Digital Transformation and Modeling of Nature-Inspired Systems

Abstract

With the tightening of environmental regulations, the need to identify tools that foster the development of sustainable systems is growing. The shift toward closed-loop, bio-like systems promotes the creation of nature-inspired systems. However, the transformation processes and toolkits vary across meso-level systems with differing economic activity. This research reveals the patterns of formation and develops governance models for the evolution of nature-inspired systems, considering the specifics of digital transformation and innovative activity in ensuring environmental security. Methodology includes the following: correlation and regression analysis, factor and cluster analysis, along with automated neural network simulations. The study resulted in the expansion of conceptual frameworks for “nature-inspired system” formation; revealed dependencies between the formation of a nature-inspired macrosystem and mesosystems, while identifying growth hotspots for nature-inspired systems in Russia; identified the priority determinants of nature-inspired mesosystem formation; proposed a composite index (DNIS—Development of a Nature-Inspired System) to assess the cumulative impact of determinants and evaluate ecological performance responses; and developed a typology of regional mesosystems based on economic/ecological performance and “green” technology adoption, enabling differentiated approaches to guiding nature-inspired system development. The findings presented in this study are recommended for applications in improving regional socio-economic development programs.

1. Introduction

Environmental problems have an impact on economic systems at various levels. Linear production models have proven ineffective [1,2]. The “extract-produce-dispose” chain drives resource depletion and disrupts natural ecological balances, thus failing to meet sustainable development requirements and becoming obsolete. To address this problem under resource constraints, the implementation of resource cycle closure principles is being pursued.

The Russian Federation executed its «Ecology» national project (2019–2024) comprising several federal initiatives: (1) “Clean Country”, (2) “Integrated municipal solid waste management system”, (3) “Infrastructure for hazard class I-II waste management”, (4) “Clean Air” (implementation period extended until 31 December 2026), (5) “Volga River Rehabilitation” and others [3]. During the specified period, it was possible to increase the share of municipal solid waste sent for processing and disposal, reduce the total volume of pollutant emissions into the atmosphere, decrease contaminated wastewater discharges, improve the ecological state of water reservoirs, and enhance the environmental living conditions of the population. However, the achieved impact of the national project is not spatially proportional. This is attributed to the specific distribution of natural resources, uneven concentration of economic, scientific–technological, and innovation activity across mesosystems, significant interregional disparities in gross regional product (GRP) per capita, deteriorating demographic conditions in various mesosystems, supply chain restructuring, and growing geopolitical tensions [4]. Consequently, development rates, applied sustainable development tools, and environmental conditions vary across different mesosystems.

The present study focuses on analyzing the specified tools that contribute to improved ecological well-being. These tools include innovations, digital transformation, and the technological modernization of economic systems [5]. The core of environmental restoration tools consists of nature-like technologies and algorithms.

We deliberately distinguish between these concepts. We define nature-inspired algorithms as computational methods that are inspired by the principles and processes of natural systems and are used in a digital environment to solve complex problems efficiently. Such algorithms exist as software code or mathematical models designed to optimize, automate, and predict the behavior of complex technical systems. Nature-like technologies are technologies that emulate natural processes, take the form of physical objects or systems, and are implemented in industry to enhance energy/resource efficiency and the environmental sustainability of economic systems [6,7]. Thus, natural processes and mechanisms have been transformed into both modeling tools and reproduction tools for production systems.

The implementation of nature-like technologies and algorithms is carried out within the framework of innovative activities by economic systems through the adoption of “green” technologies and environmental innovations. Researchers have documented the significant impact of “green” innovations on the digital activity of economic systems [8,9], competitive advantages of organizations [10], with the success of “green” transformation being determined by open innovation models [11], and the presence of developed “green” innovation strategies [12]. The ability to implement “green” technologies is determined by corporate leadership in “green” transformation and environmental orientation (internal—corresponding standards and values within the organization; external—consideration of environmental requirements from partners and customers) [13]. At the same time, in the context of distinguishing between substantive and strategic “green” innovations, heterogeneous effects have been identified: the first type of developments contributes to improved financial performance, while the second type leads to their decline [14]. From a spatial development perspective, improving the quality of “green” innovations in core cities fosters economic growth in nearby towns (≤300 km from the central hub), while conversely inhibiting growth in remote territories beyond this threshold [15].

Nature-inspired algorithms represent a class of metaheuristic optimization methods [16], which are, in turn, interpreted as intelligent algorithms. Consequently, an interdisciplinary research field has emerged, integrating knowledge from biology and mathematics [17]. When technical and economic systems face complex nonlinear problems, nature-inspired optimization algorithms enable solutions to numerous scientific and technical challenges.

The scope of intelligent optimization methods is sufficiently broad, encompassing natural resource extraction, manufacturing, logistics, and supply chain management. Specific examples include the following:

• production process planning within industrial system operations [18,19];
• development of dispatching rules for intelligent manufacturing systems in the processing industry [20];
• logistics and technical supply management for smart manufacturing [21];
• optimal resource allocation in continuous production systems [22];
• minimization of energy consumption in industrial production process planning [23,24];
• determination of optimal well placement in gas reservoirs [25];
• data management in manufacturing industries [26];
• identification of unknown groundwater contamination sources [27];
• wastewater monitoring in electroplating production [28];
• chemical reaction control [29], etc.

The advantages of these methods lie in their universality and flexibility through the handling of both discrete and continuous variables, combination of diversification (full solution space exploration) and intensification (focused search on promising solutions), noise resistance, and capability to work with non-differentiable and nonlinear functions [30,31,32]. However, alongside their advantages, certain challenges exist in applying nature-inspired optimization algorithms. These include problems related to assessing algorithm convergence and stability, parameter calibration, mathematical foundations, scalability, and benchmarking [33].

Examples of metaheuristic algorithms include genetic algorithms, which are based on simulating natural selection [34]. Genetic algorithms are applied in the following: forecasting innovative development of mesosystems [35], supply chain organization and logistics problem-solving [36,37], modeling additive manufacturing under digital transformation [38,39], simulating “green” production systems [40], and enhancing production system reliability through failure prediction [41], among other applications.

