incremental problems of elastoplastic analysis with some different yield criteria. It has been demonstrated through numerical experiments that these methods can outperform conventional optimization-based approaches in computational plasticity. However, in literature these algorithms are described individually for specific yield criteria, and hence there exists no guide for application of the algorithms to other yield criteria. This short paper presents a general form of algorithm design, independent of specific forms of yield criteria, that unifies the existing proximal gradient methods. Clear interpretation is also given to each step of the presented general algorithm so that each update rule is linked to the underlying physical laws in terms of mechanical quantities.

A unidirectional SH wave transducer based on phase-controlled antiparallel thickness-shear (d₁₅) piezoelectric strips

Mingtong Chen, Qiang Huan, Faxin Li

Accepted Manuscript

[Abstract] (0) [FullText HTML] (0) [PDF 3118KB] (0)

Abstract:
In recent years, shear horizontal (SH) waves are being paid more and more attention to in structural health monitoring as it has only one displacement component. In this paper, a unidirectional SH wave transducer based on phase-controlled antiparallel thickness-shear (d₁₅) piezoelectric strips (APS) is proposed. Here two pairs of identical APS were used each of which is a bidirectional SH wave transducer. By setting the interval between the two pairs of APS as 1/4 wavelength and the excitation delay between them as 1/4 period of the central operating frequency, unidirectional SH waves can be excited. Both finite element simulations and experiments were performed to validate the proposed design. Results show that SH₀ waves were successfully excited only along one direction and those along the unwanted directions were suppressed very well. The proposed unidirectional SH wave transducer is very helpful to study the fundamentals and applications of SH waves.

Modeling rock fragmentation by coupling Voronoi diagram and discretized virtual internal bond

Sai Liu, Zhennan Zhang

Accepted Manuscript , doi: 10.1016/j.taml.2020.01.045

[Abstract] (76) [FullText HTML] (42) [PDF 3136KB] (0)

Abstract:
The rock fragmentation involves the inter-block and the intra-block fracture. A simulation method for rock fragmentation is developed by coupling Voronoi diagram (VD) and discretized virtual internal bond (DVIB). The DVIB is a lattice model that consists of bonds. The VD is used to generate the potential block structure in the DVIB mesh. Each potential block may contain any number of bond cells. To characterize the inter-block fracture, a hyperelastic bond potential is employed for the bond cells that are cut by the VD edges. While to characterize the intra-block fracture, an elastobrittle bond potential is adopted for the bonds in a block. By this method, both the inter-block and intra-block fracture can be well simulated. The simulation results suggest that this method is a simple and efficient approach to rock fragmentation simulation with block smash.

Achieving an optimal shock-wave mitigation inside open channels with cavities for weak shock waves: A computational study

N. Brahmi, A. Hadjadj

Accepted Manuscript , doi: 10.1016/j.taml.2020.01.046

[Abstract] (72) [FullText HTML] (42) [PDF 3952KB] (0)

Abstract:
This paper deals with a numerical study of weak shock-waves propagation and their attenuation in channel flow having different heights and exhibiting a hollow circular cavities with different depths and diffraction angles inside. The effect of initial diffraction angle and cavity depth on the shock mitigation is investigated. A better shock attenuation is achieved with diffraction angle

\begin{document}$ \theta_{w} = 90^\circ $\end{document}

by a factor of approximately 17% in terms of shock-Mach number and 38% in terms of total energy. The obtained results show also, in addition to the initial diffraction angle and cavity depth, the importance of reducing the channel heights as well as the position of the reduced section in achieving an optimal shock-wave attenuation. The presence of a cavity inside the channel helps to attenuate faster the shock wave. The underlying physics relies on the shock diffraction phenomenon that generates large amount of vortical structures capable of dissipating part of the shock energy by inducing a pressure loss behind it. A subtle arrangement of channel position/height and a cavity location leads to an efficient pressure attenuation by approximately a factor of 57% for

\begin{document}$ M_s = 1.6 $\end{document}

and 16% for

\begin{document}$ M_s = 1.1 $\end{document}

Numerical investigations to design a novel model based on the fifth order system of Emden-Fowler equations

