Deep Symbolic Optimization for Electric Component Sizing in Fixed Topology Power Converters

Power converters (PC) are a major component in any current electronic hardware device. The development and design is usually guided by expert knowledge and heavily relies on human intuition and experience. The process is a very time consuming and costly activity and it is generally hard to improve upon current designs. As a first step towards autonomous PC design, we are here proposing a new framework for the sizing of components for fixed topology PCs based on given design requirements. To this end, we developed surrogate models for rapid evaluation of new topologies and adapt the deep symbolic optimization (DSO) framework to generate new topologies guided by a reinforcement learning training signal. In an empirical evaluation, we show that our DSO based approach is able to find the optimal configuration for all investigated topologies, while reducing the learning time by at least a factor of 100 compared to popular RL algorithms. Introduction and Background Power converters (PC) are an integral component in today’s electronic devices and play a major role in technological development. With the increasing rate of electrification and digitalization, the PC market is projected to grow continuously over the next years. This will mainly be driven by developments in the energy and power sector, as well as by massive growth of the aerospace and robotics industries, having implications on many aspects of our daily lives (Vertical 2021). Designing efficient PCs is an expensive task, requiring human experience and costly testing and simulation. The basic building blocks are electronic components such as resistors, capacitors, inductors, diodes, and switching devices. The complexity and difficulty come from the combination of these blocks in highly interconnected circuits. As small changes can lead to inefficiencies, the whole process is timeconsuming, inefficient, and labor intensive. This effect is intensified by application-specific considerations, such as cost, thermal, or packaging constraints. Nevertheless, the state-ofthe-art process is still heavily reliant on human experts to se*These authors contributed equally. Copyright © 2022, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved. lect the optimal topology and search for design parameters based on the expert’s experience and intuitions. On the other hand, Machine Learning (ML) as a tool to automate general processes has started to make an increasing impact. Deep Learning (DL) (LeCun, Bengio, and Hinton 2015) approaches have led to a number of breakthroughs in computer vision (Voulodimos et al. 2018), natural language processing (Otter, Medina, and Kalita 2020), and recommendation systems (Batmaz et al. 2019). The representational generalization abilities of DL also led the way to new developments in autonomous decision making based on Deep Reinforcement Learning (DRL) (Arulkumaran et al. 2017; Sutton and Barto 2018). DRL has shown to learn super-human control in areas such as board games (Silver et al. 2016), Atari game playing (Mnih et al. 2015; Glatt et al. 2020), electric vehicle control (Pettit et al. 2019; Silva et al. 2019), robotics (Levine et al. 2016), energy applications (Zhang, Zhang, and Qiu 2019; Liang et al. 2021), chip design (Mirhoseini et al. 2020) and many other domains. More recently, ML has been employed into power electronics system design with the goal of speeding up the process. Dragičević, Wheeler, and Blaabjerg (2018) establish a functional relationship between design parameters and reliability metrics, and use them as the basis for optimal design in a grid-connected photo-voltaic converter case study. Wang et al. (2018) leverage reinforcement learning to automatically search circuit parameters and evaluate their methods on two different trans-impedance amplifiers circuits. Their approach is able to design circuits with better performance than random search, Bayesian Optimization and human experts. In an extension of their work, Wang et al. (2020) propose GCN-RL Circuit Designer, an RL agent based on Graph Convolutional Neural Network (GCN) architecture to transfer knowledge between different technology nodes and topologies for transistor sizing. Their experiments demonstrate that the method can achieve better results than others through knowledge transfer and enables more effective and efficient transistor sizing and design porting. Despite the efforts in those works, autonomous development (or recommendation) of efficient PC topologies remains a challenging and unresolved research field. Given the successful recent history of ML-powered design specification, we propose a method to support the development of Figure 1: The figure shows different representations of the same converter topology with varying detail and structure: 1) topology description in a tree structure as generated with our framework, 2) simple circuit diagram derived from the tree, and 3) full model generated using a simulation software . PC topologies as part of an intelligent system for automatic selection of DC-DC converters (Wang et al. 2022). The main contributions of this paper are (1) the representation of PC topologies as a tree structure, (2) an RL based framework to optimize component selection for a desired topology, and (3) an empirical evaluation showing that our method is useful for this task. Power Converter Representation Figure 1 illustrates how electric circuits are interchangeably represented in different levels of abstraction by our approach. In this example, we use a step-down converter, or buck converter, to regulate a voltage level, designated as Vin, to a lower voltage of Vout. We depict the buck converter because it can can be ubiquitously found in almost all modern electronics devices and is also one of the fundamental topologies in power electronics. In Figure 1 (1), a high-level representation of the circuit as a discrete token tree is shown. Tokens can either represent how components are linked (serial or parallel connections) or actual components. This token tree representation is convenient for manipulation by our learning algorithm, described in the next section. By traversing the tree from left to right, we can uniquely recover an electric circuit from the token tree, illustrated in Figure 1 (2). This simple circuit model can be fully implemented through physical components or by using commercial simulation software, as in Figure 1 (3). Deep Symbolic Optimization (DSO) Given the circuit token tree representation discussed in the previous section, we propose to use the Deep Symbolic Optimization (DSO) framework to learn how to optimize circuits. DSO is a framework that allows to explore the space of possible solutions that optimize hierarchical, variable-length discrete objects under a black box performance metric (Petersen et al. 2021; Landajuela et al. 2021a,b). DSO refers to solutions as programs τ = [τ0, τ1, . . . , τ|τ |] which are generated by the sequential combination of functional tokens that are sampled from a token library L = {τ, . . . , τ } under the consideration of prior knowledge and logical constraints. The programs form an expression tree with tokens that present internal nodes, which are operators, and terminal nodes which are constants or the input variables of the dataset. The programs are evaluated based on a reward function which indicates how good a specific program is. DSO is composed of a sequence generating neural network, is based on a Recurrent Neural Network (RNN) architecture. The RNN provides a parameterized distribution over all tokens in the library p(τ |θ) with parameters θ. The RNN is trained using a batch of programs T and backpropagating the gradients of a defined loss function, naturally, intended to learn to generate programs that optimize the reward: