Physics-Based Self-Learning Spiking Neural Network enhanced time-integration scheme for computing viscoplastic structural finite element response

Computer Methods in Applied Mechanics and Engineering, vol. 422, pp. 116847

Abstract

The present study introduces a new physics-based self-learning spiking neural framework to compute geometrically and physically nonlinear structural response. While the so-called traditional or second-generation deep neural networks are used in many applications in the class of physics-informed neural networks, we propose a hybrid model that consists of third-generation Leaky-Integrated and Fire (LIF) neurons, Recurrent Leaky-Integrated and Fire (RLIF) neurons and second-generation dense transformation. The third-generation neurons are inspired by the human brain’s energy-efficient functioning which introduces inherent temporal and sparse behavior leading to a more sustainable AI approach. However, the sparse nature of the spiking neurons poses a challenge to tackle nonlinear regression tasks. Thus, in the present study, we use an autoencoding strategy that converts the real-valued signals to its spiking representation and enables the spiking neurons to learn nonlinear material response. The proposed hybrid network is firstly pretrained with combined data-driven and physics-based loss functions and then deployed in the plastic corrector step of the implicit integration which is used in the Finite Element solver and is validated on a series of Boundary Value Problems (BVPs) consisting of plate elements. A self-learning strategy is introduced for the hybrid network to train itself during FE simulation using the proposed physics-based loss function. Two major advantages were observed: an overall computational gain in the excess of 30% and the self-learning/online training ability of the model that bolsters its convergence behavior. Finally, the proposed third-generation layers are deployed on the Xylo-Av2 neuromorphic chip and its energy performance is compared with the second-generation Recurrent Neural Networks (RNNs).

Authors 2

1. Saurabh Balkrishna Tandale Aachen Institut für Allgemeine Mechanik

   RWTH Aachen University

   Affiliation as printed

   Institut für Allgemeine Mechanik, RWTH Aachen University, Eilfschornsteinstraße 18, 52062 Aachen, Germany

2. Marcus Stoffel corresponding Aachen Institut für Allgemeine Mechanik

   RWTH Aachen University

   Affiliation as printed

   Institut für Allgemeine Mechanik, RWTH Aachen University, Eilfschornsteinstraße 18, 52062 Aachen, Germany