Physics Meets Machine Learning to Predict the Full Seismic Response of Steel–Concrete Composite Structures

Engineers trying to anticipate how buildings will behave in an earthquake have long faced an awkward trade-off. Detailed numerical simulations of steel frames and composite walls are physically rigorous but slow and dependent on many modeling assumptions, while machine learning models are fast but typically predict only a single characteristic point, such as the peak load a member can carry, and operate as inscrutable black boxes. A new study addresses both problems at once with a physics-informed machine learning framework that reproduces the complete hysteretic response of steel frame structures and energy-dissipating composite walls, including stiffness degradation, strength deterioration, and energy dissipation, even when trained on very limited experimental data. In validation against cyclic laboratory tests, the framework achieved coefficients of determination above 0.90 for every specimen examined, outperforming both purely data-driven neural networks and a machine learning-based numerical simulation method.

The research, focused on prefabricated light steel frame and frame–composite wall systems, embeds established mechanical laws directly into the training process of neural networks. Rather than allowing a network to fit cyclic load–displacement data freely, the authors add physics-guided terms to the loss function, the quantity a neural network minimizes during training. These terms encode the Bouc–Wen hysteretic model, loading and unloading stability, dissipated energy constraints, elastic recovery behavior, and plastic damage in concrete, so that every prediction must remain consistent with the dynamics governing structures under low-cycle repeated loading. The authors frame this as a specialized form of machine learning in which the loss contains both data-driven and physics-guided components, a combination intended to preserve accuracy and physical interpretability under the small-sample conditions that are common in structural testing, where building full-scale specimens is expensive and slow.

The starting point is the classical equation of motion for a structure subjected to external loading, in which mass times acceleration, viscous damping, and the restoring force balance the applied load. The restoring force itself is decomposed into an elastic contribution and a hysteretic contribution governed by an internal variable, the hysteretic displacement, which evolves according to a set of differential equations in the Bouc–Wen formulation. Because this internal variable cannot be solved directly from the implicit differential equations, the authors integrate the evolution equation and assign the task of representing it to a long short-term memory network, which learns the shape parameters of the hysteresis model as part of the physical loss. The restoring-force equation is likewise rewritten in differential form, with its evolution coupled to displacement, dissipated energy, and the hysteretic variable through a function that the network is asked to learn.

The choice of an LSTM is deliberate. Conventional recurrent neural networks struggle to capture long-term dependencies in sequence data because gradients can vanish or explode during training, but LSTM architectures circumvent this with gate structures, namely a forget gate, an input gate, and an output gate, that control how information is retained in or discarded from the cell state across time steps. This makes the network well suited to hysteresis, which is inherently path-dependent: the force a specimen resists at a given displacement depends on the entire loading history that preceded it. The LSTM takes displacement histories, loading sequences, and structural parameters as inputs and was implemented with two hidden LSTM layers of 64 and 32 units followed by a fully connected output layer, using tanh activation and the Adam optimizer with a learning rate of 0.001, a batch size of 32, and 2000 training epochs.

A companion multilayer perceptron, a feedforward network with fully connected layers, handles the restoring force. The authors derive, using Leibniz’s integration rule, a differential equation for the restoring force that couples it to displacement, dissipated energy, and the hysteretic variable, then define the bracketed function in that equation as an MLP. The network uses three hidden layers with 64, 32, and 16 neurons and ReLU activation, again trained with Adam for 2000 epochs on min–max normalized data with an 80/20 train–validation split. Seven distinct physical loss terms are then combined with the conventional data-driven loss: consistency with the Bouc–Wen evolution of the hysteretic displacement, stability of the restoring force at displacement reversals, non-negative dissipated energy, monotonically decaying stored energy after the elastic stage, elastic recovery to zero displacement below the yield load, plastic constraints based on Drucker’s hypothesis, and concrete tensile and compressive damage indices calculated from experimentally calibrated constitutive responses and numerical simulation results rather than treated as direct network outputs.