The analytical toolkit in this field abounds with various nature-inspired algorithms. A widely used optimization tool is swarm intelligence, which describes the collective behavior of self-organizing systems [42]. It is particularly suitable for solving complex nonlinear, multidimensional problems. Swarm intelligence mimics the following:

• collective behavior of ants seeking shortest paths (ant colony optimization algorithm); application areas include the following: transportation problem solutions, traveling salesman problem, pipeline route design [43], inter-cluster interactions in mesosystems [44], parallel machine optimization [45], assembly line balancing [46], air quality monitoring network configuration [47], among others;
• flocks of birds or schools of fish that exchange information and move toward optimal solutions when foraging (particle swarm optimization algorithm); application example—optimization of manufacturing process parameters [48,49];
• behavior of employed bees, onlooker bees, and scout bees during nectar collection (artificial bee colony optimization); application examples—logistics, energy supply optimization [50,51];
• behavior of fireflies moving toward brighter individuals (firefly algorithm) [52,53,54];
• echolocation behavior of bats (bat algorithm); application examples—electrical load forecasting [55], wind power generation prediction [56], robotics [57], among others;
• wolf pack hierarchy—alpha, beta, delta, omega (grey wolf optimization algorithm); application examples—water resource allocation optimization [58], carbon price forecasting [59], etc.

Core optimization algorithms have evolved into advanced mathematical solutions such as the following: frog-leaping algorithm [60], elk herd optimizer [61], elephant herding optimization [62], the naked mole-rat algorithm [63], among others.

The choice of a particular algorithm is based on performance testing of the simulated system (mean error, standard deviation, etc.) [64].

Despite the diversity of nature-inspired optimization algorithms, there is a growing shift toward hybrid metaheuristic methods that combine multiple algorithms. This approach enhances algorithmic stability, optimization efficiency, and result reliability [65,66,67,68], including in the organization of eco-friendly production systems [69].

In addition to the aforementioned nature-inspired optimization algorithms, automated neural networks have gained significant popularity due to their proven effectiveness in regression and classification tasks [26,70].

The next block of theoretical–methodological principles forming the conceptual framework of this study comprises works elucidating the specifics of nature-like technologies. These encompass both technical and territorial systems. The focus of modern production systems on natural processes stems from nature being “a sustainable, resource-efficient system where materials are utilized and recycled in a circular fashion” [71] (p. 1). The following approaches to developing nature-inspired systems contribute to achieving sustainable development goals: closed-loop systems, waste minimization, utilization of renewable energy sources (solar panels, wind turbines, hydrogenerators [72,73,74]), and renewable natural materials [75], as well as biomimicry (or biomimetics) as a method for studying natural systems to innovate economic and technical systems [76,77,78], among others. Additional examples of nature-inspired technologies include innovations in polymer development [79], heat exchanger technology incorporating fractal geometry, surface wettability control, and evaporative cooling [80], solar interfacial distillation-based water purification [81], natural degradation of oil pollution [82], and nature-like geotechnologies for subsurface resource extraction [83]. In works [84,85], the concept of nature-inspired systems is exemplified through cities, framed in terms of urban metabolism—a system where cities extract and process resources, with resulting waste outputs discharged into the environment.

Thus, the literature review suggests a predominance of studies focusing on microeconomic systems and the development of nature-inspired systems at the enterprise, production, factory, and workshop levels. In our view, the potential for researching the impact of environmental innovations, “green” technologies, and digitalization on environmental preservation at the mesoeconomic systems level remains underexplored.

This research reveals the patterns of formation and develops governance models for the evolution of nature-inspired systems, considering the specifics of digital transformation and innovative activity in ensuring environmental security.

The study aims to identify patterns of formation and develop a management model for the evolution of nature-inspired systems, accounting for the specifics of digital transformation and innovation activity in the field of environmental safety.

Research stages are as follows: systematize the methodological foundation of the study; expand conceptual frameworks for nature-inspired system formation; conduct spatial analysis of nature-inspired systems at macro- and meso-management levels; develop a differentiated management system for nature-inspired system development.

The research focuses on two-tiered territorial mesosystems in Russia, differentiated by industrial, innovation, and sustainable development indicators, as well as digital transformation rates. The first mesosystem level comprises federal districts, while the second level consists of constituent regions.

The novelty of the research lies in the development and testing of a methodological framework for assessing the development of nature-inspired mesosystems. The scientific contribution is presented by the following results:

• conceptual provisions for the development of nature-inspired systems have been formulated, including clarification of the concept, formative factors, and underlying principles;
• the patterns of formation of the nature-inspired macrosystem and mesosystems have been identified, which has made it possible to localize the growth points of nature-inspired systems in Russia;
• a methodological approach has been proposed for assessing the innovative, digital, and technological development of regional mesosystems in the form of a composite DNIS (development of a nature-inspired system) index, which makes it possible to evaluate the cumulative influence of determinants shaping nature-inspired mesosystems and to identify the response of environmental efficiency indicators;
• a typology of regional mesosystems has been proposed based on indicators of economic and environmental efficiency and the use of “green” technologies, designed to develop a differentiated approach to identifying directions for the development of nature-inspired systems.

The structure of the paper comprises five sections. “2. Materials and Methods” describes the datasets and sources underpinning the findings and results, outlines the step-by-step analytical research design, and details the research methods employed, including the authors’ proprietary methodology. “3. Results” presents the authors’ conceptual framework advancing the discourse on nature-inspired systems development, along with an analytical study of nature-inspired mesosystem formation in Russia, which revealed development patterns and mesosystem types within the transition to a nature-inspired systems model. “4. Discussion” explores the alignment of the authors’ propositions with existing research and outlines limitations of the study’s findings. “5. Conclusions” summarizes key insights, lists scientific contributions, suggests practical applications, and identifies avenues for future research.

2. Materials and Methods

2.1. Dataset

At the first stage, the study was conducted for two-tier systems.

• Analysis of nature-inspired system formation at the macro level. At this level, the contribution of eight federal districts of the Russian Federation (RF) to restoring macro-ecosystems is assessed: Central Federal District (CFD); Northwestern Federal District (NWFD); Southern Federal District (SFD); North Caucasus Federal District (NCFD); Volga Federal District (VFD); Ural Federal District (UFD); Siberian Federal District (SibFD); Far Eastern Federal District (FEFD).
• Diagnostics of nature-inspired systems formation at the meso-level. In this case, 82 regions of the Russian Federation are examined.

