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With the growing performance and wide application of deep neural networks (DNNs), recent years have seen enormous efforts on DNN accelerator hardware design for platforms from mobile devices to data centers. The systolic array has been a popular architectural choice for many proposed DNN accelerators with hundreds to thousands of processing elements (PEs) for parallel computing. Systolic array-based DNN accelerators for datacenter applications have high power consumption and nonuniform workload distribution, which makes power delivery network (PDN) design challenging. Server-class multicore processors have benefited from distributed on-chip voltage regulation and heterogeneous voltage regulation (HVR) for improving energy efficiency while guaranteeing power delivery integrity. This paper presents the first work on HVR-based PDN architecture and control for systolic array-based DNN accelerators. We propose to employ a PDN architecture comprising heterogeneous on-chip and off-chip voltage regulators and multiple power domains. By analyzing patterns of typical DNN workloads via a modeling framework, we propose a DNN workload-aware dynamic PDN control policy to maximize system energy efficiency while ensuring power integrity. We demonstrate significant energy efficiency improvements brought by the proposed PDN architecture, dynamic control, and power gating, which lead to a more than five-fold reduction of leakage energy and PDN energy overhead for systolic array DNN accelerators.