Condensing the multi-dimensional digital model of green urban design, and constructing a digital method system of it progressively layer by layer. Based on this research background, the dissertation designs the spatial form of landscape architecture based on the data visualisation of nonlinear technology. The article uses the colour zoning method to design the actual scene of the garden landscape with nonlinear parameteriszation. The simulation result analyses that the proposed nonlinear algorithm has realised the efficiency improvement purpose of landscape architecture design.

#### Keywords

- Landscape design
- extensive data analysis
- nonlinearity
- feature extraction
- spatial form design

#### MSC 2010

- 34A34

Before the emergence of landscape ecology, the status of landscape architecture belonged to architecture. Landscape design serves the construction and provides a place for leisure and entertainment in the crowded city. With the emergence of landscape ecology, the discipline of landscape architecture has gradually moved towards a self-independent development path. Landscape architecture in this period went hand in hand with architecture and urban planning, and each developed in its professional field [1]. This separation of disciplines destroys the diversity of places and humans to a certain extent. Due to the fragmentation of disciplines in the Chinese context, part of the landscape design is still attached to architecture, and the landscape is fragmented and homogeneous. Design pursues single issues such as form, function, style, and ecology within the discipline, and the limitations brought about by the separation of disciplines are becoming increasingly apparent.

Nonlinear science is regarded as “another revolution” in the history of science in the 20th century. It has almost spread to all fields of natural sciences, humanities, and social sciences and is changing people's traditional views of the real world. The scientific community believes that the research of nonlinear science has great scientific significance, and nonlinearity is the source of complexity and variety in nature [2]. The development of nonlinear science has also caused profound changes in philosophy and methodology. Our contribution to its exploration is creating a new subject field. Still, the more far-reaching significance is that it has brought about a significant change in the outlook on nature, the outlook on science, the methodology, and even thinking. Nonlinear interaction has a more intrinsic and essential meaning than linear interaction. Linear interaction is only a highly simplified and approximate treatment of nonlinear interaction. Information technology closely related to nonlinear science is developing rapidly, making today's society a transformation from a post-industry to an information society. Information technology is based on computer, communication and control technology. In recent years, information technology has developed database technology, artificial intelligence, expert system, remote sensing technology, geographic information system, global positioning system, computer-aided decision-making system, automatic control technology, monitoring technology, multimedia technology, computer network technology and other applications. And these technologies have widely influenced all aspects of people's lives.

With the continuous advancement of ecological landscape construction and improved living environment, people's quality standards for landscape construction are constantly improving. So we need to carry out multi-dimensional nonlinear landscape design. Combining the functional positioning of the landscape to optimise the structure of multi-dimensional nonlinear landscape design can improve its urban design. The multi-dimensional nonlinear landscape design method is of great significance in improving the rationality of architectural design and improving the living environment of human settlements [3]. The planning and design of landscape construction based on its development orientationand government policy-oriented factors can help us improve the spatial expression ability. The article uses computer vision with structured image analysis and parameter simulation methods to optimise multi-dimensional design. This paper proposes a multi-dimensional nonlinear landscape design method based on parameterised models to improve the quantitative analysis ability.

To achieve a multi-dimensional nonlinear landscape design, we need to perform model parameter analysis and feature extraction. We construct a dynamic feature distribution model of multi-dimensional nonlinear landscape images through block matching detection and fusion recognition of multi-dimensional nonlinear landscape images [4]. The article combines the fuzzy associated feature point detection method to optimise the extraction of multi-dimensional nonlinear landscape data. We combine fuzzy feature extraction methods to optimise the collection and feature recognition of multi-dimensional nonlinear landscape images. This article uses the pixel feature point area reconstruction method for multi-dimensional nonlinear landscape image processing and information fusion. The geometric invariant moment generation model for constructing a multi-dimensional nonlinear landscape image is
_{i,j}_{max} − _{min}, width_{max} − _{min}, and height _{max} − _{min} of the landscape area distribution. We use the template block region matching method, traverse all sub-blocks, and combine high-resolution information fusion technology to simulate multi-dimensional nonlinear landscape parameters to obtain the scale-space:
_{c}_{c}