The impact study was conducted across 45 observations, incorporating indicators of innovation activity among organizations in the Russian Federation, its federal districts, and constituent entities in the field of environmental well-being for 2010–2021. This includes the percentage of organizations (%) engaged in innovations related to the following:

• energy conservation (E₂₀₁₀–E₂₀₂₁),
• carbon emission reduction (C₂₀₁₀–C₂₀₂₁),
• transition to safer/less hazardous raw materials (R₂₀₁₀–R₂₀₂₁),
• environmental pollution reduction (P₂₀₁₀–P₂₀₂₁),
• waste recycling (W₂₀₁₀–W₂₀₂₁).

At the first level, federal districts contributing most significantly to macro-ecosystem restoration were identified; at the second level, within these priority federal districts, regions making the greatest contribution to forming nature-inspired systems were determined. This analysis aims to identify the most active mesosystems in transitioning to nature-inspired system models.

In the second stage, an analysis of heterogeneity in the formation of nature-inspired systems across 82 regions of the Russian Federation (as of 2023) was conducted. The dataset comprises blocks of regional development indicators (Figure 1):

• economic indicator:
  • GRP—Gross Regional Product per capita, rubles;
• environmental performance indicators for organizations within the mesosystem in the field of environmental protection:
  • E₁—capture of air pollutants emitted from stationary sources (thousand tons);
  • E₂—share of captured and neutralized air pollutants in the total amount of pollutants emitted from stationary sources (%);
  • E₃—volume of recycled and sequentially used water (million cubic meters);
  • E₄—recycling and neutralization of production and consumption waste (% of total generated waste); it should be noted that in some cases, the indicator value may significantly exceed 100%, as it accounts for previously accumulated waste;
• indicators of innovative activity of regional organizations providing ecological benefits: the percentage of organizations that implemented innovations aimed at the following:
  • I₁—reducing material costs per unit of goods, works, or services (%);
  • I₂—decreasing energy consumption or carbon footprint (%);
  • I₃—reducing noise levels and soil, water, or air pollution (%);
  • I₄—replacing raw materials with safer or less hazardous alternatives (%);
  • I₅—substituting part of fossil energy sources (fuel types) with renewable energy (%);
  • I₆—recycling production waste, water, or materials (%);
• indicators of digital activity of regional organizations, namely—the percentage of organizations that used the following:
  • D₁—“cloud” services (%);
  • D₂—big data collection, processing, and analysis technologies (%);
  • D₃—Internet of Things (%);
  • D₄—artificial intelligence technologies (%);
  • D₅—digital platforms (%);
• technological indicator:
  • T—number of “green” advanced production technologies used in the region (units).

The source of data was statistical information published on the official website of Rosstat [86]. This includes the following: the section “Science, Innovation and Technologies”, the publication “Regions of Russia. Socio-Economic Indicators”, and its accompanying appendix.

2.2. Research Analytical Framework

The structure of this study is organized into five stages designed to achieve the research objective (Figure 2).

2.3. Analytical Research Methods

This multidisciplinary research utilizes a comprehensive set of analytical tools. These include correlation, regression, factor, and cluster analyses, along with automated neural network modeling.

The correlation analysis aims to identify relationships between regions’ innovation, digital, and technological activities on one hand, and their economic and environmental performance on the other. This approach enables the identification of fundamentally significant predictors for specific mesosystems within the transition to a nature-inspired development model.

Regression analysis and neural networks enable the building of predictive models that account for the combined effect of predictors on dependent variables while ranking federal districts and regions by their contribution to forming nature-inspired systems, including predictor-sensitivity indicators. The forecast error is evaluated using mean absolute percentage error (MAPE) and root mean square error (RMSE) metrics, the applicability of which for forecast assessment is justified in numerous works, including the following ([87], p. 261) [88]:

$$MAPE={\displaystyle \frac{1}{n}}\sum _{j=1}^n\left|{\displaystyle \frac{Y_j-Y_j^{*}}{Y_j}}\right|\times 100,$$

(1)

$$RMSE=\sqrt{{\displaystyle \frac{1}{n}}\sum _{j=1}^n{\left(Y_j-Y_j^{*}\right)}^2},$$

(2)

where Y_j is the actual value, Y_j^* is the predicted value, n is the number of observations, and j is the observation (federal district or region, depending on the research phase).

Factor analysis is designed to identify latent relationships among 12 indicators (I_i, D_i, T₁) in federal districts prioritized for forming nature-inspired systems. Principal component analysis is used to extract the factors. The study hypothesizes the consolidation of indicators into three factors. Factor significance testing is performed according to Kaiser’s criterion (eigenvalue must exceed 1). Based on this, we propose calculating a composite index of predictors for each of the significant federal districts (DNIS, development of a nature-inspired system) that is calculated for each significant federal district using Formula (3):

$$\begin{gathered} F_i=\sum _{j=1}^m{x}_{ij}{\lambda }_{ij}, \\ DNIS=\sum _{j=1}^n{F}_i{e}_i, \end{gathered}$$

(3)

where x_ij is the value of the j-th indicator included in the i-th factor, λ_ij is the factor loading (correlation coefficient between the i-th factor and j-th indicator), m is the number of indicators included in the i-th factor, e_i is the eigenvalue for the i-th factor (representing its contribution to variance explanation), and n—is the number of extracted factors.

Cluster analysis is intended to classify mesosystems regardless of their affiliation with federal districts. The classification features used are as follows: (1) GRP, (2) E_mean (average value of E₁, E₂, E₃, and E₄ for the corresponding region), (3) T (mesosystem activity in implementing “green” advanced production technologies). For positioning nature-inspired mesosystems, regional clustering into four groups is applied (using the k-means method).

The combination of the aforementioned research methods enhances the understanding of spatial development patterns in the context of nature-inspired mesosystem formation, generates new knowledge for making effective and evidence-based management decisions at the mesosystem level, predicts development trajectories of mesosystems, and reduces planning errors.

All specified methods were implemented using the Statistica software package (STATISTICA 10).

3. Results

3.1. Conceptual Framework of the Study

First, we clarify the terminology underlying this research. Nature-inspired systems are economic systems that are consciously managed using tools and mechanisms based on the principles of living nature, with the aim of achieving sustainability, energy and resource efficiency, and synergy within economic systems. The conceptual foundation of this definition is rooted in the environmental aspect (closing resource cycles analogous to the circulation of matter and energy in nature), cybernetics (feedback and self-regulation), and complex systems theory (emergence and self-organization). The formation of nature-inspired systems is facilitated by the following:

• best available techniques [89] and “green” technologies;
• environmental innovations based on the transition to renewable energy sources, renewable materials, safe materials, and circular economy principles;
• digital technologies that enhance production system design precision (digital engineering), enable environmental monitoring (Industrial Internet of Things, blockchain), automate processes and systems, and improve forecasting quality through big data analytics, artificial intelligence, machine learning, etc.;
• regulatory instruments stimulating the adoption of nature-like technologies (legal acts, financial tools, administrative measures).

