User interface (UI) [1] is a medium for interaction and message exchange between people and electronic computer systems, and is a comprehensive environment for users to use electronic computers. At present, the definition of UI is relatively broad, and it is not restricted to the graphical UI of human–machine interaction. In a broad sense, UI is a collection of interaction methods between users and systems [2, 3]. These systems do not only refer to computer programs, but also include a specific machine, equipment, complex tool, etc. [4] The UI can be seen as representing a face-to-face information exchange method between people and computers, and the formation of the UI comes from the properties of artificial objects. The UI is a collection of interaction methods between users and the system, and is also the software and hardware part of the electronic computer system that realises the exchange of information between the user and the computer [5]. As shown in Figure 1, the UI is divided into a hardware interface and a software interface. The hardware interface mainly refers to the computer keyboard and mouse, as shown in Figure 1(a), and the software interface mainly refers to the interface for direct information exchange between the user and the computer, as shown in Figure 1(b) and (c), that is, the user browses multimedia through the computer network, and the text web interface. The purpose of the UI is to enable the user to operate the electronic computer system conveniently and efficiently to achieve two-way interaction. Nowadays, with the rapid development of computer networks, people have steadily increasing requirements for computers to process data, as well as handle other applications, including entertainment. The amount of software installed in the computer is increasing day by day, and this puts forward requirements on how to realise the interaction of the computer with a fast and comfortable interface.

Currently, when evaluating the parameters required for the UI, we mainly consider inclusivity and usability. Since the main service object of the interactive interface is the user, the inclusive interactive interface designed by Microsoft research has been formulated in such a way that users can solve problems according to their own needs; the UI has been endowed with a capability to adapt to the diversity of individuals, and this approach has resulted in an easy-to-use, flexible and good user experience. Brandon Antonio Cárdenas-Sainz

For the usability of the interactive interface, the main point is that the computer system can stably and quickly switch to the interface required by the user in a specific situation or software interaction required by the user. Some scholars have proposed that the interactive interface should have several requirements, such as learnability, high efficiency, memorability, low error rate, and automatic repair of errors and satisfaction [13], and for users, it should have relatively simple interaction. The switching operation and system are common [14]. The evaluation of usability is mainly based on the efficiency, effectiveness and user satisfaction of interface interaction (as shown in Figure 3). The longer the response time to complete a task, the higher the efficiency; at the same time, the greater the number of interactive interfaces that are completed within the specified time frame, the faster the speed. For effectiveness, according to the error rate and degree of completion in the interactive interface, the lower the error rate, the higher the completion rate, and the better the effectiveness. In this paper, we choose the response time of a long-term and frequent switching of an interactive interface and the response time of repeated interaction of multiple interfaces as the main criteria for usability. Alomari [15] measures the utility of a UI by testing its usability and using UI and user-experience assessments; these are studies that can be used to evaluate the usefulness of e-learning environments, and they find widespread application in computer science and software engineering courses.

However, when implementing interface generation, the commonly used software applications mainly include PS, AI.AE.C4D.XD.ARP and so on. PS is mainly used for image processing, AI icon design, AE dynamic effect design, and C4D is mainly used for modelling. For a single interface, there is a need for proper processing to enable the transition to the displayed interface. Nowadays, the interface is becoming increasingly complex. Yang and Horie [16] improved the UI by including neural network, which improved the accuracy of complex gestures. Yang

The biggest working feature of Rhino is that it uses the non-spline curve modelling method [21] (i.e. NURBS modelling method). It has the advantages of high modulus accuracy and flexible use [22]. Compared with other types of modelling software, it has lower requirements on the application environment, and takes up less computer space due to its fast running speed. This advantage ensures that more interactive use of computer interfaces can be achieved under the same storage space. In addition, it can cooperate with other extension plug-ins to realise extension function and realise powerful extension by substituting parameterised design. To simplify some complex parts, parametric modelling is increasingly widely used in some complex designs and applications, and complex modelling analysis is completed with the help of parametric modelling. As Rhino's parametric design platform, Grasshopper can complete advanced controls such as visual image generation and transformation, and achieve certain effects on the surface of performance analysis. This provides not only a new imagination space for structural design but also new solutions for some complex designs. Compared with the traditional design modelling, Grasshopper has the following characteristics, as shown in Figure 4: compellability, visualisation, and extensibility. Compellability means that by writing a series of programs, it can be connected to external systems, and real-time parameter changes can be realised without causing mutation of the interactive interface, thereby ensuring the multi-dimensional stability of the interactive interface; visualisation can generate geometric models according to specified algorithms. Zhang

