用物理模型训练模拟存内计算电路，利用硬件缺陷提升能效。

Large-scale deep learning models are increasingly constrained by their immense energy consumption, limiting their scalability and applicability for edge intelligence. In-memory computing (IMC) offers a promising solution by addressing the von Neumann bottleneck inherent in traditional deep learning accelerators, significantly reducing energy consumption. However, the analog nature of IMC introduces hardware nonidealities that degrade model performance and reliability. This paper presents a novel approach to directly train physical models of IMC, formulated as ordinary-differential-equation (ODE)-based physical neural networks (PNNs). To enable the training of large-scale networks, we propose a technique called differentiable spike-time discretization (DSTD), which reduces the computational cost of ODE-based PNNs by up to 20 times in speed and 100 times in memory. We demonstrate that such large-scale networks enhance the learning performance by exploiting hardware nonidealities on the CIFAR-10 dataset. The proposed bottom-up methodology is validated through the post-layout SPICE simulations on the IMC circuit with nonideal characteristics using the sky130 process. The proposed PNN approach reduces the discrepancy between the model behavior and circuit dynamics by at least an order of magnitude. This work paves the way for leveraging nonideal physical devices, such as non-volatile resistive memories, for energy-efficient deep learning applications.