The principles for forming modern nature-inspired systems include the following: (1) economic, technical, and environmental efficiency; (2) material flow circularity and waste minimization; (3) flexibility, adaptability, and resilience; (4) decentralization; (5) digitalization.

3.2. Analytical Study on the Formation of Nature-Inspired Mesosystems in Russia

3.2.1. Dataset Formation and Descriptive Statistics

As noted earlier, the analysis covers two diagnostic blocks. The assessment of innovation activity of RF organizations and federal mesosystems in transitioning to a nature-inspired model provides a systemic perspective and demonstrates the asymmetry and heterogeneity of regional dynamics (

Table 1. Descriptive statistics of environmental innovation adoption across the country.

System	Mean, %	Standard Deviation	Kurtosis	Skewness	Range	Min	Max
RF	50.70	14.03	−0.09	0.93	50.37	33.33	83.7
CFD	52.64	12.83	−0.14	0.94	46.9	35.2	82.1
NWFD	49.47	15.80	−0.42	0.76	57.84	27.66	85.5
SFD	51.12	17.19	−0.31	0.53	65.5	24.8	90.3
NCFD	57.37	19.02	−0.75	0.38	72.73	27.27	100
VFD	51.27	14.77	−0.30	0.76	53.15	30.65	83.8
UFD	50.81	16.56	−0.01	0.52	70.72	16.98	87.7
SibFD	48.48	15.43	−0.65	0.26	60.97	20.73	81.7
FEFD	46.09	15.79	−0.53	0.71	63.4	23.8	87.2

).

The analysis comprehensively incorporates indicators of energy conservation (E₂₀₁₀–E₂₀₂₁), carbon emission reduction (C₂₀₁₀–C₂₀₂₁), transition to safer/less hazardous raw materials (R₂₀₁₀–R₂₀₂₁), environmental pollution reduction (P₂₀₁₀–P₂₀₂₁), and waste recycling (W₂₀₁₀–W₂₀₂₁) (total: 45 observations). All indicators are measured as percentages (share of organizations implementing the respective innovations). According to average values, organizations in the North Caucasus Federal District demonstrate more active innovation implementation, primarily driven by the modernization of energy-saving systems and pollutant-capture systems. At the same time, this federal district shows the highest standard deviation value, indicating a relatively large data dispersion. The negative kurtosis coefficient suggests a relatively uniform data distribution, while the Ural Federal District demonstrates normally distributed values. A positive skewness indicates a slight predominance of actual values above the mean. This pattern is less pronounced in the North Caucasus Federal District and Siberian Federal District (asymmetry coefficient values do not exceed 0.4). The greatest disparities between different types of innovations are observed in the North Caucasus Federal District (range: 72.73 percentage points) and Ural Federal District (range: 70.72 percentage points). The smallest range is characteristic of the Central Federal District, where all innovation types are implemented by organizations in relatively proportional proportions.

For the macrosystem (RF) as a whole, the distribution is approximately normal (kurtosis = −0.09). The minimum value reflects weak organizational activity in innovations for improving material safety (33.3% of organizations, 2019), while the maximum shows the widespread implementation of environmental pollution reduction innovations (83.7% of organizations, 2013).

Next, descriptive statistics were evaluated for the economic, environmental, innovation, digital, and technological development of regional mesosystems (

Table 2. Descriptive statistics of regional development indicators in the Russian Federation.

Indicator	Mean, %	Standard Deviation	Kurtosis	Skewness	Range	Min	Max
GRP	787,107.6	623,560	7.38	2.65	3,316,509.47	156,031.76	3,472,541.23
E1	584	1192.35	18.51	3.99	7436	0	7436
E2	53.3	27.2	−1.02	−0.25	96.7	0	96.7
E3	1764.1	2304.85	3.06	1.85	9934	0	9934
E4	69.4	140.96	68.7	7.97	1277.6	0	1277.6
I1	50.2	16.97	1.66	0.84	85.7	14.3	100
I2	55.2	17.95	0.69	0.44	80	20	100
I3	63.7	17.61	−0.01	0.76	68.4	31.6	100
I4	45.8	19.12	0.53	0.35	91.7	8.3	100
I5	25.7	18.55	6.95	2.32	94.7	5.3	100
I6	36.4	14.27	5.11	1.41	95.5	4.5	100
D1	25.6	3.96	1.08	0.68	23.6	16.02	39.62
D2	14.5	3.65	1.32	0.22	21.95	4.92	26.88
D3	10.8	2.49	3.62	0.83	17.07	3.88	20.95
D4	5	1.58	1.22	0.46	8.65	1.3	9.95
D5	16.7	3	1.52	0.06	18.4	7.39	25.79
T	61.9	66.06	6.55	2.38	325	3	328

).

Let us examine the kurtosis coefficient. Innovations are for pollution reduction I₃ (coefficient is −0.01) and the transition to safer materials I₄ (coefficient is −0.53). The skewness indicator of the data series revealed that, in most cases, the data distribution shows insignificant deviation from symmetry. The most symmetrical distribution is observed for D₅ (skewness coefficient is 0.06), indicating the equally intensive adoption of digital platforms across regions. Significant variations are observed in the environmental efficiency indicator E₄—waste management (coefficient is 7.97). This is explained by the fact that several regions (Moscow Region, Leningrad Region, Samara Region) included the processing and utilization of historically accumulated waste in their 2023 reporting. Innovation activity indicators reach 100% in some regions (according to official statistics), including Chechen Republic (I₁–I₆), Republic of Kalmykia (I₁, I₂, I₃), Astrakhan Region (I₂), and Kamchatka Territory (I₂, I₃, I₅), among others. Digital technology adoption generally occurs at a smaller scale, as evidenced by the minimum and maximum values of D_i indicators. The most widely implemented are the following: cloud technologies D₁ (Chechen Republic—39.62% of organizations, Novgorod Region—34.82%), digital platforms D₅ (Chechen Republic—25.79%, Moscow Region—24.24%) and Big data collection, and processing and analysis technologies D₂ (Chechen Republic—26.88%, Moscow Region—24.42%).