There are many GH auxiliary external plug-ins, which are mainly divided into the following categories, as shown in Figure 5: design, algorithm, structure, conversion, and interactive simulation; these are mentioned here as several common external plug-ins. By simulating some related physical phenomena such as gravity, the modulation of physical formulas in the system can be improved; the algorithm class is mainly for parameterisation and improving data processing speed. The structural class can be targeted to give force analysis to each specific location, etc.; the conversion class is mainly to realise multi-software intercommunication, realise the Internet of things, human–computer exchange, visualisation, etc.; interactive simulation is mainly used to cluster data simulation and realise data visual interaction.

In the research work of this paper, LSTM and GRU algorithms are mainly used to optimise a model of the traditional interactive interface. The LSTM long-term and short-term neural network is evolved from the RNN [26]. The RNN adds weights to the neural network of the same layer, and introduces real-time feedback to correct the neural network. The LSTM neural network changes and processes the structure of the RNN based on RNN to solve the problem of its gradient disappearance [27]. This is mainly because the LSTM operates almost linearly, with the entire operation as linked rows. The long-term and short-term neural network is mainly composed of three control units: forget gate, input gate and output gate [28]. Its basic unit structure is shown in Figure 6. The main working formula is as follows:

The formula for calculating the input gate is
^{f}^{f}

GRUs is a gating mechanism in RNN [29]. Similar to LTMS network, GRU neural network is also a variation model of RNN network, but it is more concise than LTMS network. There are only update gates and reset gates in the network model [30, 31, 32]. The special significance of these two gating mechanisms is that the information in the sequence is preserved for a long time, and the information in the sequence is not cleared over time or removed because it is irrelevant to prediction [33]. The update gate formula is as follows:
_{t}_{z}_{z}_{z}_{t}_{−1} represents the information at time

The main function of the reset gate is to determine the abandoned information, using the formulas:

_{t}_{t}_{−1} represents the part of the final memory information retained at the previous moment.

The stability and rapid performance of the UI are affected by many factors. The selection of evaluation indicators is important for the interactive interface, and the training of the model is very important. In the experiment, the mean square error function is selected as the target cost function, and the experimental model is trained.

The process aims to make the objective cost function increasingly smaller and the prediction accuracy increasingly higher [34, 35]. The mean squared error is taken as the target cost function, which can stabilise the model effectively. The mean square error calculation is shown in Eq. (10):

For atrained model, the goodness of fit is used to determine the accuracy of the model. The closer the goodness of fit is to 1, the better the fit, and vice versa. The goodness of fit is calculated as in Eq. (11)
_{i}_{p}

The parameter selection of the model directly determines the effect of the model, through a large number of parameter adjustments. The specific parameters of the model selected in this paper are shown in Table 1.

Model parameter table

Value | 2 | 256 | 0.83 | 500 | 0.005 | 10 |

The target cost function uses the mean square error function to make the prediction more accurate. In order to avoid overfitting of the model, a dropout layer is added during the model training process, and the number of neurons in each layer is 256. In each round, 500 datasets are input for training, for a total of 10 rounds of training.

The experiment carried out multi-dimensional optimisation design for the reliability and inclusiveness of the interactive interface, and used LSTM and GRU algorithms to perform expansion, whereas Rhino/GH platform was used to enhance its data processing capability, ensure the reliability of the interactive interface, and avoid the occurrence of jamming and other phenomena. The experiment was carried out on Window10, 64-bit operating system, and the computer running memory was 16GB. The experiment selects a specific interface and performs 100 cycles of switching experiments on the same operating system to compare and analyse the impact time of the switching interfaces; in addition, to verify the inclusiveness of its interactive interfaces, we selected 20 interfaces on the same computer operating system, performed mutual switching of these 20 interfaces, and compared and analysed the response obtained when the interface is switched; additionally, to verify the reliability of the interactive interface, we used the same computer operating system. The number of interfaces was also compared.