The thesis uses the virtual space visual planning method to simulate multi-dimensional nonlinear landscape design [7]. Combining the distribution characteristics of each pixel to perform multi-dimensional nonlinear landscape image similarity analysis, the expression of the spatial and regional feature matching model for landscape design is:

We combined the RGB feature decomposition method to perform parameterised segmentation of multi-dimensional nonlinear landscape models [9]. The thesis extracts the fuzzy degree matching feature quantity of the multi-dimensional nonlinear landscape image. The estimated value of the parameters of the salient feature points in the inner and outer areas of the target edge of the landscape image is:
_{01} and _{02} to denote the edge blur characteristics of multi-dimensional nonlinear landscape images, respectively [11]. We use the block fusion technology to obtain the edge template area of the landscape design that satisfies the normal distribution in the _{c}_{r}_{k}_{i}

The experiment adopts a Matlab simulation design. The sample pixel scale of landscape images is 100~ 600. The pixel distribution of the landscape image is 300 × 300. The modulus of metric learning is 100. The number of iterations is 1200. The descriptive statistical analysis results of the correlation parameters are shown in Table 1.

Descriptive statistical analysis results

100 | 0.723 | 0.456 | 0.775 | 0.532 |

200 | 0.434 | 0.556 | 0.565 | 0.545 |

300 | 0.531 | 0.434 | 0.454 | 0.554 |

400 | 0.534 | 0.643 | 0.554 | 0.545 |

500 | 0.422 | 0.434 | 0.324 | 0.544 |

600 | 0.345 | 0.454 | 0.455 | 0.434 |

According to the descriptive statistical analysis results in Table 1, multi-dimensional nonlinear landscape image sampling is performed. We use the virtual scene space visual planning method to simulate multi-dimensional nonlinear landscape design parameters to achieve landscape optimisation design [13]. The design effect results are shown in Figures 2–4. Analysing Figures 2–4, we know that our multi-dimensional nonlinear landscape design method has a better effect.

The test regression analysis value and test value, and other parameter results are shown in Table 2. Analysing Table 2 shows that we adopt the method of this paper to carry out multi-dimensional nonlinear landscape design with better visual feature expression ability. The parameter distribution structured fitting accuracy is high.

Regression analysis value and test value

Landscape planning structure | 0.456 | 1.432 | 0.456 |

Habitat satisfaction level | 0754 | 1.544 | 0.656 |

Environmental risk factor | 0.467 | 1.676 | 0.265 |

Ecological improvement level | 0.435 | 1.545 | 0.645 |

Landscape construction scale | 0.567 | 0.545 | 0.367 |

Decision evaluation value | 0.365 | 0.567 | 0.655 |

Overall planning configuration efficiency | 0.545 | 0.545 | 0.345 |

Regression standard deviation | 0.567 | 0.753 | 0.655 |

This paper proposes a multi-dimensional nonlinear landscape design method based on a parameterised model to extract a multi-dimensional nonlinear landscape view model. We use parameteried model methods to achieve multi-dimensional lnonlinear landscape design. The article uses the computer vision image analysis method to carry out multi-dimensional nonlinear landscape design and constructs a parametric analysis model of multi-dimensional nonlinear landscape design. We combine fuzzy feature extraction methods to optimise the collection and feature recognition of multi-dimensional nonlinear landscape images. The analysis shows that we have a solid ability to express visual characteristics of multi-dimensional nonlinear landscape design using this method. Moreover, the landscape design effect obtained by this method is better.

