Neural Network-Based Preconditioning of Adaptive Tabulation for Reactive Flow Applications

燃烧是当今世界的主要能源，预计到2050年仍将如此。此外，对于许多工程应用(例如，航天运载火箭)来说，这是唯一可行的选择。因此，继续研究燃烧物理和开发新的、更高效、更清洁的燃烧装置是当今工程界的高度优先事项。在过去的五十年里，燃烧模拟对这一努力起到了无价的作用，但它们仍然构成了许多挑战。这个项目旨在解决一个这样的挑战，特别是如何快速评估化学性质。这里提出的方法是将机器学习方法与以前开发的制表方法相结合，机器学习方法可以给出感兴趣的属性的粗略估计，制表方法通过弥合相对较少的评估之间的差距来工作。这种结合的方法将允许燃烧模拟更快，使用更复杂的化学模型，更准确。该项目将涉及研究生和本科生，并为他们提供指导和经验，这对他们未来在学术界和工业界的职业生涯将是有价值的。本研究旨在提高化学性质评估的计算效率，化学性质评估是详细化学反应流动模拟中的大部分计算成本。所提出的方法是使用神经网络(NN)和原位自适应制表(ISAT)的组合，结合了两者的优点。虽然神经网络可以以较低的存储成本提供函数逼近，但如果不最终对数据进行过拟合，它们的精度就无法提高。相比之下，ISAT可以达到任何期望的精度水平，但随着最大允许误差的降低，结果表的大小和计算成本都会增加。ISAT表的大小随着被逼近的函数的Hessian而缩放，因此减少该Hessian也将导致更小的表和更低的计算成本。这种缩减将通过使用ISAT来实现，它不仅列出了感兴趣的全部函数，而且还列出了它与近似其黑森函数的NN函数之间的差异。两种黑森近似的方法将被开发和评估。在第一种方法中，将训练一个简单的神经网络实现来逼近化学函数本身，从而仅隐含地逼近黑森函数。对于第二种方法，显式Hessian近似将通过基于邻接点之间的有限差的自定义NN损失定义来实现。NN+ISAT组合的有效性将在部分搅拌反应器(PaSR)测试案例和复杂几何反应流模拟中进行测试。建议方法的成功可以显著加速反应流动模拟，从而能够使用更大、更准确的化学机理。这一奖项反映了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。

Combustion is the prevalent source of energy in today’s world, and is projected to remain so until the year 2050. Moreover, it is the only viable option for many engineering applications (for example, space launch vehicles). Therefore, the continued study of combustion physics and development of new, more efficient, and cleaner combustion devices is a high priority in today’s engineering world. Over the past five decades, combustion simulations have been invaluable to this effort, and yet they still pose a multitude of challenges. This project aims to tackle one such challenge, specifically how to quickly evaluate chemical properties. The approach proposed here is to combine machine learning methods, which can give a rough estimate of the property of interest, with previously developed tabulation methods that work by bridging the gaps between a relatively small number of evaluations. This combined approach will allow for combustion simulations that are faster, use more complex chemical models, and are more accurate. The project will involve graduate and undergraduate students and provide them with mentoring and experience that will be valuable for their future careers in academia and industry. This research aims to improve the computational efficiency of chemical property evaluations, which comprise most of the computational cost in reactive flow simulations with detailed chemistry. The proposed approach is to use a combination of neural networks (NN) and in situ adaptive tabulation (ISAT), combining the strengths of both. Whereas NN can provide a function approximation at low memory cost, their accuracy cannot be improved without eventually overfitting the data. In contrast, ISAT can achieve any desired level of accuracy, but the size of the resulting table, and hence the computational cost, increases as the maximum allowable error is decreased. The ISAT table size scales with the Hessian of the function being approximated, and so reduction of this Hessian will also lead to a smaller table and lower computational cost. Such reduction will be achieved by using ISAT to tabulate not the full function of interest, but rather the difference between it and an NN function which approximates its Hessian. Two approaches for Hessian approximation will be developed and evaluated. In the first, a simple NN implementation will be trained to approximate the chemical function itself, and will thus approximate the Hessian only implicitly. For the second, an explicit Hessian approximation will be implemented via custom NN loss definitions based on finite differences between adjacent points. The effectiveness of the NN+ISAT combination will be tested on both partially-stirred reactor (PaSR) test cases and complex geometry reacting flow simulations. Success of the proposed methods can lead to significant speedup in reactive flow simulations, enabling the use of larger and more accurate chemical mechanisms.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.