The dataset was built from cyclic tests of two families of specimens. The first comprised six bolted beam–column joint specimens, including one ordinary bolted connection and five L-shaped connection joints, with columns ranging from square steel tubes to concrete-filled square steel tubes and H-shaped steel columns, paired with H-shaped steel beams. The second comprised six half-scale light steel frame energy-dissipating composite shear wall specimens, each combining a steel tube frame of recycled concrete-filled columns and H-shaped steel beams with a recycled concrete wall panel containing a concealed steel support, varying in support type between reinforced steel and steel plate, bar spacing from 100 to 200 millimeters, and reinforcement ratio from 0.33 percent down to 0.16 percent. Each loading history was discretized at uniform intervals into roughly 360 to 450 time steps, producing about 5000 sequential data points, split at the specimen level into 70 percent training, 15 percent validation, and 15 percent testing.

Against this benchmark, the physics-informed framework outperformed both the conventional machine learning model and the machine learning-based numerical simulation method that uses contact stiffness corrections. For the six frame specimens, the proposed method achieved R² values between 0.954 and 0.970, with a reported minimum of 0.95 and maximum of 0.97, compared with a maximum of 0.939 for the ML-based simulation and roughly 0.902 to 0.918 for traditional machine learning. On average, the framework raised the R² from 0.929 for the ML-based simulation to 0.964 while cutting root mean square error and mean absolute error by approximately 45.8 percent and 47.1 percent respectively. Cumulative energy dissipation error fell below 4 percent for the proposed method, where traditional machine learning errors ranged from about 12.1 to 14.1 percent and ML-based simulation errors from about 9.0 to 10.8 percent across the six joint specimens.

The composite wall specimens, being structurally more complex, yielded somewhat lower but still strong accuracy. The proposed method achieved R² values from 0.902 to 0.934 across the six walls, against a maximum of 0.872 for the ML-based simulation and about 0.818 to 0.841 for traditional machine learning, and reduced cumulative energy dissipation error to roughly 4.6 to 5.9 percent, compared with about 16.9 to 19.0 percent for traditional machine learning and 12.5 to 14.1 percent for the ML-based simulation. Qualitatively, the predicted hysteresis curves tracked the measured force–displacement loops closely, capturing the energy dissipation and the elastic–plastic bearing capacity evolution that the purely data-driven network visibly failed to reproduce, and the results reflected the two distinct seismic defense lines observed experimentally in the frame–wall system.

Beyond raw accuracy, the authors argue the approach removes much of the burden of conventional finite element modeling. The fusion algorithm requires no mesh partitioning, no inter-component contact constraints between steel frames and walls, no explicit handling of welded degree-of-freedom coupling, and no idealized elastoplastic constitutive assumptions; a prediction model is built directly from measured geometry, loading scheme, and material information. Because physical laws are encoded as computable constraints, the predictions remain interpretable and physically admissible even with small samples, mitigating the overfitting and lack of interpretability that limit purely data-driven models. The researchers present the framework as a tool for performance-based seismic assessment of steel frames and energy-dissipating composite wall systems, and as a step toward deeper integration of structural engineering with artificial intelligence, while the modest accuracy decline observed for the more complex wall assemblies indicates that physical complexity still taxes even physics-guided learning.

Subject of Research: Physics-informed machine learning for predicting the full hysteretic seismic response of steel frame and composite wall structures

Article Title: A hysteretic performance prediction model for steel–concrete composite structures integrating physical processes and machine learning

Article References: Wei, D., & Suizi, J. (2026). A hysteretic performance prediction model for steel–concrete composite structures integrating physical processes and machine learning. Results in Engineering, 32, Article 113571. https://doi.org/10.1016/j.rineng.2026.113571

Image Credits: AI Generated

DOI: 10.1016/j.rineng.2026.113571

Keywords: physics-informed machine learning, seismic performance, hysteresis, Bouc–Wen model, LSTM, steel–concrete composite structures, energy dissipation, prefabricated structures, structural engineering, neural networks, small-sample learning, stiffness degradation