Numerical simulations of Incremental Sheet Metal Forming enable researchers to track material deformation in detail throughout the manufacturing process. However, their high computational cost limits their use for tool path optimisation, comparison of forming strategies, and die-shape compensation. Researchers from IT4Innovations National Supercomputing Center at VSB – Technical University of Ostrava and the Fraunhofer Institute for Machine Tools and Forming Technology IWU have therefore developed a surrogate model trained on a large dataset of FEM simulations. The model can predict the state of the formed sheet within tens of milliseconds while maintaining the required level of accuracy.
Incremental Sheet Metal Forming (ISMF) is a flexible manufacturing technology in which a sheet is gradually deformed by a forming tool following a predefined toolpath. In this respect, the technology has certain similarities to 3D printing: the resulting geometry is largely determined by a digitally defined manufacturing process that can be modified relatively easily. ISMF is therefore particularly attractive for rapid prototyping, small-batch manufacturing, and geometrically customised components, where manufacturers need to switch quickly between different product variants.
However, as with 3D printing, the final geometry does not necessarily correspond exactly to that originally specified for the manufacturing process. In additive manufacturing, for example, thermally induced deformation can occur during cooling. In incremental forming, deviations arise primarily from plastic deformation of the material, local wall thinning, and subsequent sheet springback once unloaded. To obtain the desired final shape, these deformations therefore need to be predicted in advance and the manufacturing geometry or tool trajectory compensated accordingly.
Numerical simulations based on the finite element method (FEM) are commonly used to analyse these phenomena. A high-fidelity FEM model can describe the forming process with high accuracy, but a single simulation may take tens of hours. This represents a major limitation, particularly when a large number of variants need to be evaluated – for example, when optimising the tool trajectory, identifying a suitable forming strategy, and compensating the geometry so that the final component matches the desired shape after springback as closely as possible.
Researchers from IT4Innovations and the Fraunhofer Institute for Machine Tools and Forming Technology IWU have therefore developed a surrogate model. Its purpose is not to replace physics-based simulations when generating reference data, but rather to learn from simulations that have already been performed and capture the relationship between the forming process and the resulting material response. Once trained, the model can evaluate new variants without the need to solve the complete FEM problem again.
The work was based on a large-scale numerical dataset generated on the Karolina supercomputer at IT4Innovations. It contains the results of thousands of FEM simulations of incremental sheet metal forming, covering variations in geometry and forming process conditions.
More than four million samples were subsequently used to train the time-aware variant of the model. These capture not only the final state of the sheet but also the individual stages of its progressive deformation.
The temporal evolution of the forming process is one of the key elements of the proposed approach. Rather than relying solely on information about the target geometry, the model also takes into account the time history of the forming tool trajectory. For any selected point in time, it can therefore directly predict the corresponding state of the sheet without having to generate all preceding time steps sequentially.
This formulation also limits the accumulation of numerical errors that can occur in autoregressive neural network models, where each new state is derived from the preceding prediction.
The proposed Transformer Cross-Attention U-Net (TCAU) neural architecture combines temporal and spatial representations of the problem. The Transformer processes the forming tool trajectory, while the convolutional U-Net component represents the spatial deformation field of the sheet. The cross-attention mechanism allows the network to fuse information about the tool movement with the deformation of individual parts of the material.
The model is not limited to predicting the final geometry. In its extended variant, it simultaneously predicts several physical quantities that describe the state of the material, including the sheet geometry, thickness, equivalent plastic strain, and internal energy. A separate component of the model was also designed to predict material springback upon completion of the forming process.
The numerical data were generated on the Karolina supercomputer, while the neural network models were trained using the GPU partition of the European LUMI supercomputer.
The results show that the neural network model can reproduce the response of the reference FEM simulations with high accuracy, dramatically reducing the time required to evaluate a new variant.
A single prediction takes approximately 34 to 90 milliseconds on a GPU.
A calculation that may require hours using a high-fidelity FEM model can therefore be performed in a fraction of a second once the model is trained.
Such a speed-up changes how numerical models can be used in manufacturing process design. FEM simulations can be used to create a physically consistent data foundation and to validate selected solutions. Meanwhile, the neural network model enables rapid exploration of a large space of possible manufacturing parameters.
One practical example is geometry compensation. Similar to 3D printing, where a model can be adjusted in advance so that the desired shape is achieved after thermal shrinkage or deformation, incremental forming can be used to identify a tool trajectory or input geometry that will produce the desired result after deformation and springback. For this type of optimisation task, the ability to rapidly evaluate numerous variants is essential, as doing so using high-fidelity FEM simulations alone is computationally very expensive.
Research data:
https://doi.org/10.5281/zenodo.17917675
Research article:
AI-based surrogate modelling for incremental sheet metal forming using large-scale dataset
https://doi.org/10.1016/j.rineng.2026.109927
This research was carried out within the FutureMold project, supported under the M-ERA.NET 3 Joint Transnational Call 2023 and co-funded by the Technology Agency of the Czech Republic under the SIGMA Programme (TQ05000004).