Zulqurnain Sabir, Mehmet Giyas Sakar, Manshuk Yeskindirova, Onur Saldir

Accepted Manuscript , doi: 10.1016/j.taml.2020.01.049

[Abstract] (0) [FullText HTML] (0) [PDF 2750KB] (0)

Abstract:
The aim of the present study is to design a new fifth order system of Emden-Fowler equations and related four types of the model. The standard second order form of the Emden-Fowler has been used to obtain the new model. The shape factor that appear more than one time discussed in detail for every case of the designed model. The singularity at η = 0 at one point or multiple points is also discussed at each type of the model. For validation and correctness of the new designed model, one example of each type based on system of fifth order Emden-Fowler equations are provided and numerical solutions of the designed equations of each type have been obtained by using variational iteration scheme. The comparison of the exact results and present numerical outcomes for solving one problem of each type is presented to check the accuracy of the designed model.

Ultrasound calibration with ladder phantom at multiple depths for breast biopsy navigation system

Jackrit Suthakorn, Narucha Tanaiutchawoot, Cholatip Wiratkapan

Accepted Manuscript , doi: 10.1016/j.taml.2020.01.037

[Abstract] (112) [FullText HTML] (74) [PDF 2952KB] (1)

Abstract:
Ultrasound guided breast biopsy navigation system with a graphical user interface and a passive robotic needle holder is developed to increase the performance and reliability of the radiologist. Ultrasound calibration and tool tip calibration are required before using the system. A ladder phantom is developed to be used for ultrasound calibration in real time system with only one ultrasound image required. The passive robotic needle holder structure results in an identity matrix for the makes the rotation matrix; therefore, only translation and scaling are required in the system. This method can be applied to multiple ultrasound depths, which has a relationship at each depth and a relationship to the ultrasound image on the display. The results show high accuracy (<1 mm.) and rapid calibration (5-10 minutes) which is suitable for a real time system like a breast biopsy navigation system based on tests with a breast phantom.

A unidirectional SH wave transducer based on phase-controlled antiparallel thickness-shear (d₁₅) piezoelectric strips

Mingtong Chen, Qiang Huan, Faxin Li

Accepted Manuscript

[Abstract] (0) [PDF 3118KB] (0)

Numerical investigations to design a novel model based on the fifth order system of Emden-Fowler equations

Zulqurnain Sabir, Mehmet Giyas Sakar, Manshuk Yeskindirova, Onur Saldir

Accepted Manuscript , doi: 10.1016/j.taml.2020.01.049

[Abstract] (0) [PDF 2750KB] (0)

Review on charging model of sand particles due to collisions

Li Xie, Junjie Li, Yakui Liu

Accepted Manuscript , doi: 10.1016/j.taml.2020.01.047

[Abstract] (79) [FullText HTML] (43) [PDF 2830KB] (0)

Abstract:
In this paper, the models describing the charge transfer between two sand particles due to collisions are reviewed. By comparing the experimental results and the calculated results by the models carried on an individual particle due to a single collision, it indicates the Mosaic model is more reasonable to describe the collision charging mechanism. The Mosaic model cannot only describe the dependence of the collision charges on the relative collision speed and the particle size, but also reveal the relationship between the collision charges with the environmental temperature, the relative humidity and the material parameters, e.g., the absorption energy. Based on the Mosaic model, the model to describe the charges transfer due to multiple collisions is also developed, which can be used to calculate the charges carried by sand particles due to multiple collisions in the wind blown sand flux.

On the mechanism by which nose bluntness suppresses second-mode instability

Armani Batista, Arham Amin Khan, Joseph Kuehl

Corrected proof , doi: 10.1016/j.taml.2020.01.024

[Abstract] (215) [FullText HTML] (282) [PDF 3178KB] (10)

Abstract:
A physical mechanism by which nose bluntness suppresses second-mode instability is proposed. Considered are 7 degree half-angle straight cones with nose bluntness radii of 0.15 mm, 3.556 mm, 5 mm, 9.525 mm, 12.7 mm and 25.4 mm at tunnel conditions relevant to the AFOSR-Notre Dame Large Mach 6 Quiet Tunnel. It is shown that second-mode suppression is achieved via entropy layer modulation of the basic state density gradient. A weakening of the density gradient disrupts the acoustic resonance necessary to sustain second-mode growth. These results are consistent with the thermoacoustic interpretation which posits that second-mode instability can be modeled as thermoacoustic resonance of acoustic energy trapped within an acoustic impedance well. Furthermore, the generalized inflection point criterion of Lees and Lin is applied to develop a criterion for the existence of second-mode instability based on the strength of the basic state density gradient.

Particles-induced turbulence: A critical review of physical concepts, numerical modelings and experimental investigations

Guodong Gai, Abdellah Hadjadj, Sergey Kudriakov, Olivier Thomine

Corrected proof , doi: 10.1016/j.taml.2020.01.026

[Abstract] (190) [FullText HTML] (115) [PDF 2986KB] (2)

Abstract:
The presence of solid particles or water droplets in continuous fluid flow can either induce turbulence attenuation or amplification. The modification of the state of the turbulence depends on the characteristics of the particles, such as volume fraction, mean diameter, mass density, or carrier phase flow properties. In this brief review, the main physical concepts related to the most important physical aspects of turbulence modulation are summarized. Different criteria used to distinguish the enhancement or the attenuation effects of the particles on the carrier phase flows are recalled. For the interest of large-scale industrial applications, several theoretical, experimental and empirical approaches are discussed, which provides an interesting framework for the study of the effect of particles on turbulence behavior modification.

An improved semi-empirical friction model for gas-liquid two-phase flow in horizontal and near horizontal pipes

M. Gharehasanlou, M. Emamzadeh, M. Ameri

Corrected proof , doi: 10.1016/j.taml.2020.01.013

[Abstract] (174) [FullText HTML] (98) [PDF 3402KB] (3)

Abstract:
Pressure drop and liquid hold-up are two very important fluid flow parameters in design and control of multiphase flow pipelines. Friction factors play an important role in the accurate calculation of pressure drop. Various empirical and semi-empirical closure relations exist in the literature to calculate the liquid-wall, gas-wall and interfacial friction in two-phase pipe flow. However most of them are empirical correlations found under special experimental conditions.In this paper by modification of a friction model available in the literature, an improved semi-empirical model is proposed. The proposed model is incorporated in the two-fluid correlations under equilibrium conditions and solved. Pressure gradient and velocity profiles are validated against experimental data.Using the improved model, the pressure gradient deviation from experiments diminishes by about 3%; the no-slip condition at the interface is satisfied and the velocity profile is predicted in better agreement with the experimental data.

Investigation on Savonius turbine technology as harvesting instrument of non-fossil energy: Technical development and potential implementation

Aditya Rio Prabowo, Dandun Mahesa Prabowoputra

Corrected proof , doi: 10.1016/j.taml.2020.01.034

[Abstract] (164) [FullText HTML] (94) [PDF 3189KB] (6)

Abstract:
Environmental risk due to excessive residual emission is rising. Greenhouse effect, ice melting in the Arctic, reduction of air quality are several concerns which need immediate development and change. Energy harvesting equipment is one of the key solutions. Environment potential, e.g. water resource can be collaborated with mechanical equipment to harvest clean energy. Savonius turbine has been proposed and studied for this purpose and can be placed on several energy resources, i.e. water and wind. Still, real-world implementation of this technology is lacking, especially in tropical archipelago countries which have abundant water resources. In this work, assessment of Savonius turbine technology as instrument to harvest clean energy is conducted. A series of development on the turbine performance and technical modification is considered as reference to implement the technology in water and open air environments. It is noted that rotor design, operation depth and nozzle attachment are several key influencing factors.