#### Regression analysis value and test value

Landscape planning structure | 0.456 | 1.432 | 0.456 |

Habitat satisfaction level | 0754 | 1.544 | 0.656 |

Environmental risk factor | 0.467 | 1.676 | 0.265 |

Ecological improvement level | 0.435 | 1.545 | 0.645 |

Landscape construction scale | 0.567 | 0.545 | 0.367 |

Decision evaluation value | 0.365 | 0.567 | 0.655 |

Overall planning configuration efficiency | 0.545 | 0.545 | 0.345 |

Regression standard deviation | 0.567 | 0.753 | 0.655 |

#### Descriptive statistical analysis results

100 | 0.723 | 0.456 | 0.775 | 0.532 |

200 | 0.434 | 0.556 | 0.565 | 0.545 |

300 | 0.531 | 0.434 | 0.454 | 0.554 |

400 | 0.534 | 0.643 | 0.554 | 0.545 |

500 | 0.422 | 0.434 | 0.324 | 0.544 |

600 | 0.345 | 0.454 | 0.455 | 0.434 |

Law of interest rate changes in financial markets based on the differential equation model of liquidity Basalt fibre continuous reinforcement composite pavement reinforcement design based on finite element model Industrial transfer and regional economy coordination based on multiple regression model Response model for the psychological education of college students based on non-linear finite element equations Satisfactory consistency judgement and inconsistency adjustment of linguistic judgement matrix Analysis of the relationship between industrial agglomeration and regional economic growth based on the multi-objective optimisation model Constraint effect of enterprise productivity based on constrained form variational computing The impact of urban expansion in Beijing and Metropolitan Area urban heat Island from 1999 to 2019 Ultrasonic wave promoting ice melt in ice storage tank based on polynomial fitting calculation model Regarding new wave distributions of the non-linear integro-partial Ito differential and fifth-order integrable equations Badminton players’ trajectory under numerical calculation method Innovations to Attribute Reduction of Covering Decision System Based on Conditional Information Entropy Nonlinear Differential Equations in the Teaching Model of Educational Informatisation The evaluation of college students’ innovation and entrepreneurship ability based on nonlinear model Smart Communities to Reduce Earthquake Damage: A Case Study in Xinheyuan, China Institutional investor company social responsibility report and company performance Mathematical analysis of China's birth rate and research on the urgency of deepening the reform of art education First-principles calculations of magnetic and mechanical properties of Fe-based nanocrystalline alloy Fe _{80}Si_{10}Nb_{6}B_{2}Cu_{2}Has the belt and road initiative boosted the resident consumption in cities along the domestic route? – evidence from credit card consumption Attitude control for the rigid spacecraft with the improved extended state observer Cognitive Computational Model Using Machine Learning Algorithm in Artificial Intelligence Environment Research on tourism income index based on ordinary differential mathematical equation Application of Higher-Order Ordinary Differential Equation Model in Financial Investment Stock Price Forecast Sports Science Teaching of Athletics Based on Nonlinear Mathematical Equation Informatisation of educational reform based on fractional differential equations Research on the control of quantitative economic management variables under the numerical method based on stochastic ordinary differential equations Network monitoring and processing accuracy of big data acquisition based on mathematical model of fractional differential equation System dynamics model of output of ball mill Sensitivity Analysis of the Waterproof Performance of Elastic Rubber Gasket in Shield Tunnel Design of Morlet wavelet neural network to solve the non-linear influenza disease system Motion about equilibrium points in the Jupiter-Europa system with oblateness Badminton players’ trajectory under numerical calculation method Optimal preview repetitive control for impulse-free continuous-time descriptor systems Development of main functional modules for MVB and its application in rail transit Study on the impact of forest fire prevention policy on the health of forest resources Value Creation of Real Estate Company Spin-off Property Service Company Listing Selection by differential mortality rates Digital model creation and image meticulous processing based on variational partial differential equation The modelling and implementation of the virtual 3D animation scene based on the geometric centre-of-mass algorithm The policy efficiency evaluation of the Beijing–Tianjin–Hebei regional government guidance fund based on the entropy method The transfer of stylised artistic images in eye movement experiments based on fuzzy differential equations Research on behavioural differences in the processing of tenant listing information: An eye-movement experiment A review of the treatment techniques of VOC Some classes of complete permutation polynomials in the form of ( x ^{pm}−x +δ )^{s}+ax ^{pm}+bx overF _{p2m}Deformation and stress theory of surrounding rock of shallow circular tunnel based on complex variable function method The consistency method of linguistic information and other four preference information in group decision-making Research on the willingness of Forest Land’s