FPGA-accelerated Binary Neural Networks as a surrogate model for a viscoplastic constitutive law in impulsively loaded beams

In the present study, constitutive equations are replaced by a new type of energy-efficient neural networks that lead to significantly shorter computation times. We propose this method for impulsively loaded structures exhibiting strain-rate-dependent plasticity and replacing the material law with a so-called Binarized Neural Network (BNNs) in an in-house Finite Element algorithm. BNNs share the same architecture as the Feedforward Neural Networks (FFNNs) but utilize binary layers in place of dense layers. The motivation for employing BNNs lies in the possibility that the binary operations within the binary layers can be optimized for hardware implementation. Specifically, BNNs allow for effective programming of Field Programmable Gate Arrays (FPGAs), enabling the efficient execution of BNNs forward passes in terms of computation time and energy consumption, thus improving the performance of real-time dynamic simulations. Thus in the present study, a BNN is deployed to learn the non-linear viscoplastic material law and the PYNQ Z2 FPGA board has been programmed to process the forward pass of the BNN efficiently. The computation time of the BNN forward pass in the PYNQ Z2 FPGA is 60% faster than in 13th Gen. Intel i7-13700K CPU and 26% faster than in NVIDIA GeForce RTX 4090 GPU. • A Binary Neural Network (BNN) is proposed to act as a surrogate of a constitutive model. • FPGA hardware optimization for a BNN topology is implemented. • The BNN forward pass in FPGA outperforms CPU and GPU. • BNNs are incorporated in an in-house FEM solver for impulsively loaded beams. • The hybrid BNN-FEM solver correlates well to classical FEM solver.