Nonlinear energy harvesting from vibratory disc-shaped piezoelectric laminates

Abdolreza Pasharavesh, Reza Moheimani, Hamid Dalir

Corrected proof , doi: 10.1016/j.taml.2020.01.032

[Abstract] (189) [FullText HTML] (106) [PDF 3072KB] (17)

Abstract:
Implementing resonators with geometrical nonlinearities in vibrational energy harvesting systems leads to considerable enhancement of their operational bandwidths. This advantage of nonlinear devices in comparison to their linear counterparts is much more obvious especially at small-scale where transition to nonlinear regime of vibration occurs at moderately small amplitudes of the base excitation. In this paper the nonlinear behavior of a disc-shaped piezoelectric laminated harvester considering midplane-stretching effect is investigated. Extended Hamilton's principle is exploited to extract electromechanically coupled governing partial differential equations of the system. The equations are firstly order-reduced and then analytically solved implementing perturbation method of multiple scales. A nonlinear finite element method (FEM) simulation of the system is performed additionally for the purpose of verification which shows agreement with the analytical solution to a large extent. The frequency response of the output power at primary resonance of the harvester is calculated to investigate the effect of nonlinearity on the system performance. Effect of various parameters including mechanical quality factor, external load impedance and base excitation amplitude on the behavior of the system are studied. Findings indicate that in the nonlinear regime both output power and operational bandwidth of the harvester will be enhanced by increasing the mechanical quality factor which can be considered as a significant advantage in comparison to linear harvesters in which these two factors vary in opposite ways as quality factor is changed.

Deformation and failure in nanomaterials via a data driven modelling approach

M. Amir Siddiq

Corrected proof , doi: 10.1016/j.taml.2020.01.029

[Abstract] (146) [FullText HTML] (98) [PDF 2522KB] (6)

Abstract:
A data driven computational model that accounts for more than two material states has been presented in this work. Presented model can account for multiple state variables, such as stresses, strains, strain rates and failure stress, as compared to previously reported models with two states. Model is used to perform deformation and failure simulations of carbon nanotubes and carbon nanotube/epoxy nanocomposites. The model capability of capturing the strain rate dependent deformation and failure has been demonstrated through predictions against uniaxial test data taken from literature. The predicted results show a good agreement between data set taken from literature and simulations.

Simulation of shear layers interaction and unsteady evolution under different double backward-facing steps

Fang Deng, Guilai Han, Zonglin Jiang

Corrected proof , doi: 10.1016/j.taml.2020.01.020

[Abstract] (232) [FullText HTML] (142) [PDF 2687KB] (4)

Abstract:
High-order accurate schemes are employed to numerically simulate the interaction of a supersonic jet and a co-directional supersonic inflow. A double backward-facing step model is proposed to investigate the interaction between the jet shear layer and the supersonic inflow shear layer. It is found that due to the interaction of the shear layer, a secondary jet is injected into the recirculation zone at the intersection of the two shear layers. The secondary jet produced by the interaction of the two shear layers has a periodicity because of shear layers interaction. The distinction in the shape of double backward-facing steps will induce changes in the period of the secondary jet. The analysis and discussion of the periodicity of the secondary jet are mainly focused in this letter.

On plane Λ-fractional linear elasticity theory

K.A. Lazopoulos, A.K. Lazopoulos

Accepted Manuscript , doi: 10.1016/j.taml.2020.01.035

[Abstract] (112) [FullText HTML] (77) [PDF 2679KB] (0)

Abstract:
Non-local plane elasticity problems are discussed in the context of Λ-fractional linear elasticity theory. Adapting the Λ-fractional derivative along with the Λ-fractional space, where geometry and mechanics are valid in the conventional way, non-local plane elasticity problems are solved with the help of biharmonic functions. Then, the results are transferred into the initial plane. Applications are presented to homogeneous and the fractional beam bending problem.