Before conducting the experiment, we first conducted a comparative analysis of the LSTM and GRU models, analysed and compared the accuracy of the models and their root mean squares (RMSs), and selected the optimal algorithm suitable for the Rhino/GH platform expansion combination. The accuracy and loss of the model are shown in Table 2. It can be seen from Table 2 that the parameter accuracy of the LSTM and GRU algorithms can reach >98%. Using the GRU algorithm to process data on the Rhino/GH platform yields a higher relative accuracy, which can reach 99.3%, and the model training loss function is only 0.00212, which is 50% of that observed in the case of the LSTM algorithm. The main reason is that the GRU algorithm can update the data in real-time and train continuously during multi-interface interaction, thereby ensuring the usability and mutual inclusiveness of the interactive interface.

Model accuracy table

LSTM | 0.00452 | 98.2% |

GRU | 0.00212 | 99.3% |

GRU, Gated recurrent unit;

LSTM, long short-term memory

In order to evaluate the two algorithms from various aspects, we use RMS and goodness-of-fit analysis for further analysis and comparison, and the specific results are shown in Table 3.

RMS and fit table

^{2} |
||
---|---|---|

LSTM | 0.983 | 0.835 |

GRU | 0.879 | 0.910 |

GRU, Gated recurrent unit;

LSTM, long short-term memory;

RMSE, root mean square error

From the table, we can see that the RMS of GRU algorithm is smaller than that of LSTM, and the fitting degree is 91%, which is better than the 83.5% observed in the case of LSTM. Therefore, when optimising the interactive interface, choosing the GRU algorithm will be more realistic.

Figure 7(a) shows a comparison chart of the time required to switch between the traditional interactive interface and the Rhino/GH platform. In the actual test of 100 switching times, we can find that for the traditional interactive interface, the time is between 245 ms and 361 ms, and the fluctuation range is 47.3%. In contrast, the interactive interface based on the Rhino/GH platform yields excellent performance and high stability in the test. The interaction time is between 118 ms and 146 ms, and the maximum fluctuation range is only 23.7%; and compared with the traditional method, the decline rate is about 50%. In addition, the switching time has also dropped by >50% as a whole. In order to further verify the stability of the interactive interface of the Rhino/GH platform, we selected 20 interfaces to be online at the same time, and compared the change of the interaction response time with the results observed in the case of the traditional interaction method. The results are shown in 7(b). As can be seen from Figure 7(b), when multiple interface switching is frequent, the traditional interactive interface technology shows a gradual increasing trend with the increase of the number of interfaces, the response time is between 295 ms and 450 ms, and the fluctuation range is as high as 52.5%; and it shows an increasing trend with the increase of the interface. In addition, the overall response time is between 45 ms and 89 ms longer than the single interface's 245–361 ms. In contrast, the optimised interactive interface of Rhino/GH has a response time of 123–159 ms when 20 interfaces are switched, the maximum fluctuation range is 29.2%, and the response time remains within the stable range; additionally, the overall response time is only 13 ms longer than the 118–146 ms range of the monomer. The comprehensive results show that the optimised interactive interface of Rhino/GH has obvious usability, and the inclusiveness between different interfaces is good.

As can be seen from Figure 8, with the increase of the number of interactive interfaces, the proportion of computer running storage gradually increases until it can no longer work. Based on the traditional interactive interface, when the number of interfaces reaches 27, the proportion of memory reaches 89.1%, at which point the computer begins to appear sluggish, inefficient and unstable. At this time, the proportion of memory based on Rhino/GH optimisation platform was 73.2%, a decrease of 15.9%. After optimising the interactive interface, when the number of interfaces reached 33, the proportion of memory reached 89.2%, and then the computer operating system began to increasingly present with the characteristics of sluggishness, inefficiency, etc. The optimised interactive interface can increase the usage rate of computer memory by 22.2%.

The interactive interface optimisation research of Rhino/GH platform optimisation proposed in this paper introduces LSTM and GRU algorithms to optimise the platform data processing, and compares the long-term frequent switching of single interface and multi-interface interaction with the traditional interactive interface. The main conclusions are as follows:

When the GRU algorithm is added to the Rhino/GH platform for data processing, the model accuracy can reach 99.3%, and the RMS remains at 0.879. The introduction of GRU can realise real-time update of data, and avoid slow response caused by untimely processing of interactive interface data when the amount of data is too large, thereby affecting the use effect.

