What question did this study set out to answer?

To develop an accurate prediction method for the vulnerability of urban ecological environments using FII-LSTM.

March 1, 2026Open Access

Research on urban ecological environment vulnerability prediction method based on FII-LSTM

Key Points

To develop an accurate prediction method for the vulnerability of urban ecological environments using FII-LSTM.
Proposed a prediction model based on Fractal Interpolation (FII) combined with Long Short-Term Memory (LSTM) technique.
Constructed an affine transformation matrix as an Iterated Function System (IFS).
Utilized equidistant sampling measures to generate interpolation points and analyze the fractal distribution of data.
Trained the LSTM model using the holdout method with MSE as the loss function and Adam as the optimizer.
The FII-LSTM model demonstrated high prediction accuracy and stability in assessing ecological vulnerabilities.
Validation was performed using multidimensional data from 35 cities in China, confirming the model's effectiveness.
Policy recommendations were provided based on model predictions for urban ecological vulnerabilities from 2021 to 2025.

Abstract

Constructing scientific and effective prediction methods for the vulnerability of urban ecological environment is of great significance for effectively managing and controlling the risks of urban ecological environment vulnerability. Existing prediction methods often overlook the self-similar characteristics of the evolution trends in complex nonlinear systems, resulting in low accuracy of the prediction results. A prediction method for urban ecological environment vulnerability based on the Fractal Interpolation (FII) - Long Short-Term Memory (LSTM) model was proposed. Using the FII model, constructed an affine transformation matrix as the Iterated Function System (IFS). By estimating the scaling factor of the FII model and using equidistant sampling measures, interpolation points were generated within the interpolation interval according to certain rules. These generated interpolation points were incorporated into the FII model to calculate the corresponding interpolation results, describe the fractal interpolation curve, and reveal the distribution state of the data. Constructed the LSTM neural network structure, selecting MSE and Adam as the loss function and optimizer, respectively. Used the holdout method to train the LSTM model, establishing a method for predicting urban ecological environment vulnerability. Based on multidimensional data from 35 cities in China, the model's prediction accuracy and stability were validated. The comparison results indicated that the constructed FII-LSTM model had high prediction accuracy and stability, making it suitable for decision-making management in urban ecological environment vulnerability prediction. The FII-LSTM model was used to predict the ecological vulnerability of the sample cities in 2021–2025 and to make policy recommendations. • Proposed a prediction model for urban environmental vulnerability based on FII-LSTM. • The proposed model had high prediction accuracy and stability. • Put forward policy suggestions for the management of urban environmental vulnerability.

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