Governing equations in the form of differential equations are fundamental modeling elements for understanding, controlling, and optimizing chemical processes. While significant advances in machine learning allow for high-performance surrogate modeling, the resulting models typically fail to extrapolate to regimes beyond the training data and provide little physical insight regarding the underlying phenomena. In this work, we propose a moving horizon dynamic nonlinear optimization strategy that recovers parsimonious governing equations from large-scale, noisy data sets. Differently from prior works, our approach does not rely on significant structural assumptions (mainly concerning linearity with respect to estimated model coefficients), which provides greater modeling flexibility and permits distilling governing equations of systems involving chemical reactions occurring under nonisothermal conditions. The main advantages and contributions of our proposed approach are demonstrated through two numerical case studies consisting of a continuously stirred tank reactor operated under isothermal and nonisothermal conditions.

中文翻译：

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通过移动视野学习发现控制方程：反应系统的案例

微分方程形式的控制方程是用于理解、控制和优化化学过程的基本建模元素。虽然机器学习的重大进步允许高性能代理建模，但生成的模型通常无法推断训练数据之外的机制，并且几乎没有提供有关潜在现象的物理洞察力。在这项工作中，我们提出了一种移动水平动态非线性优化策略，可以从大规模、嘈杂的数据集中恢复简约的控制方程。与以前的工作不同，我们的方法不依赖于重要的结构假设（主要是关于估计模型系数的线性），它提供了更大的建模灵活性，并允许提取涉及在非等温条件下发生的化学反应的系统控制方程。我们提出的方法的主要优点和贡献通过两个数值案例研究得到证明，这些案例研究包括在等温和非等温条件下运行的连续搅拌罐反应器。