Universal scaling law of an origami paper spring

Bo-Hua Sun

Accepted Manuscript , doi: 10.1016/j.taml.2020.01.002

[Abstract] (354) [FullText HTML] (207) [PDF 2469KB] (5)

Abstract:
This letter solves an open question of origami paper spring risen by Yoneda et al.(Phys. Rev. E 2019). By using both dimensional analysis and data fitting, an universal scaling law of a paper spring is formulated. The scaling law shows that origami spring force obeys power square law of spring extension, however strong nonlinear to the total twist angle. The study has also successfully generalized the scaling law from the Poisson ratio 0.3 to an arbitrary Poisson's ratio with the help of dimensional analysis.

Neurodynamics analysis of cochlear hair cell activity

Weifeng Rong, Rubin Wang, Jianhai Zhang, Wanzeng Kong

Accepted Manuscript

[Abstract] (325) [PDF 3000KB] (2)

Abstract:
There have been many studies on the effect of cochlea basal membrane movement on the resolution of different frequencies and intensities. However, these studies did not take into account the influence of power and energy consumption of the hair cells in the process of the electromotility movement, as well as the neurodynamic mechanism that produced this effect. This makes previous studies unable to fully clarify the function of outer hair cells and the mechanism of sound amplification. To this end, we introduce the gate conductance characteristics of the hair cells in the mechanical process of increasing frequency selectivity. The research finds that the low attenuation of outer hair cell (OHCs) membrane potential and the high gain in OHC power and energy consumption caused that OHC amplification is driven by electromotility. The research results show that the amplification of the outer hair cells is driven by low attenuation of membrane potential and high gain of power and energy consumption. This conclusion profoundly reveals the physiological mechanism of the electromotility movement.

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Mechanistic Machine Learning: Theory, Methods, and Applications

2020, 10(3): 141 -142. doi: 10.1016/j.taml.2020.01.041

[Abstract] (203) [FullText HTML] (112) [PDF 3081KB] (21)

Abstract:
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Letter

Deep density estimation via invertible block-triangular mapping

Keju Tang, Xiaoliang Wan, Qifeng Liao

2020, 10(3): 143 -148. doi: 10.1016/j.taml.2020.01.023

[Abstract] (216) [FullText HTML] (184) [PDF 2663KB] (18)

Abstract:
In this work, we develop an invertible transport map, called KRnet, for density estimation by coupling the Knothe–Rosenblatt (KR) rearrangement and the flow-based generative model, which generalizes the real-valued non-volume preserving (real NVP) model (arX-iv:1605.08803v3). The triangular structure of the KR rearrangement breaks the symmetry of the real NVP in terms of the exchange of information between dimensions, which not only accelerates the training process but also improves the accuracy significantly. We have also introduced several new layers into the generative model to improve both robustness and effectiveness, including a reformulated affine coupling layer, a rotation layer and a component-wise nonlinear invertible layer. The KRnet can be used for both density estimation and sample generation especially when the dimensionality is relatively high. Numerical experiments have been presented to demonstrate the performance of KRnet.

Classifying wakes produced by self-propelled fish-like swimmers using neural networks

Binglin Li, Xiang Zhang, Xing Zhang

2020, 10(3): 149 -154. doi: 10.1016/j.taml.2020.01.010

[Abstract] (240) [FullText HTML] (149) [PDF 2705KB] (10)

Abstract:
We consider the classification of wake structures produced by self-propelled fish-like swimmers based on local measurements of flow variables. This problem is inspired by the extraordinary capability of animal swimmers in perceiving their hydrodynamic environments under dark condition. We train different neural networks to classify wake structures by using the streamwise velocity component, the crosswise velocity component, the vorticity and the combination of three flow variables, respectively. It is found that the neural networks trained using the two velocity components perform well in identifying the wake types, whereas the neural network trained using the vorticity suffers from a high rate of misclassification. When the neural network is trained using the combination of all three flow variables, a remarkably high accuracy in wake classification can be achieved. The results of this study can be helpful to the design of flow sensory systems in robotic underwater vehicles.

Physics-constrained indirect supervised learning

Yuntian Chen, Dongxiao Zhang

2020, 10(3): 155 -160. doi: 10.1016/j.taml.2020.01.019

[Abstract] (220) [FullText HTML] (147) [PDF 2624KB] (9)

Abstract:
This study proposes a supervised learning method that does not rely on labels. We use variables associated with the label as indirect labels, and construct an indirect physics-constrained loss based on the physical mechanism to train the model. In the training process, the model prediction is mapped to the space of value that conforms to the physical mechanism through the projection matrix, and then the model is trained based on the indirect labels. The final prediction result of the model conforms to the physical mechanism between indirect label and label, and also meets the constraints of the indirect label. The present study also develops projection matrix normalization and prediction covariance analysis to ensure that the model can be fully trained. Finally, the effect of the physics-constrained indirect supervised learning is verified based on a well log generation problem.

Physics-constrained bayesian neural network for fluid flow reconstruction with sparse and noisy data

Luning Sun, Jian-Xun Wang

2020, 10(3): 161 -169. doi: 10.1016/j.taml.2020.01.031

[Abstract] (210) [FullText HTML] (124) [PDF 2942KB] (8)

Abstract:
In many applications, flow measurements are usually sparse and possibly noisy. The reconstruction of a high-resolution flow field from limited and imperfect flow information is significant yet challenging. In this work, we propose an innovative physics-constrained Bayesian deep learning approach to reconstruct flow fields from sparse, noisy velocity data, where equation-based constraints are imposed through the likelihood function and uncertainty of the reconstructed flow can be estimated. Specifically, a Bayesian deep neural network is trained on sparse measurement data to capture the flow field. In the meantime, the violation of physical laws will be penalized on a large number of spatiotemporal points where measurements are not available. A non-parametric variational inference approach is applied to enable efficient physics-constrained Bayesian learning. Several test cases on idealized vascular flows with synthetic measurement data are studied to demonstrate the merit of the proposed method.

Reducing parameter space for neural network training

Tong Qin, Ling Zhou, Dongbin Xiu

2020, 10(3): 170 -181. doi: 10.1016/j.taml.2020.01.043

[Abstract] (151) [FullText HTML] (93) [PDF 5600KB] (4)

Abstract:
For neural networks (NNs) with rectified linear unit (ReLU) or binary activation functions, we show that their training can be accomplished in a reduced parameter space. Specifically, the weights in each neuron can be trained on the unit sphere, as opposed to the entire space, and the threshold can be trained in a bounded interval, as opposed to the real line. We show that the NNs in the reduced parameter space are mathematically equivalent to the standard NNs with parameters in the whole space. The reduced parameter space shall facilitate the optimization procedure for the network training, as the search space becomes (much) smaller. We demonstrate the improved training performance using numerical examples.

Nonnegativity-enforced Gaussian process regression

Andrew Pensoneault, Xiu Yang, Xueyu Zhu

2020, 10(3): 182 -187. doi: 10.1016/j.taml.2020.01.036

[Abstract] (175) [FullText HTML] (97) [PDF 2842KB] (5)

Abstract:
Gaussian process (GP) regression is a flexible non-parametric approach to approximate complex models. In many cases, these models correspond to processes with bounded physical properties. Standard GP regression typically results in a proxy model which is unbounded for all temporal or spacial points, and thus leaves the possibility of taking on infeasible values. We propose an approach to enforce the physical constraints in a probabilistic way under the GP regression framework. In addition, this new approach reduces the variance in the resulting GP model.

