A mesh-based neural energy method for the simulation of heterogeneous composites

Key points

• Modeling heterogeneous materials remains a challenge for physics-informed neural networks such as the deep energy method (DEM).1
• The DEM and its variants, here collectively referred to as the neural energy method (NEM), offer a differentiable variational framework.1
• Furthermore, the method replaces automatic differentiation with algebraic shape function derivatives for strain computation and employs high-order Gaussian quadrature for accurate energy integration.1
• 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).1

Sources (1)

• [1]A mesh-based neural energy method for the simulation of heterogeneous composites
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 7, 08:08 PM

  This work introduces the mesh-based neural energy method (M-NEM), extending the NEM through a mesh-based discretization of the displacement field.

  Modeling heterogeneous materials remains a challenge for physics-informed neural networks such as the deep energy method (DEM).

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