We introduce the interactive interface optimised by the Rhino/GH platform. When a single interface is frequently interacted for a long time, the overall response time is 50%, which is a similarity observed with the traditional interactive interface; again, the time fluctuation is within 23.7%, which is approximately 23.6% lower than the 47.3% observed in the case of the traditional interactive interface.

In the case of multi-interface interaction, the traditional interactive interface shows a trend of increasing response time as the interactive interface increases, and the fluctuation range also increases to 52.5%, which means that the instability of the interactive interface increases. The interactive interface optimised by the Rhino/GH platform maintains a fluctuation range within 29.2%, and the time increases by 13 ms, with good stability.

The optimised interactive interface of Rhino/GH platform can increase the utilisation rate of storage space by 22.2% when it is in use.

#### Model parameter table

Value | 2 | 256 | 0.83 | 500 | 0.005 | 10 |

#### Model accuracy table

LSTM | 0.00452 | 98.2% |

GRU | 0.00212 | 99.3% |

#### RMS and fit table

^{2} |
||
---|---|---|

LSTM | 0.983 | 0.835 |

GRU | 0.879 | 0.910 |

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main melody based on quadratic wave equation Analysis of wireless English multimedia communication based on spatial state model equation Optimization of Linear Algebra Core Function Framework on Multicore Processors Research on classification of e-commerce customers based on BP neural network The Control Relationship Between the Enterprise's Electrical Equipment and Mechanical Equipment Based on Graph Theory Mathematical Modeling and Forecasting of Economic Variables Based on Linear Regression Statistics Nonlinear Differential Equations in Cross-border E-commerce Controlling Return Rate 3D Mathematical Modeling Technology in Visualized Aerobics Dance Rehearsal System Fractional Differential Equations in Electronic Information Models BIM Engineering Management Oriented to Curve Equation Model Leakage control of urban water supply network and mathematical analysis and location of leakage points based on machine learning Analysis of higher education management strategy based on entropy and dissipative structure theory Prediction of corporate financial distress based on digital signal processing and multiple regression analysis Mathematical Method to Construct the Linear Programming of Football Training Multimedia sensor image detection based on constrained underdetermined equation The Size of Children's Strollers of Different Ages Based on Ergonomic Mathematics Design Application of Numerical Computation of Partial Differential Equations in Interactive Design of Virtual Reality Media Stiffness Calculation of Gear Hydraulic System Based on the Modeling of Nonlinear Dynamics Differential Equations in the Progressive Method Knowledge Analysis of Charged Particle Motion in Uniform Electromagnetic Field Based on Maxwell Equation Relationship Between Enterprise Talent Management and Performance Based on the Structural Equation Model Method Term structure of economic management rate based on parameter analysis of estimation model of ordinary differential equation Influence 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transmission effect based on degree of debt concentration and product market competitive advantage Study on transmission characteristics in three kinds of deformed finlines based on edge-based finite element method Asymptotic stability problem of predator–prey system with linear diffusion Research on loyalty prediction of e-commerce customer based on data mining Algebraic Equations in Educational Model of College Physical Education Course Education Professional English Translation Corpus Under the Binomial Theorem Coefficient Geometric Tolerance Control Method for Precision Machinery Based on Image Modeling and Novel Saturation Function Retrieval and Characteristic Analysis of Multimedia Tester Based on Bragg Equation Semiparametric Spatial Econometric Analysis of Household Consumption Based on Ordinary Linear Regression Model Video adaptive watermark embedding and detection algorithm based on phase function equation English Learning Motivation of College Students Based on probability 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Performance of Shot Put Application of Nonlinear Differential Equation in Electric Automation Control System Higher Mathematics Teaching Curriculum Model Based on Lagrangian Mathematical Model Computational Algorithm to Solve Two–Body Problem Using Power Series in Geocentric System Decisions of competing supply chain with altruistic retailer under risk aversion Optimization of Color Matching Technology in Cultural Industry by Fractional Differential Equations The Marketing of Cross-border E-commerce Enterprises in Foreign Trade Based on the Statistics of Mathematical Probability Theory Application of Linear Partial Differential Equation Theory in Guiding Football Scientific Training Nonlinear Channel Estimation for Internet of Vehicles Some Necessary Conditions for Feedback Functions of de Bruijn Sequences The Evolution Model of Regional Tourism Economic Development Difference Based on Spatial Variation Function System Model of Shipping Enterprise Safety Culture Based on Dynamic 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algorithm-based congestion control optimisation for mobile data network