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

The biological inspiration at the heart of NB-Net comes from a structural principle familiar to neuroscientists. In living nervous systems, a single neuron frequently fans its output out to many downstream targets, and those signals are later gathered and integrated at convergent junctions further along the pathway. This divergent-convergent pattern allows nervous systems to process multiple aspects of a stimulus simultaneously before reconciling them into a unified response. The research team asked a deceptively simple question: if biological computation relies so heavily on this broad, parallel organization rather than on arbitrarily long chains of processing, could artificial networks benefit from a similar width-first philosophy, achieving strong representation quality without resorting to very deep backbones?

NB-Net answers that question with a concrete architectural recipe. The building block of the network is the Neuron Bundle Layer, a multi-branch structure in which several parallel convolutional branches all receive the same input tensor and process it simultaneously. Rather than forcing every branch to use identical operations, the design employs grouped convolutions with different kernel sizes across the branches. This means that at any given stage of the network, the model is simultaneously extracting features at multiple spatial scales from the very same signal. Small kernels capture fine-grained local detail, while larger kernels perceive coarser structure, and the network as a whole maintains a rich, multi-scale view of its input that a single-pathway design of comparable cost would struggle to match.

Of course, running many branches in parallel creates its own challenge: at some point, the network must fuse the separate streams of features back together into a coherent representation. Early attempts at such fusion in multi-branch architectures have often relied on a single 1×1 convolution that collapses all channels at once, a move that can be numerically unstable when the incoming branches are numerous or heterogeneous. NB-Net instead introduces a two-stage 1×1 convolution fusion module. In the first stage, the module performs a moderate compression of the concatenated channel dimension, gently reducing the volume of information rather than merging everything in one abrupt step. In the second stage, the module completes the integration of the compressed features. The authors report that this progressive fusion improves training stability compared with a single 1×1 merge, because the network is never forced to reconcile wildly different feature distributions in a single transformation.

Repeat the Neuron Bundle Layer and its fusion module in succession, and the result is a network that grows primarily in width rather than depth. The team subjected this design to a systematic set of ablation experiments, examining how branch configuration, residual connections, and width settings each affect performance. Residual connections, the shortcut pathways popularized by deep residual networks, were found to interact meaningfully with the multi-branch structure, helping gradients flow through the widened architecture during training. The analysis of width settings demonstrated that the framework scales in a controlled fashion: increasing the number of parallel channels raises capacity, but parameter counts grow in a disciplined, predictable manner rather than exploding as they often do when architectures are naively broadened.

The empirical case for NB-Net rests on two of the most widely used benchmarks in computer vision. On CIFAR-10, the standard small-image classification suite that serves as a proving ground for new architectural ideas, the network delivered competitive classification accuracy against established baselines. More significantly, on ImageNet, the large-scale benchmark whose thousand object categories have historically rewarded sheer architectural depth, NB-Net achieved accuracy on par with competing designs while keeping parameter growth under tight control. In a field where improvements are often purchased with dramatic increases in model size, the ability to hold the line on parameters while remaining competitive is itself a noteworthy result, and it supports the paper’s central claim that width-oriented design, when done systematically, deserves a seat at the table alongside depth scaling.

The publication arrives at a moment of genuine ferment in architectural research. As the costs of training ever-larger monolithic models attract scrutiny, many groups are revisiting efficiency-driven strategies such as grouped convolutions, multi-branch topologies, and staged feature fusion. NB-Net contributes to this conversation a coherent biological rationale that ties these elements together. The divergent-convergent organization it emulates is not merely a decorative metaphor; it dictates the concrete structure of the network, from the parallel branches of each Neuron Bundle Layer to the progressive, two-stage reconciliation of their outputs. The result is an architecture in which the biological principle and the engineering mechanism reinforce one another, a combination that has historically produced some of the most durable ideas in machine learning, from convolutional receptive fields to attention mechanisms.

Openness was clearly a priority for the research team. The article is published open access under a Creative Commons Attribution 4.0 license, meaning that anyone can read, reuse, and build upon the work with appropriate credit. In addition, the authors have released their implementation in a public code repository on GitHub, allowing other researchers to reproduce the reported benchmarks, stress-test the two-stage fusion module on their own tasks, or graft Neuron Bundle Layers into entirely different network families. The study was supported by funding from the National Natural Science Foundation of China, the Hunan Provincial Natural Science Foundation, and the Science and Technology Innovation Program of Hunan Province, reflecting sustained institutional investment in fundamental artificial intelligence research in China.

Whether NB-Net or its descendants will change mainstream practice remains to be seen, but the study makes a persuasive case that the width of a network is not a second-class design variable. By borrowing a page from the divergent-convergent wiring of biological neurons, the researchers have shown that parallel, multi-scale branches, fused with care, can rival deep stacks of layers on the benchmarks that matter, all while keeping parameter budgets in check. For a discipline searching for ways to advance without simply building bigger and taller models, the message is timely: sometimes the most productive direction is sideways.

Subject of Research: A biologically inspired, width-oriented multi-branch neural network architecture with two-stage feature fusion

Article Title: NB-Net: A Biologically-Inspired Framework for Neural Network Width Expansion

Article References: Tan, L., Zhao, H., & Meng, W.-L. (2026). NB-Net: A Biologically-Inspired Framework for Neural Network Width Expansion. Neural Processing Letters. https://doi.org/10.1007/s11063-026-11880-z

Image Credits: AI Generated

DOI: 10.1007/s11063-026-11880-z

Keywords: neural networks, network width, biologically-inspired architecture, NB-Net, feature fusion, grouped convolutions, deep learning, image classification, CIFAR-10, ImageNet, multi-branch architecture, parameter efficiency