Sample-wise Interpolation of Fluid Simulations using Physics-informed Neural Networks

  • Sakamoto, Riku (RICOS Co. Ltd.)
  • Horie, Masanobu (RICOS Co. Ltd.)

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Many engineering applications require high-fidelity fluid simulation to analyze performance, safety, and efficiency. Although such data provide accurate representations of fluid dynamics, it is often impractical to run full simulations for every scenario because they consume significant computational resources and time even when simulation parameters or geometric configurations change slightly. When dealing with such situation, we can utilize sample-wise interpolation to get the approximated results for new conditions without running a full simulation. However, previous studies indicated that traditional interpolation methods such as k-nearest neighbours show low accuracy in capturing the complex dynamics of fluid flows governed by the Navier-Stokes equations. This suggests that the solution space of fluid simulations is highly non-linear, making it difficult for simple interpolation techniques to provide accurate results. To address this challenge, we propose an approach that leverages Physics-Informed Neural Networks (PINNs) to interpolate fluid simulation data. PINNs are a class of neural networks that try to minimize the residuals of governing equations, such as the Navier-Stokes equations, in addition to fitting loss of the training data. Basic PINNs architectures cannot explicitly learn multiple simulation scenarios since they learn a single function mapping from spatial and temporal coordinates to output values. For interpolation of fluid simulation data, we add sample-specific features as inputs to the PINN, such as distance from the walls or boundary conditions. This allows the PINN to learn the relationship between the sample-specific features and the fluid dynamics, enabling it to interpolate between different simulation scenarios. In this work, we focus on interpolating fluid simulation data across varying boundary conditions and geometric parameters. We demonstrate the effectiveness of our approach through numerical experiments on various simulation scenarios comparing with traditional interpolation methods, and discuss the potential applications and limitations of our method.