# COMMET: orders-of-magnitude speed-up in finite element method via batch-vectorized neural constitutive updates

arXiv: https://arxiv.org/abs/2510.00884 · HTML: https://mlsanity.com/paper/2510.00884/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 83 references that are in the map.
- First posted on arXiv 1 Oct 2025.

## Builds on (most cited first, 29 of 29)

- [Input Convex Neural Networks](https://mlsanity.com/paper/1609.07152/) (2016)
- [Polyconvex anisotropic hyperelasticity with neural networks](https://mlsanity.com/paper/2106.14623/) (2021)
- [Unsupervised discovery of interpretable hyperelastic constitutive laws](https://mlsanity.com/paper/2010.13496/) (2020)
- [Geometric deep learning for computational mechanics Part I: Anisotropic Hyperelasticity](https://mlsanity.com/paper/2001.04292/) (2020)
- [A new family of Constitutive Artificial Neural Networks towards automated model discovery](https://mlsanity.com/paper/2210.02202/) (2022)
- [Neural networks meet hyperelasticity: A guide to enforcing physics](https://mlsanity.com/paper/2302.02403/) (2023)
- [JAX-FEM: A differentiable GPU-accelerated 3D finite element solver for automatic inverse design and mechanistic data science](https://mlsanity.com/paper/2212.00964/) (2022)
- [A review on data-driven constitutive laws for solids](https://mlsanity.com/paper/2405.03658/) (2024)
- [Automated discovery of generalized standard material models with EUCLID](https://mlsanity.com/paper/2211.04453/) (2022)
- [NN-EUCLID: deep-learning hyperelasticity without stress data](https://mlsanity.com/paper/2205.06664/) (2022)
- [Discovering plasticity models without stress data](https://mlsanity.com/paper/2202.04916/) (2022)
- [Viscoelasticty with physics-augmented neural networks: Model formulation and training methods without prescribed internal variables](https://mlsanity.com/paper/2401.14270/) (2024)
- [Data-driven Modeling of the Mechanical Behavior of Anisotropic Soft Biological Tissue](https://mlsanity.com/paper/2107.05388/) (2021)
- [Can KAN CANs? Input-convex Kolmogorov-Arnold Networks (KANs) as hyperelastic constitutive artificial neural networks (CANs)](https://mlsanity.com/paper/2503.05617/) (2025)
- [Theory and implementation of inelastic Constitutive Artificial Neural Networks](https://mlsanity.com/paper/2311.06380/) (2023)
- [Neural networks meet hyperelasticity: A monotonic approach](https://mlsanity.com/paper/2501.02670/) (2025)
- [Physics-informed Data-driven Discovery of Constitutive Models with Application to Strain-Rate-sensitive Soft Materials](https://mlsanity.com/paper/2304.13897/) (2023)
- [Cooperative data-driven modeling](https://mlsanity.com/paper/2211.12971/) (2022)
- [HyperCAN: Hypernetwork-Driven Deep Parameterized Constitutive Models for Metamaterials](https://mlsanity.com/paper/2408.06017/) (2024)
- [Polyconvex Physics-Augmented Neural Network Constitutive Models in Principal Stretches](https://mlsanity.com/paper/2503.00575/) (2025)
- [Automatically Differentiable Model Updating (ADiMU): conventional, hybrid, and neural network material model discovery including history-dependency](https://mlsanity.com/paper/2505.07801/) (2025)
- [History-Aware Neural Operator: Robust Data-Driven Constitutive Modeling of Path-Dependent Materials](https://mlsanity.com/paper/2506.10352/) (2025)
- [A universal material model subroutine for soft matter systems](https://mlsanity.com/paper/2404.13144/) (2024)
- [Physics Augmented Machine Learning Discovery of Composition-Dependent Constitutive Laws for 3D Printed Digital Materials](https://mlsanity.com/paper/2507.02991/) (2025)
- [Nonlinear electro-elastic finite element analysis with neural network constitutive models](https://mlsanity.com/paper/2402.07007/) (2024)
- [Input convex neural networks: universal approximation theorem and implementation for isotropic polyconvex hyperelastic energies](https://mlsanity.com/paper/2502.08534/) (2025)
- [Calibration of Elastoplastic Constitutive Model Parameters from Full-field Data with Automatic Differentiation-based Sensitivities](https://mlsanity.com/paper/2010.03649/) (2020)
- [Advanced discretization techniques for hyperelastic physics-augmented neural networks](https://mlsanity.com/paper/2306.09866/) (2023)
- [Input Specific Neural Networks](https://mlsanity.com/paper/2503.00268/) (2025)

## Built on by (most cited first, 2 of 2)

- [Towards Rapid Constitutive Model Discovery from Multi-Modal Data: Physics Augmented Finite Element Model Updating (paFEMU)](https://mlsanity.com/paper/2604.07746/) (2026)
- [CANN-EUCLID: unsupervised constitutive artificial neural network model discovery from full-field data](https://mlsanity.com/paper/2606.14565/) (2026)

## Abstract (arXiv)

Constitutive evaluations often dominate the computational cost of finite element (FE) simulations whenever material models are complex. Neural constitutive models (NCMs) offer a highly expressive and flexible framework for modeling complex material behavior in solid mechanics. However, their practical adoption in large-scale FE simulations remains limited due to significant computational costs, especially in repeatedly evaluating stress and stiffness. NCMs thus represent an extreme case: their large computational graphs make stress and stiffness evaluations prohibitively expensive, restricting their use to small-scale problems. In this work, we introduce COMMET, an open-source FE framework whose architecture has been redesigned from the ground up to accelerate high-cost constitutive updates. Our framework features a novel assembly algorithm that supports batched and vectorized constitutive evaluations, compute-graph-optimized derivatives that replace automatic differentiation, and distributed-memory parallelism via MPI. These advances dramatically reduce runtime, with speed-ups exceeding three orders of magnitude relative to traditional non-vectorized automatic differentiation-based implementations. While we demonstrate these gains primarily for NCMs, the same principles apply broadly wherever for-loop based assembly or constitutive updates limit performance, establishing a new standard for large-scale, high-fidelity simulations in computational mechanics.