Graph Neural Network Surrogate Modeling for Soft Pneumatic Actuator Simulation

Graph Neural Network Surrogate Modeling for Soft Pneumatic Actuator Simulation Problem. Soft robotic actuators made from compliant, deformable materials offer significant advantages for safe human-robot interaction and adaptive manipulation. Designing and controlling these systems requires accurate physical simulation, typically performed using finite element method (FEM) solvers. FEM simulation is computationally expensive, often requiring seconds to minutes per run, making it impractical for real-time control, large-scale design optimization, or deployment in resource-constrained environments. A 2023 Annual Review survey of soft robotics [1] explicitly identifies using high-dimensional FEM data to train a neural network forward model for soft robots as an open problem that has not yet been demonstrated in practice. Approach. We address this gap by applying MeshGraphNets [2], a graph neural network framework for mesh-based physical simulation, to FEM simulation data for soft pneumatic actuators. FEM meshes are naturally graph-structured: mesh nodes carry physical quantities including position and displacement, while edges encode spatial relationships between connected nodes. Our planned pipeline has three stages. First, we will generate training data by running parametrized simulations of a PneuNet-style soft bending actuator in the open-source FEM framework SOFA, varying geometric parameters such as chamber count, chamber height, wall thickness, and inter-chamber gap. Material properties and the loading profile are held fixed, since neither is observable in the mesh fields the network receives; varying them would map identical inputs to differing outputs. Each simulation run will produce a trajectory of 400 timesteps, exporting five fields at every step: mesh connectivity, node-type labels distinguishing deformable-body nodes from clamped-base nodes, initial undeformed node coordinates, deformed node positions, and a per-node scalar field intended for von Mises stress. Second, we represent each trajectory as a sequence of graphs: mesh nodes become graph nodes with features encoding velocity estimated from the previous timestep and a one-hot node-type vector, and mesh edges carry features encoding relative displacement between connected nodes in both mesh space and world space, plus their norms. Third, we train a MeshGraphNets model with an Encode-Process-Decode architecture. An MLP encoder maps raw node and edge features to 128-dimensional latent vectors; a processor runs 15 rounds of message passing with residual connections, each round updating edge embeddings from neighboring node features and then updating node embeddings by aggregating edge messages; and an MLP decoder maps final node embeddings to predicted per-node displacement at the next timestep. The model is trained end-to-end with a normalized mean squared error loss on deformable-body nodes only, with clamped nodes masked out. We will split the data by geometry, so validation designs are never seen in training. Results (planned). This work is currently in the implementation and data generation phase. We will report one-step prediction RMSE on a held-out soft actuator validation set, multi-step rollout stability over 50 or more chained predictions, and wall-clock speedup of the trained GNN surrogate relative to the FEM solver. The original MeshGraphNets paper reports a 120x speedup and one-step RMSE of 0.00025 on a hyperelastic plate in the structural mechanics domain, which motivates the expectation that a graph-network surrogate is well suited to the soft pneumatic actuator case. Context. Prior work on learned forward models for soft robot control [3, 4] has used sparse state representations such as motion-capture marker positions, capturing only a handful of surface points with no information about internal deformation. MeshGraphNets applied to FEM data provides a significantly richer state representation, capturing the full volumetric deformation field across all mesh nodes. This richer representation is expected to improve forward-model accuracy and enable downstream applications including model-based control, rapid design optimization, and sim-to-real transfer research. References. [1] Yasa et al. An Overview of Soft Robotics. Annu. Rev. Control Robot. Auton. Syst., 2023. [2] Pfaff et al. Learning Mesh-Based Simulation with Graph Networks. ICLR, 2021. [3] Thuruthel et al. Model-Based RL for Closed-Loop Dynamic Control of Soft Robotic Manipulators. IEEE T-RO, 2019. [4] Gillespie et al. Model-Based Control of Soft Actuators Using Learned Nonlinear Discrete-Time Models. Front. Robot. AI, 2018.