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

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.