Thus, the descriptive analysis confirms significant heterogeneity in the formation of nature-inspired mesosystems at both federal and regional levels.

3.2.2. Data Normalization

The normalization of indicators GRP, E_i, I_i, D_i, and T was implemented using the Min-Max method, which prevents negative values while preserving the original data distribution. The normalization formula is as follows:

$$x_{norm}={\displaystyle \frac{x_i-x_{min}}{x_{max}-x_{min}}},$$

(4)

where x_i is the actual indicator value and x_min and x_max are the minimum and maximum values of x in the sample.

After normalization, all values range within [0; 1]. Notably, Formula (4) uses the minimum non-zero values from the sample as baseline, which reduces calculation errors.

3.2.3. Analysis of RF Dependence on Federal Mesosystem Development

To identify local growth points, a comprehensive study was conducted to determine key federal mesosystems. Correlation analysis revealed stable relationships between all federal districts, with correlation coefficients exceeding 0.6 in all cases. The greatest contribution to enhancing the country’s competitiveness comes from the Volga Federal District (Pearson’s r is 0.973), Central Federal District (r is 0.968), and Northwestern Federal District (r is 0.935).

The systemic relationship between the RF development level and federal districts’ contributions is expressed through a multiparameter regression (

Table 3. Regression results for the dependent variable RF.

Regression Coefficients							R	R2	F(6,38)	p-Level
Intercept	CFD	NWFD	SFD	VFD	UFD	FEFD
−0.5199	0.291	0.1046	0.0936	0.3213	0.1431	0.048	0.9986	0.997	2219.6	<0.0000

). The method used was stepwise elimination regression. The modeling results are statistically significant.

The predictive model of the macrosystem’s development is expressed by Equation (5):

RF = −0.5199 + 0.291 × CFD + 0.1046 × NWFD + 0.0936 × SFD + 0.3213 × VFD + 0.1431 × UFD + 0.048 × FEFD.

(5)

All variables (federal mesosystems) contribute to strengthening the development vector and the transition of the macrosystem to a nature-inspired model, as evidenced by the positive values of the regression coefficients. The greatest influence is exerted by the mesosystem of the Volga Federal District. This is due to the following factors:

• the Volga Federal District is characterized by a high concentration of manufacturing industries—petrochemicals and mechanical engineering (in 2023, the VFD accounted for the largest share of value added generated by manufacturing industries, at 21.8%); this is accompanied by a high level of environmental pollution and creates a strong demand for environmental innovations;
• The Volga Federal District possesses high research, innovation, and digital potential, as evidenced by the extensive activities of leading technical universities (HSE University in Nizhny Novgorod, Nizhny Novgorod State Technical University named after R.E. Alekseev, Kazan National Research Technological University, Kazan National Research Technical University named after A.N. Tupolev (KAI), Samara National Research University), IT centers (Innopolis University, NEIMARK University), technoparks, etc.;
• The Volga Federal District is implementing pilot projects to address environmental issues (including the project for the rehabilitation of the Volga River).

Moreover, the predictive model’s accuracy can be enhanced by incorporating new relevant data in the field of environmental innovations, reducing noise in the data (e.g., innovation activity reported at 100%), and analyzing nonlinear relationships between variables.

The modeling results were validated using a nature-inspired algorithm—neural network modeling. The output also represents the RF macrosystem. Default sample sizes were applied: training—70%, test—15%, validation—15%. The choice of multilayer perceptron (MLP) was driven by several advantages, including architectural flexibility due to alternative nonlinear activation functions, enabling an approximation of any continuous function. Unlike elimination regression analysis, the neural network accounts for all input mesosystems (

Table 4. Alternative architectures of high-performance neural networks.

No.	Neural Network Name	Sampling Performance			Activation Functions
		Training	Test	Validation	Hidden Layer Neurons	Output Neurons
1	MLP 8-10-1	0.999994	0.996965	0.999424	logistic	identity
2	MLP 8-10-1	0.999912	0.998391	0.999402	hyperbolic tan	logistic
3	MLP 8-8-1	0.998653	0.995679	0.998931	logistic	hyperbolic tan
4	MLP 8-11-1	0.991682	0.996649	0.998938	identity	logistic
5	MLP 8-5-1	0.999848	0.997666	0.999034	logistic	hyperbolic tan

). Network No. 1 (MLP 8-10-1) was selected as optimal based on performance metrics.

The sensitivity indicators (S) identified through Network No. 1 (MLP 8-10-1) corroborate the correlation–regression analysis results: S_VFD = 5925.18; S_CFD = 4731.2; S_UFD = 2326.32; S_NWFD = 1991.1; S_FEFD = 762.86; S_SibFD = 674.11; S_SFD = 662.22; S_NCFD = 80.36.

The accuracy evaluation of both regression and neural network models yielded the following results:

• model (5): MAPE—1.24%, RMSE—0.86425;
• MLP 8-10-1 model: MAPE—0.0865%, RMSE—0.05153.

Given the superior accuracy of neural networks, further research relies on sensitivity analysis results.

3.2.4. Analysis of Federal Mesosystems’ Dependence on Regional Mesosystems

The next analysis level incorporates findings about the influence of Volga Federal District and Central Federal District on the nature-inspired macrosystem. The evaluation algorithm follows the steps outlined in Section 3.2.3, with one distinction: VFD comprises 14 regions, CFD comprises 18 regions. Correlation analysis results determined the inclusion of 8 regions for the VFD case and 10 regions for the CFD case.

The results of the stepwise elimination regression analysis are summarized in

Table 5. Regression results for dependent variable VFD.

Regression Coefficients							R	R2	F(6,38)	p-Level
Intercept	RB	RT	ChR	PK	NNO	SO
−1.433	0.103	0.331	0.108	0.185	0.153	0.121	0.991	0.982	353.19	<0.0000

and

Table 6. Regression results for dependent variable CFD.

Regression Coefficients										R	R2	F(6,35)	p-Level
Intercept	BelO	VlO	VoO	KlO	KsO	MO	TlO	YrO	MC
−4.106	0.112	0.074	0.078	0.107	0.041	0.224	0.076	0.115	0.218	0.994	0.989	336.34	<0.0000

. Region codes are explained in the “Abbreviations” section. The predictive models are statistically significant and reliable (p < 0.0001). All regional mesosystems contribute positively to their federal district’s development.

