Construction of end-to-end machine learning surrogate model and its application in detonation driving problem
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摘要: 人工智能/机器学习方法能够发现数据中隐藏的物理规律，构建状态参数与动态结果之间端到端的代理模型，可高效解决强耦合、非线性、多物理等复杂工程问题。在高度非线性的爆炸与冲击动力学领域，选择了一个经典的爆轰驱动问题作为研究对象，以数值模拟结果作为机器学习代理模型的训练数据，将正向模拟与逆向设计有机结合起来，基于深度神经网络技术，构建了特征位置速度剖面、材料动态变形与工程因素之间端到端的代理模型，给出了代理模型的计算精确度，验证了代理模型从速度剖面反演工程因素的能力。结果表明，端到端代理模型具有较高的预测能力，其预测的速度剖面与工程因素估计的相对误差均小于1%，可用于高度非线性的爆炸与冲击动力学问题的快速设计、高精度预测和敏捷迭代。Abstract: Artificial intelligence/machine learning methods can discover hidden physical patterns in data. By constructing an end-to-end surrogate model between state parameters and dynamic results, many complex engineering problems such as strong coupling, nonlinearity, and multiphysics can be efficiently solved. In the field of highly nonlinear explosion and shock dynamics, a classic detonation driving problem was chosen as the research object. Using numerical simulation results as training data for machine learning surrogate models, and combining forward simulation and reverse design organically. Based on deep neural network technology, an end-to-end surrogate model was constructed between feature position velocity profiles, material dynamic deformation, and engineering factors. And the calculation accuracy of the surrogate model was provided, verifying the ability to invert engineering factors from velocity profiles. The research results indicate that the end-to-end surrogate model has high predictive ability, with relative errors of less than 1% in both velocity profile prediction and engineering factor estimation. It can be applied to the rapid design, high-precision prediction, and agile iteration of highly nonlinear explosion and impact dynamics problems.
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图 4 BFGS和ADAM算法优化结果与模拟结果的比较
Figure 4. Comparison of optimization results of BFGS and ADAM algorithm with simulation results
图 5 不同神经网络结构的代理模型计算结果与解析解的比较
Figure 5. Comparison of calculation results and analytical solutions of surrogate models with different neural network structures
图 8 训练点上速度代理模型和数值模拟的计算结果比较
Figure 8. Results calculated by the speed surrogate model at the training points and the numerical simulation result
图 9 预测点上速度代理模型给出的计算结果及其与数值模拟结果的比较
Figure 9. Results calculated by the speed surrogate model at the prediction points with their comparison with the numerical simulation results
图 10 应用代理模型依据速度剖面反向求解h值
Figure 10. Applying the surrogate model to solve the h values according to velocity profiles
图 11 t=25 µs时训练点上流场中材料动态时空分布代理模型计算的流场体积分数与数值模拟结果的比较
Figure 11. Comparison of material distribution surrogate model with numerical simulation results at training point at t=25 μs
图 12 预测点上流场中材料动态时空分布代理模型计算的流场体积分数与数值模拟结果的比较
Figure 12. Material distribution calculated by surrogate model at prediction points with comparison to simulation data
图 14 代理模型计算的P1处的速度剖面与数值模拟结果的比较
Figure 14. Numerical simulation and surrogate model calculation results of speed history at P1
图 15 c=1 mm、d=1 mm、t=25 µs时代理模型计算的流场体积分数与数值模拟结果的比较
Figure 15. Numerical simulation of material distribution and calculation results of surrogate model at the point while c=1 mm, d=1 mm, t=25 µs
表 1 不同神经网络结构对代理模型的计算效果分析
Table 1. Analysis of calculation effect of surrogate model with different neural network structures
组合序号 dh wh 标准误差 0 10 20 3.8845 ×10−31 15 20 3.4626 ×10−32 10 15 4.4272 ×10−33 10 25 3.3092 ×10−34 5 15 2.3908 ×10−35 15 25 1.0031 ×10−2
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表 2 训练点上速度剖面代理模型计算的相对误差
Table 2. Relative errors of velocity surrogate model calculation at training points
h/mm 相对误差/% P1 P2 0 0.0034 0.0040 1 0.0078 0.0094 2 0.0063 0.0036 3 0.0057 0.0014 4 0.0027 0.0094 5 0.0035 0.0067
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表 3 预测点上速度剖面代理模型计算的相对误差
Table 3. Relative errors calculated by velocity surrogate model at prediction points
h/mm 相对误差/% P1 P2 0.5 0.0571 0.6665 1.5 0.0524 0.8081 2.5 0.0034 0.4332 3.2 0.0116 0.1963 4.7 0.0129 0.1669
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表 4
$t $ =25 µs时训练点上流场中材料动态时空分布代理模型计算的标准差和相对误差Table 4. Standard and relative errors calculated by the material distribution surrogate model at training points at t=25 μs
h/mm 标准差 相对误差/% 0 5.99×10−2 0.3953 1 5.81×10−2 0.2721 2 5.95×10−2 0.0955 3 6.15×10−2 0.3082 4 6.30×10−2 0.3415 5 6.39×10−2 0.2211
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