A perspective on regression and Bayesian approaches for system identification of pattern formation dynamics

Zhenlin Wang, Bowei Wu, Krishna Garikipati, Xun Huan

2020, 10(3): 188 -194. doi: 10.1016/j.taml.2020.01.028

[Abstract] (138) [FullText HTML] (96) [PDF 2835KB] (8)

Abstract:
We present two approaches to system identification, i.e. the identification of partial differential equations (PDEs) from measurement data. The first is a regression-based variational system identification procedure that is advantageous in not requiring repeated forward model solves and has good scalability to large number of differential operators. However it has strict data type requirements needing the ability to directly represent the operators through the available data. The second is a Bayesian inference framework highly valuable for providing uncertainty quantification, and flexible for accommodating sparse and noisy data that may also be indirect quantities of interest. However, it also requires repeated forward solutions of the PDE models which is expensive and hinders scalability. We provide illustrations of results on a model problem for pattern formation dynamics, and discuss merits of the presented methods.

Multi-fidelity Gaussian process based empirical potential development for Si:H nanowires

Moonseop Kim, Huayi Yin, Guang Lin

2020, 10(3): 195 -201. doi: 10.1016/j.taml.2020.01.027

[Abstract] (128) [FullText HTML] (75) [PDF 2952KB] (3)

Abstract:
In material modeling, the calculation speed using the empirical potentials is fast compared to the first principle calculations, but the results are not as accurate as of the first principle calculations. First principle calculations are accurate but slow and very expensive to calculate. In this work, first, the H-H binding energy and H₂-H₂ interaction energy are calculated using the first principle calculations which can be applied to the Tersoff empirical potential. Second, the H-H parameters are estimated. After fitting H-H parameters, the mechanical properties are obtained. Finally, to integrate both the low-fidelity empirical potential data and the data from the high-fidelity first-principle calculations, the multi-fidelity Gaussian process regression is employed to predict the H-H binding energy and the H₂-H₂ interaction energy. Numerical results demonstrate the accuracy of the developed empirical potentials.

Learning material law from displacement fields by artificial neural network

Hang Yang, Qian Xiang, Shan Tang, Xu Guo

2020, 10(3): 202 -206. doi: 10.1016/j.taml.2020.01.038

[Abstract] (173) [FullText HTML] (106) [PDF 2912KB] (10)

Abstract:
The recently developed data-driven approach can establish the material law for nonlinear elastic composite materials (especially newly developed materials) by the generated stress-strain data under different loading paths (Computational Mechanics, 2019). Generally, the displacement (or strain) fields can be obtained relatively easier using digital image correlation (DIC) technique experimentally, but the stress field is hard to be measured. This situation limits the applicability of the proposed data-driven approach. In this paper, a method based on artificial neural network (ANN) to identify stress fields and further obtain the material law of nonlinear elastic materials is presented, which can make the proposed data-driven approach more practical. A numerical example is given to prove the validity of the method. The limitations of the proposed approach are also discussed.

Physics-informed deep learning for incompressible laminar flows

Chengping Rao, Hao Sun, Yang Liu

2020, 10(3): 207 -212. doi: 10.1016/j.taml.2020.01.039

[Abstract] (148) [FullText HTML] (93) [PDF 4183KB] (15)

Abstract:
Physics-informed deep learning has drawn tremendous interest in recent years to solve computational physics problems, whose basic concept is to embed physical laws to constrain/inform neural networks, with the need of less data for training a reliable model. This can be achieved by incorporating the residual of physics equations into the loss function. Through minimizing the loss function, the network could approximate the solution. In this paper, we propose a mixed-variable scheme of physics-informed neural network (PINN) for fluid dynamics and apply it to simulate steady and transient laminar flows at low Reynolds numbers. A parametric study indicates that the mixed-variable scheme can improve the PINN trainability and the solution accuracy. The predicted velocity and pressure fields by the proposed PINN approach are also compared with the reference numerical solutions. Simulation results demonstrate great potential of the proposed PINN for fluid flow simulation with a high accuracy.