DeepFEAv2: Deep Learning for Transient Finite Element Analysis Beyond Structured Meshes

A deep learning surrogate framework enabling transient FEA predictions across diverse mesh topologies and element types

Georgios Triantafyllou; Panagiotis G. Kalozoumis; Dimitris K. Iakovidis· 2026· DOI 10.48550/arXiv.2609.26426

The core problem

Finite Element Analysis (FEA) is a cornerstone of transient mechanical simulations, but its high computational cost hinders real-time and high-resolution applications. Deep learning surrogate models offer a promising alternative by approximating FEA outputs at a fraction of the cost. However, existing approaches often are limited to steady-state predictions or cannot jointly predict Node- and Element-based Outputs (NEO) over time. The state-of-the-art DeepFEA framework addressed these issues but was restricted to structured finite element (FE) meshes. This work proposes DeepFEAv2, which overcomes this limitation by enabling predictions across different FE mesh topologies and element types. The main contributions are: (a) a module that uses the FE connectivity matrix to organize input features by element and arrange them into an input sequence guided by mesh topology; (b) a novel neural network architecture designed to process the input sequence and jointly predict NEO over time; and (c) an FEA-informed optimization strategy for regularizing these NEO predictions. DeepFEAv2 was evaluated on structured and unstructured 3D linear elastic datasets, as well as on a pressure-driven aorti

DeepFEAv2 was evaluated on structured and unstructured 3D linear elastic datasets, as well as on a pressure-driven aortic valve dataset. The framework achieved R² values up to 0.99 and normalized errors as low as 0.38%. Compared to DeepFEA, it achieved up to a 38.0% relative increase in R² and up to an 87.1% reduction in normalized error. Furthermore, DeepFEAv2 performed inference up to three orders of magnitude faster than traditional FEA. These results demonstrate that DeepFEAv2 can efficiently model transient FEA simulations across increasingly complex FE settings, providing a scalable surrogate framework. The improvements are particularly notable on unstructured meshes, where DeepFEA was previously inapplicable. The aortic valve dataset further validates the framework's ability to handle real-world biomechanical simulations with complex geometries and boundary conditions.

Finite Element Analysis (FEA) is a cornerstone of transient mechanical simulations, but its high computational cost hinders real-time and high-resolution applications. Deep learning surrogate models offer a promising alternative by approximating FEA outputs at a fraction of the cost. However, existing approaches often are limited to steady-state predictions or cannot jointly predict Node- and Element-based Outputs (NEO) over time. The state-of-the-art DeepFEA framework addressed these issues but was restricted to structured finite element (FE) meshes. This work proposes DeepFEAv2, which overcomes this limitation by enabling predictions across different FE mesh topologies and element types. The main contributions are: (a) a module that uses the FE connectivity matrix to organize input features by element and arrange them into an input sequence guided by mesh topology; (b) a novel neural network architecture designed to process the input sequence and jointly predict NEO over time; and (c) an FEA-informed optimization strategy for regularizing these NEO predictions. DeepFEAv2 was evaluated on structured and unstructured 3D linear elastic datasets, as well as on a pressure-driven aortic valve dataset, demonstrating significant improvements over DeepFEA and traditional FEA.

DeepFEAv2 comprises three key components. First, the **connectivity-based input organization module** leverages the FE connectivity matrix to group input features by element and arrange them into a sequence that respects the mesh topology. This allows the model to handle arbitrary mesh structures, including unstructured meshes and mixed element types. Second, a **novel neural network architecture** processes this sequence to jointly predict NEO over time. The architecture likely employs sequence modeling techniques (e.g., recurrent or transformer-based layers) to capture temporal dependencies and spatial relationships encoded in the input sequence. Third, an **FEA-informed optimization strategy** regularizes the NEO predictions by incorporating physical constraints or loss terms derived from FEA principles, ensuring that predictions remain physically plausible. The framework is trained end-to-end on simulation data. For evaluation, three datasets were used: structured 3D linear elastic, unstructured 3D linear elastic, and a pressure-driven aortic valve dataset. Performance metrics include R² and normalized error, and inference speed is compared to traditional FEA. The methodology is summarized in the following Mermaid diagram:

The results indicate that DeepFEAv2 successfully addresses the limitations of its predecessor by extending support to unstructured meshes and multiple element types. The connectivity-based input organization is crucial for handling arbitrary topologies, while the novel architecture effectively captures temporal and spatial dependencies. The FEA-informed optimization ensures physical consistency, which is vital for engineering and biomedical applications. The significant speedup (up to 1000x) makes real-time simulation feasible, potentially enabling interactive design and surgical planning. However, the framework's performance may depend on the quality and diversity of training data, and generalization to unseen mesh topologies or element types remains to be fully explored. Future work could investigate adaptive mesh refinement, multi-physics coupling, and uncertainty quantification. Overall, DeepFEAv2 represents a significant step toward scalable, accurate, and fast transient FEA surrogates.

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