The intricate process of bubble growth dynamics involves a broad spectrum of
physical phenomena from microscale mechanics of bubble formation to macroscale
interplay between bubbles and surrounding thermo-hydrodynamics. Traditional
bubble dynamics models including atomistic approaches and continuum-based
methods segment the bubble dynamics into distinct scale-specific models. In
order to bridge the gap between microscale stochastic fluid models and
continuum-based fluid models for bubble dynamics, we develop a composite neural
operator model to unify the analysis of nonlinear bubble dynamics across
microscale and macroscale regimes by integrating a many-body dissipative
particle dynamics (mDPD) model with a continuum-based Rayleigh-Plesset (RP)
model through a novel neural network architecture, which consists of a deep
operator network for learning the mean behavior of bubble growth subject to
pressure variations and a long short-term memory network for learning the
statistical features of correlated fluctuations in microscale bubble dynamics.
Training and testing data are generated by conducting mDPD and RP simulations
for nonlinear bubble dynamics with initial bubble radii ranging from 0.1 to 1.5
micrometers. Results show that the trained composite neural operator model can
accurately predict bubble dynamics across scales, with a 99% accuracy for the
time evaluation of the bubble radius under varying external pressure while
containing correct size-dependent stochastic fluctuations in microscale bubble
growth dynamics. The composite neural operator is the first deep learning
surrogate for multiscale bubble growth dynamics that can capture correct
stochastic fluctuations in microscopic fluid phenomena, which sets a new
direction for future research in multiscale fluid dynamics modeling.

利用复合神经算子模型，从微观到宏观尺度上统一分析非线性气泡动力学，包含正确的微观流体现象的随机波动，为多尺度流体动力学建模领域的未来研究指明了新方向。

利用神经操作器学习实现具有相关波动的多尺度泡泡生长动力学的尺度桥接

Bridging scales in multiscale bubble growth dynamics with correlated  fluctuations using neural operator learning

Many Artificial Intelligence (AI) algorithms are inspired by physics and
employ stochastic fluctuations. We connect these physics-inspired AI algorithms
by unifying them under a single mathematical framework that we call
Thermodynamic AI. Seemingly disparate algorithmic classes can be described by
this framework, for example, (1) Generative diffusion models, (2) Bayesian
neural networks, (3) Monte Carlo sampling and (4) Simulated annealing. Such
Thermodynamic AI algorithms are currently run on digital hardware, ultimately
limiting their scalability and overall potential. Stochastic fluctuations
naturally occur in physical thermodynamic systems, and such fluctuations can be
viewed as a computational resource. Hence, we propose a novel computing
paradigm, where software and hardware become inseparable. Our algorithmic
unification allows us to identify a single full-stack paradigm, involving
Thermodynamic AI hardware, that could accelerate such algorithms. We contrast
Thermodynamic AI hardware with quantum computing where noise is a roadblock
rather than a resource. Thermodynamic AI hardware can be viewed as a novel form
of computing, since it uses a novel fundamental building block. We identify
stochastic bits (s-bits) and stochastic modes (s-modes) as the respective
building blocks for discrete and continuous Thermodynamic AI hardware. In
addition to these stochastic units, Thermodynamic AI hardware employs a
Maxwell's demon device that guides the system to produce non-trivial states. We
provide a few simple physical architectures for building these devices and we
develop a formalism for programming the hardware via gate sequences. We hope to
stimulate discussion around this new computing paradigm. Beyond acceleration,
we believe it will impact the design of both hardware and algorithms, while
also deepening our understanding of the connection between physics and
intelligence.

提出了一个称为热力学 AI 的数学框架，它将许多物理启发的人工智能算法统一起来，并将其与热力学系统中的随机波动相结合，以实现利用波动作为一种计算资源的计算范式，从而加速这些算法。该框架使用了新型的构建基块，即随机位（s-bits）和随机模（s-modes），并提供了一些简单的物理体系结构来构建这些设备。