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

燃烧是当今世界普遍使用的能源，预计这种情况将持续到2050年。此外，它是许多工程应用（例如，空间运载火箭）的唯一可行选择。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当务之急。在过去的五十年里，燃烧模拟在这方面的努力是无价的，但它们仍然提出了许多挑战。该项目旨在解决这样一个挑战，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（可以对感兴趣的属性进行粗略估计）与先前开发的制表方法（通过弥合相对较少的评估之间的差距）相结合。这种结合的方法将允许更快的燃烧模拟，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，这将对他们未来在学术界和工业界的职业生涯有价值。本研究旨在提高化学性质评估的计算效率，而化学性质评估占详细化学反应流模拟计算成本的大部分。该方法将神经网络（NN）和原位自适应制表（ISAT）相结合，结合两者的优势。虽然神经网络可以在低内存成本下提供函数近似，但如果最终不过度拟合数据，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，但是结果表的大小，以及因此的计算成本，随着最大允许误差的减少而增加。ISAT表的大小随着逼近函数的Hessian的大小而变化，因此减小该Hessian也会导致表更小，计算成本更低。这种减少将通过使用ISAT来实现，而不是将感兴趣的完整函数制成表格，而是将其与近似其黑森函数的神经网络函数之间的差异制成表格。本文将发展和评估两种黑森近似的方法。首先，一个简单的神经网络实现将被训练来近似化学函数本身，因此将只隐式地近似Hessian。其次，将通过基于相邻点之间有限差异的自定义NN损失定义实现显式Hessian近似。NN+ISAT组合的有效性将在部分搅拌反应器（PaSR）测试用例和复杂几何反应流模拟中进行测试。所提出的方法的成功可以显著加快反应流模拟的速度，从而可以使用更大、更准确的化学机制。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值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.