ABSTRACT

This paper derives predictive reduced-order models for rocket engine combustion dynamics via Operator Inference, a scientific machine learning approach that blends data-driven learning with physics-based modelling. The non-intrusive nature of the approach enables variable transformations that expose system structure. The specific contribution of this paper is to advance the formulation robustness and algorithmic scalability of the Operator Inference approach. Regularisation is introduced to the formulation to avoid over-fitting. The task of determining an optimal regularisation is posed as an optimisation problem that balances training error and stability of long-time integration dynamics. A scalable algorithm and open-source implementation are presented, then demonstrated for a single-injector rocket combustion example. This example exhibits rich dynamics that are difficult to capture with state-of-the-art reduced models. With appropriate regularisation and an informed selection of learning variables, the reduced-order models exhibit high accuracy in re-predicting the training regime and acceptable accuracy in predicting future dynamics, while achieving close to a million times speedup in computational cost. When compared to a state-of-the-art model reduction method, the Operator Inference models provide the same or better accuracy at approximately one thousandth of the computational cost.

摘要

本文通过运算符推断（Operator Inference）推导了火箭发动机燃烧动力学的预测降阶模型，这是一种科学的机器学习方法，将数据驱动的学习与基于物理的建模相结合。该方法的非侵入性使得可以进行公开系统结构的变量转换。本文的具体贡献是提高了运算符推断方法的公式鲁棒性和算法可扩展性。正则化被引入到配方中以避免过度拟合。确定最佳正则化的任务是作为一个优化问题，该问题平衡了训练误差和长时间积分动力学的稳定性。提出了可扩展的算法和开源实现，然后针对单喷射器火箭燃烧示例进行了演示。该示例展示了丰富的动态特性，而这些动态特性很难用最新的简化模型捕获。通过适当的正则化和对学习变量的明智选择，降阶模型在重新预测训练方案方面表现出很高的准确性，在预测未来动力方面表现出可接受的准确性，同时实现了近一百万倍的计算成本加速。与最先进的模型简化方法相比，算子推断模型以大约一千分之一的计算成本提供了相同或更好的准确性。降阶模型在重新预测训练方案方面表现出很高的准确性，在预测未来动力方面表现出可以接受的准确性，同时实现了将近100万倍的计算成本加速。与最先进的模型简化方法相比，算子推断模型可提供相同或更好的精度，而计算成本仅为其一千分之一左右。降阶模型在重新预测训练方案方面表现出很高的准确性，在预测未来动力方面表现出可以接受的准确性，同时实现了将近100万倍的计算成本加速。与最先进的模型简化方法相比，算子推断模型以大约一千分之一的计算成本提供了相同或更好的准确性。