标题： 利用物理信息神经网络在二维搅拌槽流场代理建模中量化数据需求 显示英文标题

标题： Quantifying data needs in surrogate modeling for flow fields in two-dimensional stirred tanks with physics-informed neural networks

摘要： 搅拌槽在化学和生物技术过程中至关重要，尤其是在作为生物反应器时。 尽管计算流体动力学（CFD）被广泛用于模拟搅拌槽中的流动，但其高计算成本$-$，特别是在过程设计和优化的多查询场景中$-$，推动了对高效数据驱动代理模型的需求。 然而，获取足够大的数据集可能成本很高。 物理信息神经网络（PINNs）通过将基本物理嵌入神经网络（NN）训练中，提供了一种减少数据需求同时保持精度的有前景的解决方案。 本研究量化了普通PINNs在开发二维搅拌槽流场代理模型中的数据需求。 我们将这些需求与传统的监督神经网络和边界信息神经网络（BINNs）进行了比较。 我们的研究结果表明，使用最少六个数据点，代理模型可以在雷诺数从50到5000的范围内实现大约3%的预测误差。 此外，使用速度剖面的近似代替真实数据标签，可以实现大约2.5%的预测误差。 这些结果表明，即使在有限或近似数据集的情况下，PINNs也可以有效地训练以提供与高保真数据相当的高精度。 显示英文摘要

摘要： Stirred tanks are vital in chemical and biotechnological processes, particularly as bioreactors. Although computational fluid dynamics (CFD) is widely used to model the flow in stirred tanks, its high computational cost$-$especially in multi-query scenarios for process design and optimization$-$drives the need for efficient data-driven surrogate models. However, acquiring sufficiently large datasets can be costly. Physics-informed neural networks (PINNs) offer a promising solution to reduce data requirements while maintaining accuracy by embedding underlying physics into neural network (NN) training. This study quantifies the data requirements of vanilla PINNs for developing surrogate models of a flow field in a 2D stirred tank. We compare these requirements with classical supervised neural networks and boundary-informed neural networks (BINNs). Our findings demonstrate that surrogate models can achieve prediction errors around 3% across Reynolds numbers from 50 to 5000 using as few as six datapoints. Moreover, employing an approximation of the velocity profile in place of real data labels leads to prediction errors of around 2.5%. These results indicate that even with limited or approximate datasets, PINNs can be effectively trained to deliver high accuracy comparable to high-fidelity data.