Parallel Physics-Informed Neural Networks Method with Regularization Strategies for the Forward-Inverse Problems of the Variable Coefficient Modified KdV Equation

This paper mainly introduces the parallel physics-informed neural networks(PPINNs)method with regularization strategies to solve the data-driven forward-inverse problems of the variable coefficient modified Korteweg-de Vries(VC-MKdV)equation.For the forward problem of the VC-MKdV equation,the authors use the traditional PINN method to obtain satisfactory data-driven soliton solutions and provide a detailed analysis of the impact of network width and depth on solving accuracy and speed.Furthermore,the author finds that the traditional PINN method outperforms the one with locally adaptive activation functions in solving the data-driven forward problems of the VC-MKdV equation.As for the data-driven inverse problem of the VC-MKdV equation,the author introduces a parallel neural networks to separately train the solution function and coefficient function,successfully addressing the function discovery problem of the VC-MKdV equation.To further enhance the network’s generalization ability and noise robustness,the author incorporates two regularization strategies into the PPINNs.An amount of numerical experimental data in this paper demonstrates that the PPINNs method can effectively address the function discovery problem of the VC-MKdV equation,and the inclusion of appropriate regularization strategies in the PPINNs can improves its performance.

Amending Research on the Expression of the Contact Force of the Spindle Barrel Finishing Based on EDEM Simulation

The spindle barrel finishing is commonly used to improve the surface integrity of the important parts of the high-end equipment while it is difficult to provide enough test artifacts for the traditional trial and error experiment to obtain the desirable processing technology.The EDEM simulation of the spindle barrel finishing can provide effective help for the process design,however,the difference between the simulation and experiment is closely related to the selection of the contact model during simulation.In this paper,simulations and experiments are conducted based on the identical apparatus and conditions to facilitate the comparison and validation between each other.Based on the Hertz contact theory,the effect of the material properties of contact objects and the relative position of the workpiece on the contact force is qualified.The expression of the correlation coefficient of the contact model is deduced.Then the formula for calculating the contact force between the barrel finishing abrasive and the workpiece that includes influence coefficient of the material properties and the relative positions is established.Finally,the contact force calculation formula is verified by changing the rotating speed.The result shows that the material correction coefficient ranges from 1.41 to 2.38,which is inversely related to the equivalent modulus E.The position correction coefficient ranges from 2.0 to 2.3.The relative error value between the calculation result and the experimental test result is from 0.58%to 14.07%.This research lay a theoretical foundation for the correction theory of the core elements of the spindle barrel finishing process.

Third-order modified coeffcient scheme based on essentially non-oscillatory scheme

A third-order numerical scheme is presented to give approximate solutions to multi-dimensional hyperbolic conservation laws only using modified coefficients of an essentially non-oscillatory （MCENO） scheme without increasing the base points during construction of the scheme. The construction process shows that the modified coefficient approach preserves favourable properties inherent in the original essentially nonoscillatory （ENO） scheme for its essential non-oscillation, total variation bounded （TVB）, etc. The new scheme improves accuracy by one order compared to the original one. The proposed MCENO scheme is applied to simulate two-dimensional Rayleigh-Taylor （RT） instability with densities 1：3 and 1：100, and solve the Lax shock-wave tube numerically. The ratio of CPU time used to implement MCENO, the .third-order ENO and fifth-order weighed ENO （WENO） schemes is 0.62：1：2.19. This indicates that MCENO improves accuracy in smooth regions and has higher accuracy and better efficiency compared to the original ENO scheme.

ESTIMATION OF DIRECTIONAL SPECTRUM AND REFLECTED COEFFICIENT OF INCIDENT AND REFLECTED WAVE IN PHASE-LOCKED WAVE FIELD

This paper analyses and compares the property of the Modified Bayesian Directional spectrum analysis Method （MBDM） and the Modified Maximum Lkelihood Method （MMLM） that can he used to estimate directional spectrum and reflected coefficient of phase-locked wave field overlapped by multi directional irregular incident and reflected waves. The numerical test verifies the results under different wave conditions, different measurement systems, and different reflection features. The computation speed and stability of the two methods is also compared. The analysis addresses that the MBDM is better than the MMLM for directional spectrum estimating, while the MMLM is better than the MBDM for reflected coefficient estimation and calculating speed and stability.

改进输出系数模型在农业面源氮磷污染物负荷估算中的应用

There is a great uncertainty in generation and formation of non-point source(NPS)pollutants,which leads to difficulties in the investigation of monitoring and control.However,accurate calculation of these pollutant loads is closely correlated to control NPS pollutants in agriculture.In addition,the relationships between pollutant load and human activity and physiographic factor remain elusive.In this study,a modified model with the whole process of agricultural NPS pollutant migration was established by introducing factors including rainfall driving,terrain impact,runoff index,leaching index and landscape intercept index for the load calculation.Partial least squares path modeling was applied to explore the interactions between these factors.The simulation results indicated that the average total nitrogen(TN)load intensity was 0.57 t km-2 and the average total phosphorus(TP)load intensity was 0.01 t km-2in Chengdu Plain.The critical effects identified in this study could provide useful guidance to NPS pollution control.These findings further our understanding of the NPS pollution control in agriculture and the formulation of sustainable preventive measures.

Impurity distribution in metallic dysprosium during distillation purification

The distribution rules of impurities contents in distilled metallic dysprosium were researched, and a theoretical analysis was carried out. The research results indicated that, the content of impurity in distilled metal, such as Al and Fe, was lower in the ini-tial stage, increased slowly in the middle stage, and increased rapidly in the last stage during the process of distillation purification. The calculated method of separation coefficient of impurity in crude metal by content of impurity in distilled metal was not suitable for high pure metals, and the modified separation coefficient was proposed, and it equaled 1/6.1 and 1/16.9 for impurity Al and Fe. The physical process of distillation was coincident with that of solidification essentially, and solute re-distribution theory in solidify-ing front could be used to describe the impurity distribution near evaporating surface. In the former stage of distillation purification, the diffusion of impurity in liquid metal could reach a quasi-equilibrium state, the calculated result of impurity content in distilled metal agreed well with experiments. In the latter stage of distillation process, the diffusion rate of impurity in liquid metal decreased, and the content in distilled metal was larger than the calculated result.