Traditional methods for selecting models in experimental data analysis are susceptible to researcher bias, hindering exploration of alternative explanations and potentially leading to overfitting. The Finite Information Quantity (FIQ) approach offers a novel solution by acknowledging the inherent limitations in information processing capacity of physical systems. This framework facilitates the development of objective criteria for model selection (comparative uncertainty) and paves the way for a more comprehensive understanding of phenomena through exploring diverse explanations. This work presents a detailed comparison of the FIQ approach with ten established model selection methods, highlighting the advantages and limitations of each. We demonstrate the potential of FIQ to enhance the objectivity and robustness of scientific inquiry through three practical examples: selecting appropriate models for measuring fundamental constants, sound velocity, and underwater electrical discharges. Further research is warranted to explore the full applicability of FIQ across various scientific disciplines.
A time series model is used in this paper to describe the progress of circulating direct condensation heat recovery of the compound condensing process (CCP) which is made of two water cooling condensing processes in series for a centrifugal chiller in the paper. A finite-time thermodynamics method is used to set up the time series simulation model. As a result, an upper bound of recoverable condensation heat for the compound condensing process is obtained which is in good agreement with experimental result. And the result is valuable and useful to optimization design of condensing heat recovery.
This paper presents a mathematical model consisting of conservation and balance laws (CBL) of classical continuum mechanics (CCM) and ordered rate constitutive theories in Lagrangian description derived using entropy inequality and the representation theorem for thermoviscoelastic solids (TVES) with rheology. The CBL and the constitutive theories take into account finite deformation and finite strain deformation physics and are based on contravariant deviatoric second Piola-Kirchhoff stress tensor and its work conjugate covariant Green’s strain tensor and their material derivatives of up to order m and n respectively. All published works on nonlinear dynamics of TVES with rheology are mostly based on phenomenological mathematical models. In rare instances, some aspects of CBL are used but are incorrectly altered to obtain mass, stiffness and damping matrices using space-time decoupled approaches. In the work presented in this paper, we show that this is not possible using CBL of CCM for TVES with rheology. Thus, the mathematical models used currently in the published works are not the correct description of the physics of nonlinear dynamics of TVES with rheology. The mathematical model used in the present work is strictly based on the CBL of CCM and is thermodynamically and mathematically consistent and the space-time coupled finite element methodology used in this work is unconditionally stable and provides solutions with desired accuracy and is ideally suited for nonlinear dynamics of TVES with memory. The work in this paper is the first presentation of a mathematical model strictly based on CBL of CCM and the solution of the mathematical model is obtained using unconditionally stable space-time coupled computational methodology that provides control over the errors in the evolution. Both space-time coupled and space-time decoupled finite element formulations are considered for obtaining solutions of the IVPs described by the mathematical model and are presented in the paper. Factors or the physics influencin
Magneto-electro-elastic (MEE) materials, a new type of composite intelligent materials, exhibit excellent multifield coupling effects. Due to the heterogeneity of the materials, it is challenging to use the traditional finite element method (FEM) for mechanical analysis. Additionally, the MEE materials are often in a complex service environment, especially under the influence of the thermal field with thermoelectric and thermomagnetic effects, which affect its mechanical properties. Therefore, this paper proposes the efficient multiscale computational method for the multifield coupling problem of heterogeneous MEE structures under the thermal environment. The method constructs a multi-physics field with numerical base functions (the displacement, electric potential, and magnetic potential multiscale base functions). It equates a single cell of heterogeneous MEE materials to a macroscopic unit and supplements the macroscopic model with a microscopic model. This allows the problem to be solved directly on a macroscopic scale. Finally, the numerical simulation results demonstrate that compared with the traditional FEM, the multiscale finite element method (MsFEM) can achieve the purpose of ensuring accuracy and reducing the degree of freedom, and significantly improving the calculation efficiency.
The energy norm convergence rate of the finite element solution of the heat equation is reduced by the time-regularity of the exact solution. This paper presents an adaptive finite element treatment of time-dependent singularities on the one-dimensional heat equation. The method is based on a Fourier decomposition of the solution and an extraction formula of the coefficients of the singularities coupled with a predictor-corrector algorithm. The method recovers the optimal convergence rate of the finite element method on a quasi-uniform mesh refinement. Numerical results are carried out to show the efficiency of the method.
In this paper, the optimal control problem of parabolic integro-differential equations is solved by gradient recovery based two-grid finite element method. Piecewise linear functions are used to approximate state and co-state variables, and piecewise constant function is used to approximate control variables. Generally, the optimal conditions for the problem are solved iteratively until the control variable reaches error tolerance. In order to calculate all the variables individually and parallelly, we introduce a gradient recovery based two-grid method. First, we solve the small scaled optimal control problem on coarse grids. Next, we use the gradient recovery technique to recover the gradients of state and co-state variables. Finally, using the recovered variables, we solve the large scaled optimal control problem for all variables independently. Moreover, we estimate priori error for the proposed scheme, and use an example to validate the theoretical results.
Dear Editor,This letter is concerned with the role of recurrent neural networks(RNNs)on the controller design for a class of nonlinear systems.Inspired by the architectures of RNNs,the system states are stacked according to the dynamic along with time while the controller is represented as the neural network output.To build the bridge between RNNs and finite-time controller,a novel activation function is imposed on RNNs to drive the convergence of states at finite-time and propel the overall control process smoother.Rigorous stability proof is briefly provided for the convergence of the proposed finite-time controller.At last,a numerical simulation example is presented to illustrate the efficiency of the proposed strategy.Neural networks can be classified as static(feedforward)and dynamic(recurrent)nets[1].The former nets do not perform well in dealing with training data and using any information of the local data structure[2].In contrast to the feedforward neural networks,RNNs are constituted by high dimensional hidden states with dynamics.
A two-grid finite element method with L1 scheme is presented for solving two-dimen-sional time-fractional nonlinear Schrodinger equation.The finite element solution in the L-norm are proved bounded without any time-step size conditions(dependent on spatial-step size).The classical L1 scheme is considered in the time direction,and the two-grid finite element method is applied in spatial direction.The optimal order error estimations of the two-grid solution in the LP-norm is proved without any time-step size conditions.It is shown,both theoretically and numerically,that the coarse space can be extremely coarse,with no loss in the order of accuracy.
The variation of the principal stress of formations with the working and geo-mechanical conditions can trigger wellbore instabilities and adversely affect the well completion.A finite element model,based on the theory of poro-elasticity and the Mohr-Coulomb rock damage criterion,is used here to analyze such a risk.The changes in wellbore stability before and after reservoir acidification are simulated for different pressure differences.The results indicate that the risk of wellbore instability grows with an increase in the production-pressure difference regardless of whether acidification is completed or not;the same is true for the instability area.After acidizing,the changes in the main geomechanical parameters(i.e.,elastic modulus,Poisson’s ratio,and rock strength)cause the maximum wellbore instability coefficient to increase.
Junyan LiuJu LiuYan WangShuang LiuQiao WangYihe Du
In this paper,we consider the truncated multiplicity finite range set problem of meromorphic functions on some complex disc.By using the value distribution theory of meromorphic functions,we establish a second main theorem for meromorphic functions with finite growth index which share meromorphic functions(may not be small functions).As its application,we also extend the result of a finite range set with truncated multiplicity.