The final models for the two federal mesosystems are expressed by Equations (6) and (7):

VFD = −1.433 + 0.103 × RB + 0.331 × RT + 0.108 × ChR + 0.185 × PK + 0.153 × NNO + 0.121 × SO.

(6)

CFD = −4.106 + 0.112 × BelO + 0.074 × VlO + 0.078 × VoO + 0.107 × KlO + 0.041 × KsO + 0.224 × MO + 0.076 × TlO +
+ 0.115 × YrO + 0.218 × MC.

(7)

To summarize the modeling results, we note that growth points are localized in the following regional mesosystems:

• Volga Federal District: Republic of Tatarstan, Perm Territory, Nizhny Novgorod Region, Samara Region;
• Central Federal District: Moscow Region, Moscow city, Yaroslavl Region, Belgorod Region.

The neural network training results identified one highest-performance network for each case (

Table 7. Architectures of high-performance neural networks.

FO	Neural Network Name	Sampling Performance			Activation Functions
		Training	Test	Validation	Hidden Layer Neurons	Output Neurons
VFD	MLP 8-4-1	0.996956	0.954325	0.965361	exponential	exponential
CFD	MLP 10-8-1	0.996138	0.965032	0.990311	identity	identity

). In the MLP 8-4-1 network, the most sensitive predictors are as follows: S_RT = 10.73; S_PK = 8.66; S_SO = 5.8. In the MLP 10-8-1 network, high sensitivity was observed for the following: S_MO = 7.42; S_MC = 5.34; S_BelO = 3.94. Thus, these regions demonstrate substantial influence on constructing the nature-inspired macrosystem.

The accuracy of regression and neural network models was as follows:

• for modeling VFD dependence on regional mesosystems:
  • model (6): MAPE—2.94%, RMSE—2.26;
  • MLP 8-4-1 model: MAPE—2.06%, RMSE—1.26;
• for modeling CFD dependence on regional mesosystems:
  • model (7): MAPE—2.4%, RMSE—1.58;
  • MLP 8-10-1 model: MAPE—1.89%, RMSE—1.18.

The neural networks again demonstrate lower prediction error in both cases. Overall, considering the regression coefficients and variable sensitivity indicators, the localization of growth points for nature-inspired systems is confirmed.

As outlined in the research framework, this stage was augmented with factor analysis to assess the influence of the composite predictor index (encompassing innovations, digitalization, and “green” technologies) on nature-inspired federal mesosystems. This approach was justified by the fact that partial pairwise relationships between the predictors I_i, D_i, and T and target variables GRP and E_i were predominantly insignificant, revealing only a clear influence of digitalization on GRP growth. However, given the core research focus, this proves insufficient. Consequently, calculating a composite predictor index DNIS using principal components is methodologically justified. Factor analysis was performed on normalized indicators (

Table 8. Factor loadings (principal component method).

VFD				CFD
Variable	Factor 1	Factor 2	Factor 3	Variable	Factor 1	Factor 2	Factor 3
I1	−0.0406	0.1744	0.8287	I1	0.0428	0.9604	0.1327
I2	0.1251	0.8694	−0.1008	I2	0.1557	0.2692	0.8962
I4	0.2009	0.8367	−0.2407	I3	0.0396	0.7943	0.3867
I5	−0.1372	0.8801	0.1389	I4	0.0504	0.0880	0.9556
I6	−0.0356	0.7916	0.4049	I6	0.3645	0.6505	−0.0034
D1	0.9091	−0.0845	0.0601	D2	0.9606	0.0568	0.0754
D2	0.8006	0.2619	−0.0198	D3	0.9634	0.0805	0.0374
D3	0.9379	0.0666	0.0981	D4	0.8552	0.0614	−0.0980
D4	−0.0315	0.0439	−0.8407	D5	0.8903	0.0341	0.2644
D5	0.9003	−0.0315	−0.1063	T	0.7541	0.2451	0.1789
T	0.2033	−0.1840	0.6031	Expl. Var	4.1066	2.1313	2.0020
Expl. Var	3.2777	3.0045	2.0335	Prp. Totl	0.4107	0.2131	0.2002
Prp. Totl	0.2980	0.2731	0.1849

). The hypothesis of three underlying factors is confirmed. Only significant predictors (λ_ij > 0.6) were included in the final factor matrix.

The left section of the table groups factors with 11 variables, while the right section contains 10 variables. Factor loadings are predominantly high. In both cases, the first factor reflects digital characteristics, the second factor represents innovation-driven components, and the third factor combines mixed attributes. In the Central Federal District, the digital factor carries greater weight (proportion of total is 0.41), while in the Volga Federal District, the factors demonstrate approximately equal influence (0.29; 0.27 and 0.18).

Next, considering the eigenvalues of factors (in all cases, e_i > 1) and Formula (3), the composite predictor index DNIS was calculated for the two studied federal mesosystems. The Pearson correlation coefficient helped identify key development trajectories for nature-inspired federal mesosystems (Figure 3). The figure displays only the strongest correlations identified in the analysis. The Volga Federal District’s economic and environmental efficiency is primarily driven by digitalization (cloud technologies and IoT adoption) and “green” technology implementation. The composite index of regional adoption of innovative, digital, and “green” production solutions drives both (1) gross regional product growth (Figure 3a) and (2) increased water recycling volumes (Figure 3b). For the Central Federal District, digital technologies (all types except cloud solutions) and “green” technologies are of critical importance. The combination of predictors drives increased activity in waste management (Figure 3c).

The comprehensive conclusion of Step 4 in this study is presented in Figure 4. The contribution to forming a nature-inspired macrosystem flows right to left—from regional mesosystems. The “Federal-level mesosystem” and “Regional-level mesosystem” blocks highlight the entities demonstrating the highest activity in ensuring environmental well-being. The diagram’s highlighted mesosystems demonstrate relatively high economic, industrial, investment, and patent activity levels. The “Dependencies in federal-level mesosystems” block contains two subblocks: (1) partial significant relationships, and (2) comprehensive predictor influence (DNIS). Functional dependencies reveal the influence of digitalization and “green” technology factors, but show no clear correlation between environmental innovations and environmental efficiency in federal mesosystems.

