A Novel CNN-Based Poisson Solver for Fluid Simulation.

Area of Science:

• Computational fluid dynamics
• Machine learning applications in scientific computing
• Deep learning for solving partial differential equations

Background:

• Solving large-scale Poisson systems is a computational bottleneck in Eulerian fluid simulations.
• Existing methods require significant computational resources, limiting simulation scale and speed.
• The projection step, crucial for enforcing incompressibility, is particularly expensive.

Purpose of the Study:

• To propose and validate a novel machine learning-based approach for accelerating Poisson system solutions in fluid simulations.
• To significantly reduce the computational cost of the projection step in Eulerian fluid simulators.
• To demonstrate the generalizability of the proposed method for diverse fluid phenomena.

Main Methods:

• Development of a deep convolutional neural network (CNN) to predict pressure fields.
• Integration of a geometric structure for spatial hierarchy representation and Principal Component Analysis (PCA) for dimensionality reduction during training.
• Implementation of a novel loss function to ensure the incompressibility constraint is met.

Main Results:

• The proposed CNN-based approach accelerates the projection step by two orders of magnitude (100x).
• Successful simulation of high-resolution smoke and liquid phenomena, validating the method's efficacy.
• Demonstrated generality through the creation of diverse animations deviating from original training datasets.

Conclusions:

• The machine learning approach effectively accelerates computationally expensive Poisson system solves in fluid dynamics.
• The method offers a significant speedup for Eulerian fluid simulators without compromising simulation quality.
• The approach shows promise for broader applications in scientific computing requiring efficient solution of large linear systems.