Finite Element Method

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The finite element method turns equations for physical systems—such as solid deformation, fluid flow, and heat transfer—into numerical problems on a mesh of small elements. It uses weak or variational formulations, specialized meshes, and iterative solvers to handle complex geometries, material behavior, and boundary conditions. Current work also uses differentiable solvers, neural surrogates, and automated modeling tools to speed up simulations and inverse problems, with applications ranging from engineering design to soft robotics. A central challenge is gaining speed and automation without sacrificing accuracy, stability, and reliability on unfamiliar geometries or difficult nonlinear problems.

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31 papers2 papers in the last four weeks, down 33% on the four weeks before. 0.0% of all new papers.

Hyperreduction accelerates finite element model updating for the discovery of neural materials
Oct 22, 2026Hagen Holthusen, Matthias Knipper, Kevin LinkaFinite Element Method Reduced-Order Modeling
Computational Mechanics in Medicine, Institute of Applied Medical Engineering, RWTH Aachen University, Pauwelsstraße 20, 52074 Aachen, Germany
Simplified Swarm Optimization for Surrogate-Assisted Reliability Design of Insulated-Gate Bipolar Transistor Power Modules Using an Open-Source Process Finite-Element Model
Oct 5, 2026Wei-Chang YehSurrogate-Assisted Optimization Semiconductor Manufacturing
Department of Industrial Engineering and Engineering Management, National Tsing Hua University, Hsinchu 300044, Taiwan
DeepFEAv2: Deep Learning for Transient Finite Element Analysis Beyond Structured Meshes
Sep 22, 2026Georgios Triantafyllou, Panagiotis G. Kalozoumis, Dimitris K. IakovidisNeural Surrogate Modeling Finite Element Method
Department of Computer Science and Biomedical Informatics, University of Thessaly, 2-4 Papasiopoulou st. 35131, Lamia, Greece
Beyond PINNs: A Unified Gauss--Newton and Petrov--Galerkin Framework for Neural and Hybrid PDE Solvers
Sep 17, 2026Nilo Schwencke, Roland MaierGauss-Newton Optimization Neural PDE Solvers
Influence of Extruded Filament Shape on Buildability in 3D Concrete Printing: A Geometry-Informed Deep Learning-FEM Approach
Sep 3, 2026Giacomo Rizzieri, Saif-Ur-Rehman, Jörg F. Unger +1Finite Element Method
Department of Civil and Environmental Engineering, Politecnico di Milano Piazza Leonardo da Vinci, 32, 20133, Milano, Italy · Bundesanstalt für Materialforschung und -prüfung (BAM) Unter den Eichen 87, 12205, Berlin, Germany
Discrete energy as an exact label-free training objective for finite-element surrogates
Aug 5, 2026Ruifeng Cao, Xidan SongSurrogate Modeling Structural Mechanics
The University of Manchester · The University of Manchester, Manchester, United Kingdom · Wuhan University +1
Convex Neural Energy Elements: Monolithic Finite-Element Assembly of Geometry-Parameterized Neural Operators with Stability and Error Guarantees
Aug 3, 2026Hongyue Jiang, Jianjiang Zhan, Chenzhuo Zhang +1Neural PDE Solvers PDE Operator Learning
School of Civil and Hydraulic Engineering, Huazhong University of Science and Technology, Wuhan, 430074, China · National Center of Technology Innovation for Digital Construction, Huazhong University of Science and Technology, Wuhan, 430074, China
PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs
Jul 22, 2026Amirhossein Sadr, Nima Soltani, Vahideh Moghtadaiee +3Neural PDE Solvers Kolmogorov-Arnold Networks
School of Computer Science, Institute for Research in Fundamental Sciences (IPM), Tehran, Iran · Department of Computer Science and Engineering, Shahid Beheshti University, Tehran, Iran · Cyberspace Research Institute, Shahid Beheshti University, Tehran, Iran +1
GReFEM: Multimodal LLMs as Zero-Shot Semantic Assistants for Physics-Guided 3D Mesh Refinement
Jul 8, 2026Kartik Bali, Mahish K. Guru, Christian J Cyron +1Multimodal Grounding Multimodal Large Language Models
Institute of Material Systems Modeling Helmholtz Zentrum Hereon Max-Planck-Straße 1, 21502 Geesthacht · Institute of Material and Process Design Helmholtz Zentrum Hereon Max-Planck-Straße 1, 21502 Geesthacht · Data-Driven Simulation and Analysis in Materials Science German Research Center for Artificial Intelligence Campus D3 2, 66123 Saarbrücken
Interface-Aware Neural Newton Preconditioning for Robust Cohesive Zone Model Simulations
Jun 30, 2026Zhangyong Liang, Huanhuan GaoStructural Mechanics Finite Element Method
National Center for Applied Mathematics, Tianjin University, Tianjin, 300072, China · School of Mechanical and Aerospace Engineering, Jilin University, Renmin Street 5988, 130025, Changchun, China
Implementation of Hyperelastic Physics-Augmented Neural Networks in the Explicit Finite Element Codes Simcenter Radioss and OpenRadioss with Applications to Impact Events
Jun 29, 2026Lukas Maurer, Sascha Eisenträger, Marian Bulla +1Neural Surrogate Modeling Efficient Neural Network Inference
Institute of Materials, Technologies and Mechanics Otto von Guericke University Magdeburg Magdeburg, D-39106 · Siemens Digital Industries Am Kabellager 9 Köln, D-51063
Attention mechanism for scalable mesh-based neural surrogates of free-surface fluids
Jun 22, 2026Federico Lanteri, Massimiliano CremonesiNeural Surrogate Modeling Self-Attention
Department of Civil and Environmental Engineering, Politecnico di Milano Piazza Leonardo da Vinci, 32, 20133, Milano, Italy
TaCauchy: An Extensible FEM Framework for Vision-Based Tactile Simulation
Jun 18, 2026Hengfei Zhao, Yifan Xie, Junhao Gong +6Vision-Based Tactile Sensing Tactile Sensing
Shenzhen International Graduate School, Tsinghua University, Shenzhen 518055, China · Huawei Inc., Shenzhen, China
Robin-Neumann Coupling of PINN and FEM Solvers: A Steklov-Poincaré View, with Application to Fluid-Structure Interaction with Contact
Jun 12, 2026Mikel LandajuelaPDE Solving Fluid-Structure Interaction
Lawrence Livermore National Laboratory
DeepJEB++: Foundation Model-Driven Large-Scale 3D Engineering Dataset via 2D Latent Space Augmentation
Jun 11, 2026Soyoung Yoo, Leekyo Jeong, Jinsu Ra +4Synthetic Data Augmentation 3D Mesh Generation