The preceding analysis has focused on mesosystems’ territorial affiliation. We propose abstracting from it through cluster analysis to identify patterns within each cluster.

3.2.5. Typology and Positioning of Regional Mesosystems

As noted in Section 2.3 of this study, clustering was performed using three normalized variables: (1) GRP, (2) E_mean, (3) T. The third criterion (T) was intentionally included alongside dependent variables as it most vividly demonstrates mesosystems’ contributions to ensuring environmental well-being. An analysis of variance confirmed the significance of both features (p < 0.00001), resulting in distinct groupings of regional mesosystems (

Table 9. Differential characteristics of identified clusters.

Indicator	Mean Values by Cluster				Indicator	Mean Values by Cluster
	1	2	3	4		1	2	3	4
GRP	2,516,326.9	519,369.3	670,372.9	1,103,569	I5	17.6	21.6	16.5	24.9
E1	399	74.3	1159.1	230	I6	37.6	25.2	31.2	35.1
E2	49	36.3	71.7	46.1	D1	26.2	24.7	26.1	28.7
E3	2506.3	546.9	2745.6	2860.3	D2	16.3	13.7	14.6	18.5
E4	33.1	45.8	67.7	456.3	D3	10.9	10.5	10.8	13.5
I1	47.8	41.1	44.6	63.2	D4	3.9	5.3	4.7	6.4
I2	54.7	46.9	50.3	50	D5	15.8	16	17.3	19.3
I3	76.4	57	56	57.6	T	49.3	16.9	74.9	311.3
I4	28	35.9	41,1	46.7

).

The clusters can be interpreted as follows:

• Cluster 1 “High-performance economic mesosystems”: economic efficiency dominates over environmental performance (GRP = 2516.33 thou. rubles, E₁ = 399 thou. tones; E₂ = 48.99%; E₃ = 2506.29 mln. cu. m; E₄ = 33.07%; T = 49 units); includes seven regions;
• Cluster 2 “Traditional development mesosystems” exhibits low GRP and pollution levels, resulting in minimal need for environmental interventions and subpar ecological efficiency (GRP = 519.37 thou. rubles, E₁ = 74.28 thou. tones; E₂ = 36.26%; E₃ = 546.88 mln. cu. m; E₄ = 45.84%; T = 17 units); comprising 36 mesosystems;
• Cluster 3 “Eco-technical mesosystems”: high environmental efficiency driven by intensive industrial activity, significant ecological footprint, strong demand for environmental measures, and advanced “green” technology development (GRP = 670.37 thou. rubles, E₁ = 1159.11 thou. tones; E₂ = 71.74%; E₃ = 2745.61 mln. cu. m; E₄ = 67.69%; T = 75 units); comprising 36 mesosystems;
• Cluster 4 “Balanced Development Mesosystems”: Features relatively high GRP, moderate ecological footprint, and exceptional “green” technology development (GRP = 1103.57 thou. rubles, E₁ = 230 thou. tones; E₂ = 46.1%; E₃ = 2860.33 mln. cu. m; E₄ = 456.33%; T = 311 units); comprising three regions.

Table 10. Distribution of mesosystems across clusters.

Cluster	Cluster Composition
1. High-performance economic mesosystems	7: Moscow city, Murmansk Region, Tyumen Region, Republic of Sakha (Yakutia), Magadan Region, Sakhalin Region, Chukotka Autonomous Area
2. Traditional development mesosystems	36: Bryansk, Vladimir, Ivanovo, Kostroma, Kursk, Orel, Tambov Regions, Republic of Karelia, Komi Republic, Arkhangelsk, Kaliningrad, Pskov Regions, Republic of Adygeya, Republic of Kalmykia, Republic of Crimea, Astrakhan Region, Sevastopol city, Republic of Daghestan, Republic of Ingushetia, Kabardino-Balkarian Republic, Karachayevo-Chircassian Republic, Republic of North Ossetia—Alania, Chechen Republic, Stavropol Territory, Republic of Mari El, Udmurtian Republic, Chuvash Republic, Kurgan Region, Republic of Altay, Republic of Tuva, Republic of Khakassia, Tomsk Region, Republic of Buryatia, Kamchatka Territory, Amur Region, Jewish Autonomous Region
3. Eco-technical mesosystems	36: Belgorod, Voronezh, Kaluga, Lipetsk, Ryazan, Smolensk, Tver, Tula, Yaroslavl, Vologda, Leningrad, Novgorod Regions, Krasnodar Territory, Volgograd Region, Rostov Region, Republic of Mordovia, Republic of Tatarstan, Perm Territory, Kirov Region, Nizhny Novgorod, Orenburg, Penza, Samara, Saratov, Ulyanovsk, Sverdlovsk, Chelyabinsk Regions, Altay Territory, Krasnoyarsk Territory, Irkutsk Region, Kemerovo Region, Novosibirsk Region, Omsk Region, Trans-Baikal Territory, Primorye Territory, Khabarovsk Territory
4. Balanced Development Mesosystems	3: Moscow Region, St. Petersburg city, Republic of Bashkortostan

provides a detailed list of mesosystems classified into the four identified clusters.

The mesosystem positioning map is presented in Figure 5. The map visualizes disparities in economic versus environmental efficiency across mesosystems, indicating stronger transition potential toward nature-inspired models for Clusters 2 and 3.

The constructed positioning matrix allows for the differentiation of measures in the formation of “green” nature-inspired systems based on their belonging to a particular cluster. Thus, regions of the first type are in the zone of ecological risk, making it essential to stimulate the use of “green” management tools for production systems and artificial intelligence in industrial systems; regions of the second cluster require technological modernization and the implementation of established “green” and nature-like technologies; regions of the third type benefit from scaling successful practices in forming nature-inspired systems by expanding innovative approaches in transitioning to alternative energy sources and increasing digital activity in the Internet of Things and artificial intelligence; and regions of the fourth type, distinguished by their adoption of “green” technologies, have the potential to enhance innovative activity in ensuring ecological well-being.

4. Discussion

The present study focuses on two key issues:

• uneven, heterogeneous development of mesosystems;
• the impact of digital transformation, innovation, and “green” technologies on the formation of nature-inspired systems in the Russian context.

Figure 4 and Figure 5 above illustrate the identified patterns. Nature-inspired systems are significantly influenced by digital technologies, particularly artificial intelligence. In this regard, it is difficult to agree with the conclusions of Tan et al. [8], who argue for a different nature of dependence—namely, the role of “green” innovations in the digital transformation of economic systems. As previously emphasized (Section 3.1), digital technologies play a fundamental role in constructing nature-inspired systems.

