Mesh based neural method improves composite material simulations accuracy and speed
A mesh-based neural energy method for the simulation of heterogeneous composites
Computational Engineering, Finance, and ScienceMachine Learning
Summary
Simulating materials made of different parts, like composites, is hard because models often give wrong or unstable results. The authors created a new way to use neural networks, called mesh-based neural energy method, that splits the material into small pieces and calculates more accurate results faster. Their method reduces errors dramatically and works better when materials have very different stiffness. They also found a special type of neural network that works best for this task.
What this means in practice
- •For materials engineers: Simulate stresses and displacements in composite materials more accurately under different conditions using the mesh-based neural energy method.
- •For design optimization teams: Perform faster and more reliable simulation-based optimization for composite structures experiencing sharp material property changes.
- •For automotive engineers: Develop more precise tools for predicting composite component performance during design, possibly improving safety and durability.$Commercial implications: Enables building better simulation software products for automotive companies needing accurate composite modeling.
Authors
Pius J. M. Wichmann, Stefan Hildebrand, Sandra Klinge
Abstract
Modeling heterogeneous materials remains a challenge for physics-informed neural networks such as the deep energy method (DEM). The DEM and its variants, here collectively referred to as the neural energy method (NEM), offer a differentiable variational framework. However, their conventional collocation-based implementation (C-NEM) often suffers from physically inadmissible displacement oscillations, integration errors, and high computational costs from automatic differentiation. This work introduces the mesh-based neural energy method (M-NEM), extending the NEM through a mesh-based discretization of the displacement field. By interpolating nodal displacements via shape functions, the M-NEM imposes a kinematic constraint that suppresses oscillations. Furthermore, the method replaces automatic differentiation with algebraic shape function derivatives for strain computation and employs high-order Gaussian quadrature for accurate energy integration. On a directly comparable benchmark problem, the M-NEM reduces stress errors by up to three orders of magnitude relative to the C-NEM while being one to two orders of magnitude faster. On two further benchmarks involving extreme stiffness contrasts, only the M-NEM converges. A comparative study of neural architectures reveals that radial basis function neural networks (RBFNNs) yield optimal performance within the M-NEM, resolving sharp gradients at material interfaces with higher accuracy than multi-layer perceptrons (MLPs) with random Fourier feature (RFF) mapping and faster convergence than Kolmogorov-Arnold networks (KANs).