Management Rights transfer under the Beijing Forestry Development A mathematical model of the fractional differential method for structural design dynamics simulation of lower limb force movement step structure based on Sanda movement Numerical calculation and study of differential equations of muscle movement velocity based on martial articulation body ligament tension Study on the maximum value of flight distance based on the fractional differential equation for calculating the best path of shot put Sports intensity and energy consumption based on fractional linear regression equation Translog function in government development of low-carbon economy Analysis of the properties of matrix rank and the relationship between matrix rank and matrix operations Research on the Psychological Distribution Delay of Artificial Neural Network Based on the Analysis of Differential Equation by Inequality Expansion and Contraction Method Study on Establishment and Improvement Strategy of Aviation Equipment Research on Financial Risk Early Warning of Listed Companies Based on Stochastic Effect Mode The Model of Sugar Metabolism and Exercise Energy Expenditure Based on Fractional Linear Regression Equation Constructing Artistic Surface Modeling Design Based on Nonlinear Over-limit Interpolation Equation Numerical Simulation Analysis Mathematics of Fluid Mechanics for Semiconductor Circuit Breaker Characteristics of Mathematical Statistics Model of Student Emotion in College Physical Education Human Body Movement Coupling Model in Physical Education Class in the Educational Mathematical Equation of Reasonable Exercise Course The contribution of structural equation model analysis to higher education agglomeration and innovation and entrepreneurship Study on the evolutionary game theory of the psychological choice for online purchase of fresh produce under replicator dynamics formula The influence of X fuzzy mathematics method in basketball tactics scoring Mathematical statistics algorithm in the bending performance test of corroded reinforced concrete beams under fatigue load Nonlinear strategic human resource management based on organisational mathematical model Back propagation mathematical model for stock price prediction Evolutionary game research on the psychological choice of online shopping of fresh agricultural products based on dynamic simulation model Differential equation model of financial market stability based on big data Multi-attribute decision-making methods based on normal random variables in supply chain risk management Linear fractional differential equations in bank resource allocation and financial risk management model Construction and reform of art design teaching mode under the background of the integration of non-linear equations and the internet Spatial–temporal graph neural network based on node attention A contrastive study on the production of double vowels in Mandarin Financial accounting measurement model based on numerical analysis of rigid normal differential equation and rigid generalised functional equation Research of cascade averaging control in hydraulic equilibrium regulation of heating pipe network Mathematical analysis of civil litigation and empirical research of corporate governance Health monitoring of Bridges based on multifractal theory College students’ innovation and entrepreneurship ability based on nonlinear model Health status diagnosis of the bridges based on multi-fractal de-trend fluctuation analysis Mathematical simulation analysis of optimal testing of shot puter's throwing path Performance evaluation of college laboratories based on fusion of decision tree and BP neural network Application and risk assessment of the energy performance contracting model in energy conservation of public buildings The term structure of economic management rate under the parameter analysis of the estimation model based on common differential equation Sensitivity analysis of design parameters of envelope enclosure performance in the dry-hot and dry-cold areas The Spatial Form of Digital Nonlinear Landscape Architecture Design Based on Computer Big Data The improvement of museum information flow based on paste functional mapping method The art design of industrialised manufacturing furniture products based on the simulation of mathematical curves TOPSIS missile target selection method supported by the posterior probability of target recognition Research on Evaluation of Intercultural Competence of Civil Aviation College Students Based on Language Operator The incentive contract of subject librarians in university library under the non-linear task importance Modelling and Simulation of Collaborative Innovation System in Colleges and Universities Based on Interpreted Structural Equation Model Small amplitude periodic solution of Hopf Bifurcation Theorem for fractional differential equations of balance point in group competitive martial arts The Optimal Solution of Feature Decomposition Based on the Mathematical Model of Nonlinear Landscape Garden Features Composite mechanical performance of prefabricated concrete based on hysteresis curve equation Higher education innovation and reform model based on hierarchical probit Application of Fuzzy Mathematics Calculation in Quantitative Evaluation of Students’ Performance of Basketball Jump Shot The teaching of sports science of track and field-based on nonlinear mathematical equations Visual error correction of continuous aerobics action images based on graph difference function Ecological balance model of effective utilization of agricultural water resources based on fractional differential equations Application of Higher Order Ordinary Differential Equation Model in Financial Investment Stock Price Forecast Precision algorithms in second-order fractional differential equations Application of Forced Modulation Function Mathematical Model in the Characteristic Research of Reflective Intensity Fibre Sensors Fractional differential equations in National Sports Training in Colleges and Universities Radioactive source search problem and optimisation model based on meta-heuristic algorithm Visualized calculation of regional power grid power data based on multiple linear regression equation Application of mathematical probabilistic statistical model of base – FFCA financial data processing Least-squares method and deep learning in the identification and analysis of name-plates of power equipment Research on a method of completeness index based on complex model Distribution network monitoring and management system based on intelligent recognition and judgement Fake online review recognition algorithm and optimisation research based on deep learning Research on the sustainable development and renewal of Macao inner harbour under the background of digitisation Support design of main retracement passage in fully mechanised coal mining face based on numerical simulation Study on the crushing mechanism and parameters of the two-flow crusher Topological optimisation technology of gravity dam section structure based on ANSYS partial differential equation operation Interaction design of financial insurance products under the Era of AIoT Modeling the pathway of breast cancer in the Middle East Corporate social responsibility fulfilment, product-market competition and debt risk: Evidence from China ARMA analysis of the green innovation technology of core enterprises under the ecosystem – Time series data Reconstruction of multimodal aesthetic critical discourse analysis framework Image design and interaction technology based on Fourier inverse transform What does students’ experience of e-portfolios suggest Research on China interregional industrial transformation slowdown and influencing factors of industrial transformation based on numerical simulation The medical health venture capital network community structure, information dissemination and the cognitive proximity The optimal model of employment and entrepreneurship models in colleges and universities based on probability theory and statistics A generative design method of building layout generated by path Analysis of the causes of the influence of the industrial economy on the social economy based on multiple linear regression equation Research of neural network for weld penetration control Analysing the action techniques of basketball players’ shooting training using calculus method Engineering project management based on multiple regression equation and building information modelling technology Research on predictive control of students’ performance in PE classes based on the mathematical model of multiple linear regression equation Beam control method for multi-array antennas based on improved genetic algorithm The influence of X fuzzy mathematical method on basketball tactics scoring Mathematical model of back propagation for stock price forecasting Application of regression function model based on panel data in bank resource allocation financial risk management Application of Logical Regression Function Model in Credit Business of Commercial Banks Research on aerobics training posture motion capture based on mathematical similarity matching statistical analysis Application of Sobolev-Volterra projection and finite element numerical analysis of integral differential equations in modern art design Research on motion capture of dance training pose based on statistical analysis of mathematical similarity matching Application of B-theory for numerical method of functional differential equations in the analysis of fair value in financial accounting Research on the influence of fuzzy mathematics simulation model in the development of Wushu market Study on audio-visual family restoration of children with mental disorders based on the mathematical model of fuzzy comprehensive evaluation of differential equation Difference-in-differences test for micro effect of technological finance cooperation pilot in China Application of multi-attribute decision-making methods based on normal random variables in supply chain risk management Exploration on the collaborative relationship between government, industry, and university from the perspective of collaborative innovation The impact of financial repression on manufacturing upgrade based on fractional Fourier transform and probability AtanK-A New SVM Kernel for Classification Validity and reliability analysis of the Chinese version of planned happenstance career inventory based on mathematical statistics Visual positioning system for marine industrial robot assembly based on complex variable