A Hybrid Simulation of DNN-based Gray Box Models

Aayushya Agarwal, Yihan Ruan, Lawrence Pileggi

Keywords: gray box modeling, simulation, neural networks

TL;DR: We present a new simulation paradigm that directly integrates DNNs with numerical engines of physics-based solvers to enable simulation of a fully implicit gray box modeling.

Abstract: Simulation is vital for scientific and engineering disciplines, as it enables the prediction and design of physical systems. However, the computational challenges inherent to large-scale simulations often arise from complex device models featuring high degrees of nonlinearities or hidden physical behaviors not captured by first principles. Gray-box models that combine deep neural networks (DNNs) with physics-based models have been proposed to address the computational challenges in modeling complex physical systems. A well-crafted gray box model capitalizes on the interpretability and accuracy of a physical model while incorporating deep neural networks to capture hidden physical behaviors and mitigate computational load associated with highly nonlinear components. Previously, gray box models have been constructed by defining an explicit combination of physics-based and black-box models to represent the behavior of sub-systems; however this alone cannot represent the coupled interactions that define the behavior of the entire physical system. We, therefore, explore an implicit gray box model, where both DNNs (trained on measurement and simulated data) and physical equations share a common set of state-variables. While this approach captures coupled interactions at the boundary of data-driven and physics-based models, simulating the implicit gray box model remains an open-ended problem. In this work, we introduce a new hybrid simulation that directly integrates DNNs into the numerical solvers of simulation engines to fully simulate implicit gray box models of large physical systems. This is accomplished by backpropagating through the DNN to calculate specific Jacobian values during each iteration of the numerical method. The hybrid simulation of implicit gray-box models improves the accuracy and runtime compared to full physics-based simulation and enables reusable DNN models with lower data requirements for training. For demonstration, we explore the advantages of this approach as compared to physics-based, black box, and other gray box methods for simulating the steady-state and electromagnetic transient behavior of power systems.

Primary Area: applications to physical sciences (physics, chemistry, biology, etc.)

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Submission Number: 4821