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<p>We present <Emphasis FontCategory="NonProportional">Ozone</Emphasis>, a Python library for solving ordinary differential equations (ODEs) within gradient-based optimization algorithms. <Emphasis FontCategory="NonProportional">Ozone</Emphasis> makes available the entire family of explicit and implicit Runge–Kutta methods and implements several solution approaches including parallel-in-time approaches. A unique feature is the ability to perform sensitivity analysis for any combination of method and solution approaches. <Emphasis FontCategory="NonProportional">Ozone</Emphasis> is implemented as a library in the Computational System Design Language (<Emphasis FontCategory="NonProportional">CSDL</Emphasis>), enabling the automatic calculation of the derivatives of the optimization objective and constraints that are outputs of the larger system within which the <Emphasis FontCategory="NonProportional">Ozone</Emphasis> model is embedded. <Emphasis FontCategory="NonProportional">Ozone</Emphasis> allows researchers to easily incorporate ODEs in multidisciplinary optimization and direct-transcript optimal control models. This paper describes the components of the software implementation of <Emphasis FontCategory="NonProportional">Ozone</Emphasis> and demonstrates its features through four illustrative applications.</p>

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Ozone: an open-source ordinary differential equation solver for gradient-based optimization

  • 期刊论文

  • 发表日期：

    2025年4月25日

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  • Mark Z. Sperry,
  • John T. Hwang

摘要

We present Ozone, a Python library for solving ordinary differential equations (ODEs) within gradient-based optimization algorithms. Ozone makes available the entire family of explicit and implicit Runge–Kutta methods and implements several solution approaches including parallel-in-time approaches. A unique feature is the ability to perform sensitivity analysis for any combination of method and solution approaches. Ozone is implemented as a library in the Computational System Design Language (CSDL), enabling the automatic calculation of the derivatives of the optimization objective and constraints that are outputs of the larger system within which the Ozone model is embedded. Ozone allows researchers to easily incorporate ODEs in multidisciplinary optimization and direct-transcript optimal control models. This paper describes the components of the software implementation of Ozone and demonstrates its features through four illustrative applications.