Physics-inspired architecture for neural network modeling of forces and torques in particle-laden flows

TL;DR

This paper introduces a physics-inspired neural network architecture that accurately predicts forces and torques on particles in sediment beds by incorporating physical principles, reducing complexity, and improving over traditional models.

Contribution

The paper proposes a novel PINN architecture that embeds physical insights, such as superposition and parameter sharing, to improve force prediction in particle-laden flows.

Findings

PINN achieves accuracy comparable to microstructure-informed models.

Parameter sharing reduces model complexity and overfitting.

Effective across a range of Reynolds numbers and volume fractions.

Abstract

We present a physics-inspired neural network (PINN) model for direct prediction of hydrodynamic forces and torques experienced by individual particles in stationary beds of randomly distributed spheres. In line with our findings, it has recently been demonstrated that conventional fully connected neural networks (FCNN) are incapable of making accurate predictions of force variations in a static bed of spheres. The problem arises due to the large number of input variables (i.e., the locations of individual neighboring particles) leading to an overwhelmingly large number of training parameters in a fully connected architecture. Given the typically limited size of training datasets that can be generated by particle-resolved simulations, the NN becomes prone to missing true patterns in the data, ultimately leading to overfitting. Inspired by our observations in developing the microstructure-informed probability-driven point-particle (MPP) model, we incorporate two main features in the architecture of the present PINN model: 1) superposition of pairwise hydrodynamic interactions between particles, and 2) sharing training parameters between NN blocks that model neighbor influences. These strategies helps to substantially reduce the number of free parameters and thereby control the model complexity without compromising accuracy. We demonstrate that direct force and torque prediction using NNs is indeed possible, provided that the model structure corresponds to the underlying physics of the problem. For a Reynolds number range of 2 <= Re <= 150 and solid volume fractions of 0.1 <= phi <= 0.4, the PINN's predictions prove to be as accurate as those of other microstructure-informed models.