The core problem the researchers tackled is the nonlinear static analysis known in the engineering community as pushover analysis. In a pushover analysis, a finite element model of a building is subjected to a progressively increasing lateral load that mimics the inertial forces of an earthquake, and the response is tracked until key structural members reach their deformation limits. The procedure produces a capacity curve, which is typically simplified into a bilinear acceleration-displacement relationship characterized by an equivalent vibration period, a yield acceleration and an available ductility. These three quantities, evaluated for both the Damage Limitation and Severe Damage limit states and for different lateral load distributions, determine whether a building can survive a design-level earthquake. The difficulty is that each pushover analysis demands an hour or more of computation on a nonlinear finite element model, which makes portfolio-level assessment of millions of buildings an intractable task.

The team’s answer is a hybrid deep neural network that fuses two architectural paradigms: Long Short-Term Memory networks, which excel at modeling sequential dependencies, and Convolutional Neural Networks, which specialize in spatial pattern recognition. The central insight behind the design is that the seismic behavior of a frame building depends simultaneously on how forces propagate vertically through the storeys and on how stiffness and strength are distributed spatially across the floor plan. Neither an LSTM alone nor a CNN alone can capture both aspects, so the researchers constructed an architecture in which fifty parallel LSTM branches process the columns of the building column by column, storey by storey, while a downstream CNN analyzes the spatial arrangement of their outputs.

The input representation is one of the most innovative features of the study. Each building is described by three complementary sources of information: nine global parameters characterizing the structure as a whole, such as the number of storeys and material properties; eight local parameters for each individual reinforced concrete column, including its lateral stiffness, plastic shear capacity and rotational capacities in both plan directions; and a mask that encodes the building’s layout on a 50 by 50 grid spanning a 50 meter square, where each one meter cell records whether a column is present. Because the columns are aligned across storeys, a single mask suffices for the whole building. Every column along a given direction of the plan is represented as a 400-dimensional feature vector, and the stack of these vectors across the storeys forms a sequence whose length equals the number of storeys, allowing the LSTM branches to learn how structural effects accumulate from the foundations upward.

The fifty LSTM outputs are then arranged as columns of a new two-dimensional matrix and combined with the layout mask to form a two-channel image, which is processed by a convolutional network with two convolutional layers and max-pooling stages. The CNN output is concatenated with the nine global building parameters and passed through fully connected layers that produce twenty regression targets: the equivalent period, yield acceleration and kinematic ductility for both limit states, across four pushover directions. The authors emphasize that the mask acts as a spatial filter, telling the network where real columns exist and filtering out the empty background of the grid, which turns out to be critical for performance. A masking layer inside each LSTM branch similarly ignores padded entries, which is what allows the same architecture to process buildings with any number of storeys without modification.

Training the network required a substantial synthetic dataset. The researchers generated 22,576 finite element models of reinforced concrete frame buildings representative of Italian construction practice after World War II, when structures were designed for gravity loads only under outdated codes. Using the OpenSEES-Py framework and high performance computing resources with AMD EPYC processors, they carried out parallel pushover analyses on buildings of two to five storeys, a range that reflects the real Italian building stock, in which two-storey and three-storey structures respectively account for 44 and 26 percent of reinforced concrete buildings. The simulated design procedure reproduced the allowable stress method, typical gravity loads and the single concrete class R’bk 250 characteristic of that era, giving the dataset a realistic grounding in a vulnerable and widespread class of structures.

The trained model, which contains roughly 8.5 million parameters and occupies about 100 megabytes, achieved errors that the authors describe as negligible for practical engineering purposes. On the test set, the mean absolute error for the equivalent period averaged about 0.022 seconds, while the yield acceleration errors averaged around 0.013 to 0.014 meters per second squared, or roughly 0.0014 g, and ductility errors averaged about 0.014. Crucially, the model generalized across building heights despite an intentionally unbalanced dataset: the average error for two-storey buildings was nearly identical to that for five-storey buildings, indicating that the network did not simply overfit the majority class. Because the architecture uses padding and masking rather than a fixed sequence length, the authors note that the design could in principle handle single-storey or taller buildings as well, although accuracy outside the validated two-to-five storey range has not yet been empirically demonstrated.

The study went well beyond a single training run. Repeating the entire training procedure with five additional random seeds produced almost identical results with low standard deviations, demonstrating that the reported performance is not the product of a lucky initialization. A stratified five-fold cross-validation confirmed the stability of the model across different data partitions. An ablation study isolated the contribution of each component: removing the masking mechanism increased the average error from 1.56 to 9.97, removing the LSTM branches raised it to 9.68, and removing the CNN caused the largest degradation, to 14.79, confirming that all three elements are essential to the architecture’s synergy. The hybrid model was also benchmarked against five baselines, including a standard deep neural network, a one-dimensional CNN, a standalone LSTM, XGBoost and a Transformer encoder. It achieved the lowest error on nearly all twenty outputs, outperforming the best baseline by approximately nineteen percent, and differential Wilcoxon signed-rank tests confirmed that the improvements over the CNN, LSTM and Transformer baselines were statistically significant across every output.

The researchers are careful to frame the tool’s role. It is not intended to replace finite element analysis of an individual structure, and practitioners will still rely on professional nonlinear analysis software when designing retrofit interventions for a specific building. What the network offers instead is a fast, interpretable second opinion, capable of checking the order of magnitude of pushover results and, more importantly, enabling vulnerability assessments at a scale that traditional methods cannot reach. Because the outputs are the same bilinear capacity parameters used in code-based performance assessment, the predictions feed directly into regional risk frameworks without requiring qualitative guesswork.

The implications extend well beyond Italy. Most of the world’s seismically exposed cities contain large stocks of pre-modern-code reinforced concrete buildings, from Los Angeles to Istanbul to Kathmandu, and the ability to triage thousands of structures rapidly could transform how governments prioritize retrofit funding before the next major earthquake. The Salerno team suggests that extending the dataset to a broader range of structural configurations and validating out-of-distribution generalization are the next steps, but the study makes a persuasive case that hybrid LSTM-CNN architectures, guided by simple geometric masks, can compress an hour of nonlinear mechanics into a fraction of a second, bringing large-scale seismic resilience assessment within practical reach.

Subject of Research: A mask-guided hybrid LSTM-CNN neural network for rapid seismic assessment of existing reinforced concrete frame buildings

Article Title: A mask-guided multi-LSTM-CNN architecture for rapid seismic analysis of existing RC frames

Article References: D’Angelo, G., Nigro, F., & Martinelli, E. (2026). A mask-guided multi-LSTM-CNN architecture for rapid seismic analysis of existing RC frames. Neural Computing and Applications, 38(18), Article 741. https://doi.org/10.1007/s00521-026-12458-5

Image Credits: AI Generated

DOI: 10.1007/s00521-026-12458-5

Keywords: seismic assessment, reinforced concrete frames, pushover analysis, LSTM networks, convolutional neural networks, deep learning, structural engineering, finite element method, earthquake engineering, neural network architecture, seismic retrofitting, machine learning