Cho Chun Shik Graduate School of Mobility, Korea Advanced Institute of Science and Technology, Daejeon 34051, Republic of Korea · Department of Mechanical Engineering, Hanyang University, Ansan 15588, Republic of Korea · Narnia Labs, Daejeon 34051, Republic of Korea
Human-Enhanced Loop Modeling (HELM): Agent-Based Finite Element Modeling of Concrete Bridge Barriers
Jun 10, 2026Quankai Wang, Yulin Xie, Tongfei Yang +2Human-in-the-Loop AI Finite Element Method
Research Assistant, College of Civil Engineering, Hunan University, Changsha, 410082, China. · Assistant Professor, Department of Civil and Architectural Engineering, University of Miami, Coral Gables, FL 33146; School of Architecture, University of Miami, Coral Gables, FL 33146. · Associate Professor, College of Civil Engineering, Hunan University, Changsha 410082, China
Structure-Preserving Neural Surrogates with Tractable Uncertainty Quantification
Jun 10, 2026Handi Zhang, Adrienne M. Propp, Brooks Kinch +2Uncertainty Quantification PDE Surrogate Modeling
Applied Mathematics and Computational Science, University of Pennsylvania, Philadelphia, PA, USA · Institute for Computational and Mathematical Engineering, Stanford University, Stanford, CA, USA · Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA, USA +1
A Constrained Natural-Language Interface for Variational Multi-Physics Finite Element Simulations in FEniCS
Jun 9, 2026Nilay Upadhyay, Wesley F. ReinhartMultiphysics Simulation PDE Solving
Department of Engineering Science and Mechanics, The Pennsylvania State University, University Park, PA 16802, USA · Department of Materials Science and Engineering, The Pennsylvania State University, University Park, PA 16802, USA
Mesh Graph Neural Network Framework for Accelerating Finite Element Simulation for Arbitrary Geometries
Jun 6, 2026Josiah D. Kunz, Kamal ChoudharyNeural Surrogate Modeling Graph Neural Networks
Illinois College, Jacksonville, IL, USA · Department of Materials Science and Engineering, Whiting School of Engineering, The Johns Hopkins University, Baltimore, MD 21218, USA
Critical evaluation of PINN for FWD inverse analysis and differentiable FEM as an alternative
Jun 2, 2026Yongjin Choi, Hyeonbin Moon, Seunghwa RyuDifferentiable Physics Physics-Informed ML
KAIST InnoCORE PRISM-AI Center, Korea Advanced Institute of Science and Technology (KAIST), Daejeon, 34141, Republic of Korea · Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology (KAIST), Daejeon, 34141, Republic of Korea · School of Civil and Environmental Engineering, Georgia Institute of Technology, Atlanta, 30332, GA, USA
A Multi-AI-agent Framework Enabling End-to-end Finite Element Analysis for Solid Mechanics Problems
May 28, 2026Titu Ranjan Sarker, Muhammed Jawaad Zulqernine, Ling Yue +3Multi-Agent LLM Systems Structural Mechanics
University of Texas at Arlington, Arlington, TX 76010, USA · Rensselaer Polytechnic Institute, Troy, NY 12180, USA · Institute for Predictive Performance Methodologies, Fort Worth, TX 76118, USA
VFEAgent: A Multimodal Agent Framework for End-to-End Automated Finite Element Analysis
May 27, 2026Jiachen Zhang, Junyi Lao, Chenghao Liu +5Program Synthesis Finite Element Method
Peking University · China Agricultural University · 1Peking University +1
WINO: A Weak-Form Physics Informed Neural Operator for Hyperelasticity on Variable Domains
May 23, 2026Bokai Zhu, Qinghui Zhang, Timon RabczukNeural PDE Solvers PDE Solving
School of Science, Harbin Institute of Technology, Shenzhen, P. R. China. · School of Science, Harbin Institute of Technology, Shenzhen, Guangdong. · Institute of Structural Mechanics, Bauhaus-Universität Weimar, Weimar, 99423, Germany.
Automatic-Differentiation-Enabled Finite Element Model Updating: Learning Constitutive Neural Networks from Structural Deformation Data
May 22, 2026Matthias Knipper, Chenyi Ji, Malte Brand +1Automatic Differentiation Hyperelasticity
Computational Mechanics in Medicine, Applied Medical Engineering, RWTH Aachen University Pauwelsstraße 20, 52074 Aachen, Germany · Institute for Continuum and Material Mechanics, Hamburg University of Technology, Eißendorfer Straße 42, 21073 Hamburg, Germany
Modeling and Control of a Pneumatic Morphing Soft Quadrotor based on the SOFA Framework for Dynamic Soft Robotic Simulation
May 20, 2026F. Labra Caso, V. Sumathy, P. Ferrentino +3Aerial Robotics Robotics Simulation
Robotics & AI Luleå University of Technology · IMEC Center VUB Brussels University
Self-Improving CAD Generation Agents with Finite Element Analysis as Feedback
May 17, 2026Guijin Son, Jehyun Park, Seyeon Park +2Parametric CAD Modeling Text-to-CAD Generation
Seoul National University · OneLineAI · Sungkyunkwan University
A finite-element-inspired bipartite graph learned simulator for manufacturability assessment in large-deformation sheet forming
May 14, 2026Yingxue Zhao, Haoran Li, Haosu Zhou +2Neural Surrogate Modeling Graph Neural Networks
Dyson School of Design Engineering, Imperial College London, London, UK · NVIDIA, UK
PDEAgent-Bench: A Multi-Metric, Multi-Library Benchmark for PDE Solver Generation
May 10, 2026Zhen Hang, Yushan Yashengjiang, Junhui Li +21PDE Solving Benchmark Design
University of Science and Technology of China · Beijing University of Posts and Telecommunications · Tencent +10
GRIFDIR: Graph Resolution-Invariant FEM Diffusion Models in Function Spaces over Irregular Domains
May 5, 2026James Rowbottom, Elizabeth L. Baker, Nick Huang +3Graph Neural Operators Finite Element Method
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, UK · Department of Applied Mathematics and Computer Science, Technical University of Denmark, Denmark · Department of Mathematics, Simon Fraser University, Canada +1
Applying Two-Grid Preconditioner for Subsurface Flow Simulation using Attention-enhanced Hybrid Network to Accelerate Multiscale Discretization in High-contrast Media
Apr 15, 2026Peiqi Li, Jie Chen, Shubin FuPorous Media Flow Finite Element Method
Department of Applied Mathemaitcs, Xi’an Jiaotong-Liverpool University, 215123, Suzhou, China · Department of Mathematical Sciences, University of Liverpool, L69 3BX, Liverpool, China · Eastern Institute for Advanced Study, Eastern Institute of Technology, 315200, Ningbo, China

