基于算子学习的液态金属喷射增材制造零件级仿真
Accelerating Part-Scale Simulation in Liquid Metal Jet Additive Manufacturing via Operator Learning
摘要：
预测增材制造（AM）工艺的零件质量需要对偏微分方程（PDE）进行高保真数值模拟，该偏微分方程（PDE）在最小可制造特征的尺度上控制工艺多物理场。这使得部分规模的预测计算要求很高，特别是当它们需要许多小规模模拟时。我们认为按需滴液态金属喷射（LMJ）作为这样的计算复杂性的一个说明性的例子。描述LMJ的液滴聚结的模型可以包括耦合的不可压缩流体流动、热传递和相变方程。当模拟由数千到数百万个液滴组成的完整部件的构建过程时，数值求解这些方程变得非常昂贵。基于神经网络（NN）或k-最近邻（kNN）算法的降阶模型（ROM）已被建立，以取代原来的基于物理的求解器，并在计算上易于处理的部分级仿真。然而，它们的快速推理能力往往是以牺牲准确性、鲁棒性和概括性为代价的。我们应用操作员学习（OL）方法来学习液滴聚结过程的初始状态和最终状态之间的映射，以实现快速准确的部分规模构建模拟。初步结果表明，OL需要的数量级比kNN方法少的数据点，并且在训练集之外是可推广的，同时实现类似的预测误差。
英文摘要：
Predicting part quality for additive manufacturing (AM) processes requires high-fidelity numerical simulation of partial differential equations (PDEs) governing process multiphysics on a scale of minimum manufacturable features. This makes part-scale predictions computationally demanding, especially when they require many small-scale simulations. We consider drop-on-demand liquid metal jetting (LMJ) as an illustrative example of such computational complexity. A model describing droplet coalescence for LMJ may include coupled incompressible fluid flow, heat transfer, and phase change equations. Numerically solving these equations becomes prohibitively expensive when simulating the build process for a full part consisting of thousands to millions of droplets. Reduced-order models (ROMs) based on neural networks (NN) or k-nearest neighbor (kNN) algorithms have been built to replace the original physics-based solver and are computationally tractable for part-level simulations. However, their quick inference capabilities often come at the expense of accuracy, robustness, and generalizability. We apply an operator learning (OL) approach to learn a mapping between initial and final states of the droplet coalescence process for enabling rapid and accurate part-scale build simulation. Preliminary results suggest that OL requires order-of-magnitude fewer data points than a kNN approach and is generalizable beyond the training set while achieving similar prediction error.
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