基于GPU的可微流体模拟器，用于学习复杂湍流模型。
PICT -- A Differentiable, GPU-Accelerated Multi-Block PISO Solver for Simulation-Coupled Learning Tasks in Fluid Dynamics
- 用PyTorch实现可微分的多块压力隐式求解器，支持GPU加速。
- 在2D/3D湍流通道流中仅凭统计特征学习到稳定子网格模型。
- 训练速度远超高分辨率参考解，且精度不降反升。
尽管历经数十年发展，流体模拟仍是科学计算中最具挑战的领域之一。得益于深度学习对梯度信息的需求，可微分模拟器已成为物理模拟中优化与学习的有效工具。本文提出流体模拟器PICT，一个基于PyTorch、支持图形处理器（GPU）的可微分压力隐式求解器。我们首先在典型基准测试如驱动腔流和湍流通道流中验证了前向模拟与推导梯度的准确性，随后展示了该求解器提供的梯度可用于学习二维和三维复杂湍流模型。通过结合物理先验的监督与无监督训练，我们仅基于参考统计量就成功学习到三维湍流通道流的稳定子网格尺度（SGS）模型。使用本求解器训练的低分辨率校正器运行速度显著快于高分辨率参考解，同时保持或超越其精度。最后，我们分析了不同求解器梯度的物理解释，并提出一种物理启发的正则化策略。为充分发挥PICT潜力，代码已开源：https://github.com/tum-pbs/PICT。
原文摘要 · Abstract (English)
Despite decades of advancements, the simulation of fluids remains one of the most challenging areas of in scientific computing. Supported by the necessity of gradient information in deep learning, differentiable simulators have emerged as an effective tool for optimization and learning in physics simulations. In this work, we present our fluid simulator PICT, a differentiable pressure-implicit solver coded in PyTorch with Graphics-processing-unit (GPU) support. We first verify the accuracy of both the forward simulation and our derived gradients in various established benchmarks like lid-driven cavities and turbulent channel flows before we show that the gradients provided by our solver can be used to learn complicated turbulence models in 2D and 3D. We apply both supervised and unsupervised training regimes using physical priors to match flow statistics. In particular, we learn a stable sub-grid scale (SGS) model for a 3D turbulent channel flow purely based on reference statistics. The low-resolution corrector trained with our solver runs substantially faster than the highly resolved references, while keeping or even surpassing their accuracy. Finally, we give additional insights into the physical interpretation of different solver gradients, and motivate a physically informed regularization technique. To ensure that the full potential of PICT can be leveraged, it is published as open source: https://github.com/tum-pbs/PICT.
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