Meta-learning Hybrid Spiking networks as physics-based nonlinear solvers for physical simulations

npj Unconventional Computing, vol. 3

Abstract

Abstract In the present study, a modified Leaky-Integrate and Fire (LIF) neuron model termed a Hybrid Spiking Neuron (HSN) is proposed and introduced as a physics-based meta-learning solver for applications in engineering mechanics. Unlike LIF neurons, HSNs produce a real-valued spiking signal. In each time step, the activation function determines whether the neuron is active and outputs its real-valued state, or inactive and outputs zero. On neuromorphic hardware such as Loihi 2, these neurons can be implemented with 32-bit integer outputs. This makes HSNs more suitable than standard LIF neurons for engineering applications, as active neurons can transmit non-binary information. Hybrid networks therefore combine the strengths of second- and third-generation models for time-dependent computations, such as in FE simulations. This study proposes a physics-based, self-learning framework that requires minimal or no online training to obtain converged solutions for nonlinear viscoplastic material behaviour in FE solvers. Using second-order gradient meta-learning such as Model Agnostic Meta-Learning (MAML), we show that Hybrid Spiking Neural Networks (HSNNs) meta-pretrained by combined physics-based and data-driven loss terms outperform HSNNs pretrained with standard first-order methods. Quantization-Aware Training (QAT) is further applied to prepare the weights for deployment on neuromorphic hardware. Furthermore, we demonstrate using nonlinear finite element plate simulations that the meta-pretrained model accelerates the FE simulation in comparison to traditional solvers since it has a more conducive initialization of the network parameters that reduce/eliminate online iteration steps required to satisfy the physics-based loss term and obtain the converged FE solution.

Authors 2

1. Saurabh Balkrishna Tandale corresponding Aachen Institute of General Mechanics

   RWTH Aachen University

   Affiliation as printed

   Institute of General Mechanics, RWTH Aachen University, Aachen, Germany

2. Marcus Stoffel Aachen Institute of General Mechanics

   RWTH Aachen University

   Affiliation as printed

   Institute of General Mechanics, RWTH Aachen University, Aachen, Germany