# A Dual-Graph Spatiotemporal GNN Surrogate for Nonlinear Response Prediction of Reinforced Concrete Beams under Four-Point Bending

arXiv: https://arxiv.org/abs/2603.07201 · HTML: https://mlsanity.com/paper/2603.07201/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 36 references that are in the map.
- First posted on arXiv 7 Mar 2026.

## Builds on (most cited first, 11 of 11)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
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- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [An Overview of Multi-Task Learning in Deep Neural Networks](https://mlsanity.com/paper/1706.05098/) (2017)
- [Structured Sequence Modeling with Graph Convolutional Recurrent Networks](https://mlsanity.com/paper/1612.07659/) (2016)
- [Physics-informed learning of governing equations from scarce data](https://mlsanity.com/paper/2005.03448/) (2020)
- [Geometric deep learning for computational mechanics Part I: Anisotropic Hyperelasticity](https://mlsanity.com/paper/2001.04292/) (2020)
- [Simulating Continuum Mechanics with Multi-Scale Graph Neural Networks](https://mlsanity.com/paper/2106.04900/) (2021)
- [A Review of Vibration-Based Damage Detection in Civil Structures: From Traditional Methods to Machine Learning and Deep Learning Applications](https://mlsanity.com/paper/2004.04373/) (2020)

## Abstract (arXiv)

High-fidelity nonlinear finite-element (FE) simulations of reinforced-concrete (RC) structures are still costly, especially in parametric settings where loading positions vary. We develop a dual-graph spatiotemporal GNN surrogate to approximate the time histories of RC beams under four-point bending. To generate training data, we run a parametric Abaqus campaign that independently shifts the two loading blocks on a mesh-aligned grid and exports full-field responses at fixed normalized loading levels. The model rolls out autoregressively and jointly predicts nodal displacements, element wise von Mises stress, element-wise equivalent plastic strain (PEEQ), and the global vertical reaction force in a single multi-task setup. A key motivation is the peak loss introduced when element quantities are forced through node-based representations. We therefore couple node- and element-level dynamics using two recurrent graph branches: a node-level graph convolutional gated recurrent unit (GConvGRU) for kinematics and an element-level GConvGRU for history-dependent internal variables, with global force predicted through pooling on the element branch. In controlled ablations, removing the Element to Node to Element pathway improves peak-sensitive prediction in localized high-gradient stress/PEEQ regions without degrading global load displacement trends. After training, the surrogate produces full trajectories at a fraction of the cost of nonlinear FE, enabling faster parametric evaluation and design exploration.