CDS&E: Extracting Models from Data - A Novel Data-Driven Simulation Strategy for Reacting Flows

真实系统反应流的数值模拟由于涉及的变量较多，在计算上具有挑战性。这项研究将开发一种新的数据驱动的建模方法，直接结合来自规范或参考测试用例的信息，以提取具有用户定义的误差限制的简化模型。特别是，新的机器学习概念将被用来生成适用于实际工程规模模拟的简化模型。这种计算效率高的模型可以对解决一系列相关的能源和环境问题产生直接影响，例如富氧燃烧(更容易捕获和封存二氧化碳)，固定和移动燃烧系统中的污染物和颗粒形成等。这里开发的技术也适用于存在许多反应歧管或路径的其他领域，如等离子体物理或大气化学。自然界中的许多系统沿着流形演化，流形是参数空间的光滑和降低复杂性的子空间，满足通常未知的物理约束。然而，开发描述这一演变的模型是具有挑战性的。这种建模方法的一个关键挑战是处理降阶模型中出现的源项。这些是全(高保真)模型中源项的反映，但必须由降阶模型参数很好地参数化，而不会导致非物理行为，如流形边界附近的发散和伪源/汇点。这将利用数据科学的力量来表征低维流形的几何形状，并使用这些信息来改进派生模型的行为。提取低维模型是具有挑战性的，因为它需要识别一个中等维度的形状，其中在维度上以指数级扩展的网格和网格化技术将失败。相反，这项工作将受到边界曲率和矢量场加速度等属性的限制，这些属性对于大多数物理定义的系统来说都是可以很好控制的。此外，这些模型将以与简单物理模型一致的稳健方式学习，尽管训练数据中的噪声可能会导致最终矢量场中的虚假关键鞍点。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Numerical simulation of reacting flows of real systems is computationally challenging because of the large number variables involved. This research will develop a new data-driven modelling approach that directly incorporates information from canonical or reference test cases to extract simplified models with user-defined error limits. In particular, novel machine learning concepts will be used to generate simplified models that are suitable for use in practical, engineering-scale simulations. Such computationally efficient models can have a direct impact in addressing a range of relevant energy and environmental problems, for example oxy-fuel combustion (for easier CO2 capture and sequestration), pollutant and particulate formation in stationary and mobile combustion systems, etc. The techniques developed here are also applicable to other fields where many reaction manifolds or pathways exist such as in plasma physics or atmospheric chemistry.Many systems in nature evolve along manifolds, which are smooth and reduced complexity subspaces of a parameter space which satisfy, often unknown, physical constraints. However, developing models to describe this evolution is challenging. A key challenge to this modeling approach is dealing with the source terms that arise in the reduced order model. These are a reflection of the source terms in the full (high-fidelity) model, but must be well-parameterized by the reduced-order model parameters without causing unphysical behavior like divergence near manifold boundaries and spurious source/sink points. This will harness the power of data science to characterize the geometry of the low-dimensional manifold and use that information to improve the behavior of the derived models. Extracting the low-dimensional model is challenging because it requires identifying a moderate dimensional shape where gridding and meshing techniques which scale exponentially in dimension will fail. This work will instead be limited by properties such as boundary curvature and vector field acceleration which are well-controlled for most physics-defined systems. Moreover, these models will be learned in a robust manner consistent with a simple physical model, in spite of noise in training data which may otherwise result in spurious critical saddle points in the resulting vector field.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.