function Application of Lane-Emden differential equation numerical method in fair value analysis of financial accounting Regression function model in risk management of bank resource allocation Application of numerical method of functional differential equations in fair value of financial accounting Optimal solution of fractional differential equations in solving the relief of college students’ mental obstacles Risk contagion in financial markets based on copula model Calculating university education model based on finite element fractional differential equations and macro-control analysis Automatic parameter selection ZVD shaping algorithm for crane vibration suppression based on particle swarm optimisation Educational research on mathematics differential equation to simulate the model of children's mental health prevention and control system Analysis of enterprise management technology and innovation based on multilinear regression model Verifying the validity of the whole person model of mental health education activities in colleges based on differential equation RETRACTION NOTE Calculation of tourism development income index based on finite element ordinary differential mathematical equation Adoption of deep learning Markov model combined with copula function in portfolio risk measurement Radar system simulation and non-Gaussian mathematical model under virtual reality technology Comparison of compression estimations under the penalty functions of different violent crimes on campus through deep learning and linear spatial autoregressive models Research and application of constructing football training linear programming based on multiple linear regression equation Research on management evaluation of enterprise sales cash flow percentage method based on the application of quadratic linear regression equations Mathematical simulation analysis of optimal detection of shot-putters’ best path Determination of the minimum distance between vibration source and fibre under existing optical vibration signals: a study Mathematical modelling of enterprise financial risk assessment based on risk conduction model Nonlinear differential equations based on the B-S-M model in the pricing of derivatives in financial markets Mathematical simulation experiment based on optimisation of heat treatment process of aluminium alloy materials Mathematical model of transforming image elements to structured data based on BP neural network Educational reform informatisation based on fractional differential equation 3D Mathematical Modelling Technology in Visual Rehearsal System of Sports Dance MCM of Student’s Physical Health Based on Mathematical Cone Sports health quantification method and system implementation based on multiple thermal physiology simulation Research on visual optimization design of machine–machine interface for mechanical industrial equipment based on nonlinear partial equations Informationisation of teaching model for track and field education based on finite element higher-order fractional differential equation Information technology of preschool education reform of fine arts based on fractional differential equation Information Teaching Model of Preschool Art Education in Colleges and Universities Based on Finite Element Higher-Order Fractional Differential Equation Application of artificial intelligence algorithm in mathematical modelling and solving College Students’ Mental Health Climbing Consumption Model Based on Nonlinear Differential Equations Communication architecture of power monitoring system based on incidence matrix model Differential equation to verify the validity of the model of the whole-person mental health education activity in Universities Optimisation of Modelling of Finite Element Differential Equations with Modern Art Design Theory Analysis and Prediction of College Students’ Mental Health Based on K-means Clustering Algorithm Mathematical function data model analysis and synthesis system based on short-term human movement Human gait modelling and tracking based on motion functionalisation Analysis and synthesis of function data of human movement Energy-saving technology of BIM green buildings using fractional differential equation Study on the training model of football movement trajectory drop point based on fractional differential equation Financial Accounting Measurement Model Based on Numerical Analysis of Rigid Normal Differential Equation and Rigid Functional Equation User online consumption behaviour based on fractional differential equation Differential equation model of financial market stability based on Internet big data Multi-attribute Decision Method Based on Normal Random Variable in Economic Management Risk Control Children’s cognitive function and mental health based on finite element nonlinear mathematical model Dichotomy model based on the finite element differential equation in the educational informatisation teaching reform model Nonlinear Dissipative System Mathematical Equations in the Multi-regression Model of Information-based Teaching Stock price analysis based on the research of multiple linear regression macroeconomic variables Fractional Linear Regression Equation in Agricultural Disaster Assessment Model Based on Geographic Information System Analysis Technology