On the other hand, factor analysis confirms the significant contribution of the innovation component within the predictor structure for forming nature-inspired systems. Our perspective aligns with the propositions of Oguntona [77], while the study’s results mathematically substantiate the impact of digital transformation, innovations, and “green” technologies on the development of nature-inspired systems.

These considerations lead us to conclude that there are substantial disparities in ecosystem development from a spatial perspective. Economic activity varies, consequently affecting pollution intensity, which in turn determines the urgency of adopting environmental innovations and “green” technologies. The findings of this study align with scholarly views on the uneven nature of regional ecological development [14,15]. Furthermore, we posit that the identified localization of growth points in nature-inspired systems could serve as a catalyst for disseminating successful environmental revitalization practices to neighboring mesosystems. In this regard, we concur with Duan et al. [15], who argue that high-quality “green” innovations in core cities foster synergistic development in peripheral urban areas.

Despite the comprehensive methodological approach to assessing nature-inspired systems, the obtained results have certain limitations. First, some conclusions are based on 2023 data, with factor and cluster analyses conducted for a single time period. While this aligns with the analytical methodology, tracking structural changes in factors and clusters over time could yield new insights into the evolution of nature-inspired mesosystems. Moreover, statistical reporting has only recently begun systematically capturing data on renewable energy transitions in response to emerging challenges. Second, while economic efficiency (measured by gross regional product per capita) was considered, the analysis did not account for the industrial sector’s contribution, despite its role as a primary source of environmental pollution. This shortcoming can be mitigated by investigating the relationships between the value added generated by the region’s industry and the indicators examined. Third, findings on federal mesosystems are partially influenced by varying sample sizes (e.g., Volga Federal District comprises 14 regions vs. Central Federal District’s 18). This discrepancy also led to the exclusion of the Ural Federal District, which ranked third in sensitivity metrics (after VFD and CFD, see Section 3.2.3). The district’s four mesosystems (Kurgan, Sverdlovsk, Tyumen, and Chelyabinsk Regions) were analyzed as undivided units due to data constraints. Fourth, the analysis results do not account for the occurrence of emergency situations within the surveyed mesosystems. Nevertheless, the study’s core propositions about asymmetric development patterns of nature-inspired mesosystems and the critical role of digital transformation remain empirically substantiated.

5. Conclusions

Russia is undergoing an intensive transition toward a nature-inspired systems model. This shift is driven by national environmental policies, the evolution of domestic industries, and the consequent increase in anthropogenic environmental pressures. Given the diverse specializations of mesosystems and the varying tools available for enhancing economic and ecological efficiency, priority areas for facilitating this transition differ significantly across regions. The present study seeks to identify the differential characteristics of this transition at both federal and regional mesosystem levels. Through this approach, the research has yielded results of both conceptual and practical significance.

• The study expands the conceptual framework of the research problem by introducing and defining the term “nature-inspired system,” identifying its formative factors (including best available technologies, “green” technologies, environmental innovations, digital technologies, and regulatory instruments), and establishing its fundamental principles. These conceptual developments formed the basis for the analytical investigation of mesosystems, particularly in assessing how digital transformation and innovation activity in ecological security contribute to the development of nature-inspired systems.
• The spatial analysis revealed dependencies between the formation of the nature-inspired macrosystems and mesosystems at both federal and regional levels, enabling the identification of growth hotspots for nature-inspired systems across Russia. The Volga, Central, and Ural Federal Districts emerged as the most significant contributors to this macrosystem’s development. Correlation analysis, regression modeling, and neural network processing further demonstrated that each district’s contribution stems from specific constituent regions with distinct environmental and technological profiles.
• The study identified priority determinants for developing nature-inspired mesosystems, which vary significantly across federal districts. Correlation and factor analysis revealed that the regional adoption of digital and “green” technologies by local organizations serves as the primary driving force behind this process.
• The study introduces a composite DNIS index (Development of Nature-Inspired Systems) that evaluates regional mesosystems’ innovation, digitalization, and technological progress to assess determinants of nature-inspired systems and their environmental impact. The analysis reveals distinct regional patterns: in Volga Federal District these factors boost GRP and water recycling rates, while the Central Federal District shows improved waste management performance.
• The study developed a typology of regional mesosystems based on economic performance, environmental efficiency, and “green” technology adoption, categorizing them into the following: (1) high-performance economic mesosystems, (2) traditional development mesosystems, (3) eco-technical mesosystems, and (4) balanced development mesosystems. This classification reveals system characteristics independent of geographical location and enables tailored strategies for advancing nature-inspired systems across different regional contexts.

The practical significance of these findings lies in their direct applicability for enhancing regional socioeconomic development programs. By incorporating the identified priority nature-inspired tools tailored to specific mesosystem types, policymakers can optimize strategic planning for sustainable growth. Specifically, the proposed models are applicable for assessing environmental risks, reducing environmental costs for businesses and the state through the adoption of best available technologies, and developing the market for domestic “green” technologies. Consequently, the transition of a mesosystem to a nature-inspired model can be replicated nationwide and contribute significantly to pollution reduction, enhanced resource efficiency, improved safety, and increased competitiveness of domestic developments.

The findings of this study can be useful for federal and regional government bodies (The Ministry of Economic Development of the Russian Federation, The Ministry of Natural Resources and Environment of the Russian Federation, The Ministry of Industry and Trade, The Ministry of Science and Higher Education of the Russian Federation) in formulating a unified state policy, disseminating best practices in the development of nature-inspired systems, and conducting research to identify the most suitable environmentally friendly model for each mesosystem.

Future research will focus on the following: (1) investigating why environmental innovations have a weaker impact than digital technologies on nature-inspired systems development; (2) conducting a longitudinal analysis of macro- and mesosystem evolution accounting for technological upgrades and improved statistical reporting; (3) extending the spatial analysis to the municipal level to examine core–periphery urban linkages in nature-inspired systems. The spatial analysis can be expanded by incorporating statistical data in the field of environmental protection published by territorial bodies of state statistics. Central cities may be defined as territories with a relatively high concentration of nature-inspired systems, modernized production facilities, and environmental innovations. It appears promising to analyze the influence of central cities on the innovative activity and environmental conditions of peripheral areas.