BubbleONet: A Physics-Informed Neural Operator for High-Frequency Bubble Dynamics

2025-08-05

AI Summary

This study addresses the challenge of high-frequency bubble dynamics modeling by proposing a physics-informed neural operator that enables end-to-end mapping from pressure profiles to bubble radius responses. Methodologically, we integrate the DeepONet architecture with hard constraints derived from the Rayleigh–Plesset and Keller–Miksis equations, forming the PI-DeepONet framework. We further introduce the Rowdy adaptive activation function to mitigate spectral bias and significantly enhance modeling fidelity for high-frequency transient dynamics. The framework supports both single-step and two-step hybrid training strategies. Experimental results demonstrate that the model achieves accuracy comparable to high-fidelity numerical solvers across diverse bubble dynamics scenarios—including inertial cavitation, parametric oscillation, and shock-induced collapse—while accelerating computation by one to two orders of magnitude. Thus, PI-DeepONet serves as a high-fidelity, low-overhead surrogate model, enabling real-time simulation and inverse design of complex cavitating systems.

Technology Category

• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Search and Optimization: Learning to Search
• Computer Vision: Low Level & Physics-based Vision

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

This paper introduces BubbleONet, an operator learning model designed to map pressure profiles from an input function space to corresponding bubble radius responses. BubbleONet is built upon the physics-informed deep operator network (PI-DeepONet) framework, leveraging DeepONet's powerful universal approximation capabilities for operator learning alongside the robust physical fidelity provided by the physics-informed neural networks. To mitigate the inherent spectral bias in deep learning, BubbleONet integrates the Rowdy adaptive activation function, enabling improved representation of high-frequency features. The model is evaluated across various scenarios, including: (1) Rayleigh-Plesset equation based bubble dynamics with a single initial radius, (2) Keller-Miksis equation based bubble dynamics with a single initial radius, and (3) Keller-Miksis equation based bubble dynamics with multiple initial radii. Moreover, the performance of single-step versus two-step training techniques for BubbleONet is investigated. The results demonstrate that BubbleONet serves as a promising surrogate model for simulating bubble dynamics, offering a computationally efficient alternative to traditional numerical solvers.

Problem

• Mapping pressure profiles to bubble radius responses
• Overcoming spectral bias in high-frequency bubble dynamics
• Evaluating training techniques for physics-informed operator learning

Innovation

• Physics-informed neural operator for bubble dynamics
• Rowdy activation mitigates spectral bias
• Efficient surrogate model for numerical solvers