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

2026-04-24 · Source: cs.LG updates on arXiv.org · Field: Science & Research — Artificial Intelligence & Machine Learning, Mathematics & Computational Sciences, Engineering & Applied Sciences · Depth: Expert, quick

Summary

Droplet-LNO introduces a Physics-Informed Laplace Operator Neural Network (PI-LNO) designed for accurately predicting droplet spreading dynamics on complex surfaces. This novel architecture utilizes the Laplace integral transform function as a learned physics-informed functional basis, enabling native modeling of the exponential transient dynamics inherent in the spreading process. PI-LNO was trained using TensorFlow on multi-surface Computational Fluid Dynamics (CFD) data, covering contact angles θsϵ[20,160]. Its training incorporated a physics-regularized composite loss function that combines data fidelity metrics (Mean Squared Error, Mean Absolute Error, Root Mean Squared Error) with constraints derived from Navier-Stokes equations, Cahn-Hilliard equations, and causality principles. Comparative benchmark studies demonstrated PI-LNO's performance against five other approaches, including UNet, UNet with attention modules (UNet-AM), DeepONet, Physics-Informed UNet (PI-UNet), and Laplace Neural Operator (LNO). This method addresses the high computational cost of traditional CFD simulations, which can take 18 to 24 hours per transient computation.

Key takeaway

For computational fluid dynamicists and machine learning engineers working on multiphysics problems, PI-LNO offers a significant reduction in simulation time for droplet spreading dynamics. You should consider integrating this physics-informed neural operator approach to overcome the prohibitive 18-24 hour computational costs of traditional CFD, potentially enabling faster design iterations and more efficient research in areas like inkjet printing or microfluidics.

Key insights

PI-LNO uses Laplace transforms and physics-informed neural networks to model droplet spreading dynamics efficiently.

Principles

• Laplace transforms model exponential transients.
• Physics regularization improves neural network accuracy.

Method

PI-LNO trains a TensorFlow model on CFD data, using a composite loss with Navier-Stokes, Cahn-Hilliard, and causality constraints to predict droplet spreading.

In practice

• Accelerate multiphysics simulations.
• Apply to inkjet printing systems.
• Enhance biomedical microfluidics.

Topics

• Droplet Spreading Dynamics
• Physics-Informed Neural Networks
• Laplace Neural Operators
• Computational Fluid Dynamics
• Multiphysics Modeling

Best for: AI Scientist, Machine Learning Engineer, Research Scientist

Related on AIssential

• LFNO: Bridging Laplace and Fourier via Transient-Steady Decomposition — LFNO unifies Laplace and Fourier operators to model dynamical systems across transient and steady-state regimes.
• Physics-informed convolutional neural networks for fluid flow through porous media — Physics-informed CNNs accurately predict fluid flow in porous media, significantly accelerating traditional LBM simulations.
• Learning Physical Operators using Neural Operators — A physics-informed framework improves neural operator generalization and temporal continuity for PDE solving via operator splitting.
• Using AI, Mathematicians Find Hidden Glitches in Fluid Equations — Bespoke PINNs can precisely identify previously unobserved unstable fluid singularity candidates across diverse fluid models.
• Neural Operator-Based Surrogate Model for CFD:Helical Coil Steam Generator in Small Modular Reactor — Neural operator-based surrogates, combined with ROMs and multi-scale techniques, enable real-time CFD for SMR digital twins.
• Engineering Hybrid Physics-Informed Neural Networks for Next-Generation Electricity Systems: A State-of-the-Art Review — Physics-informed machine learning integrates domain physics into models, enhancing accuracy and efficiency for data-scarce electricity systems.

Open in AIssential →

Editorial summary, takeaway, and curation by AIssential. Original article published by cs.LG updates on arXiv.org.