Droplet-LNO: Physics-Informed Laplace Neural Operators for Accurate Prediction of Droplet Spreading Dynamics on Complex Surfaces

TL;DR

This paper introduces PI-LNO, a physics-informed neural operator that efficiently predicts droplet spreading dynamics on complex surfaces, outperforming existing methods in accuracy and computational speed.

Contribution

The novel PI-LNO architecture leverages Laplace transforms as a physics-informed basis, enabling fast and accurate modeling of droplet spreading dynamics from CFD data.

Findings

PI-LNO outperforms five state-of-the-art approaches in benchmark tests.

It models exponential transient dynamics effectively through Laplace transforms.

The TensorFlow implementation achieves accurate predictions with physics regularization.

Abstract

Spreading of liquid droplets on solid substrates constitutes a classic multiphysics problem with widespread applications ranging from inkjet printing, spray cooling, to biomedical microfluidic systems. Yet, accurate computational fluid dynamic (CFD) simulations are prohibitively expensive, taking more than 18 to 24 hours for each transient computation. In this paper, Physics-Informed Laplace Operator Neural Network (PI-LNO) is introduced, representing a novel architecture where the Laplace integral transform function serves as a learned physics-informed functional basis. Extensive comparative benchmark studies were performed against five other state-of-the-art approaches: UNet, UNet with attention modules (UNet-AM), DeepONet, Physics-Informed UNet (PI-UNet), and Laplace Neural Operator (LNO). Through complex Laplace transforms, PI-LNO natively models the exponential transient dynamics of the spreading process. A TensorFlow-based PI-LNO is trained on multi-surface CFD data spanning contact angles $\theta_s \epsilon [20,160]$, employing a physics-regularized composite loss combining data fidelity (MSE, MAE, RMSE) with Navier-Stokes, Cahn-Hilliard, and causality constraints.