Oct 22, 2026J/K move · Enter open · S save

Hyperreduction accelerates finite element model updating for the discovery of neural materials

Hagen Holthusen, Matthias Knipper, Kevin Linka

Computational Mechanics in Medicine, Institute of Applied Medical Engineering, RWTH Aachen University, Pauwelsstraße 20, 52074 Aachen, Germany

Finite Element Method Reduced-Order Modeling Model Calibration

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Finite element model updating is among the most general approaches to discover constitutive models from structural experiments: since the displacement field is computed rather than measured, it accommodates arbitrary geometries, boundary conditions, and sparse or noisy data. However, every loss evaluation requires a nonlinear finite element solve per load step, and training neural materials requires many such evaluations. Intrusive model order reduction lowers this cost while retaining boundary conditions and variational structure. How can a reduced model remain accurate while the network weights change at every training step? We combine proper orthogonal decomposition and energy-conserving sampling and weighting with adjoint sensitivities of the reduced model, and adapt both the trial space and the sampled elements along the optimization path. The constitutive law is a polyconvex neural network: a logarithmic normalization term, together with a zero-anchored input convex architecture and a growth term, renders the energy polyconvex, coercive, and non-negative by construction, independent of the trained weights. We demonstrate the approach on two experimental datasets and one synthetic three-dimensional example. For a two-phase specimen, training time decreases from nine hours to 41 minutes compared with a full-order identification, without loss of accuracy. In the three-dimensional example, six modes replace 48 672 degrees of freedom, 116 of 15 625 elements suffice to evaluate the internal forces, and training takes 13 minutes. In all cases, the identified material reproduces the measured reaction force and predicts the displacement field from the force alone. Hyperreduction makes the discovery of neural materials from structural data affordable while retaining the advantages of finite element model updating.