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

2026-04-22

AI Summary

This work addresses the computational inefficiency of traditional computational fluid dynamics (CFD) simulations, which require 18–24 hours to model droplet spreading on complex surfaces and thus hinder rapid prediction. To overcome this limitation, the authors propose a Physics-Informed Laplace Neural Operator (PI-LNO), which uniquely integrates the Laplace integral transform into a neural operator architecture. By employing learnable physics-based basis functions, PI-LNO effectively captures the exponential transient dynamics of droplet spreading. The method incorporates Navier–Stokes and Cahn–Hilliard equations along with causality regularization into a composite loss function, enabling high-fidelity training across a wide range of static contact angles (θ_s ∈ [20°, 160°]). Experimental results demonstrate that PI-LNO significantly outperforms five state-of-the-art models—including UNet and DeepONet—in terms of MSE, MAE, and RMSE, achieving substantially accelerated predictions without compromising accuracy.

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• Machine Learning: Learning with Manifolds

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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 $θ_s ε[20,160]$, employing a physics-regularized composite loss combining data fidelity (MSE, MAE, RMSE) with Navier-Stokes, Cahn-Hilliard, and causality constraints.

Problem

• droplet spreading
• computational fluid dynamics
• multiphysics problem
• complex surfaces
• transient dynamics

Innovation

• Physics-Informed Neural Operators
• Laplace Transform
• Droplet Spreading Dynamics
• Multiphysics Modeling
• Exponential Transient Dynamics