Discontinuity-aware physics-informed neural networks for phase-field method in three-phase flows

TL;DR

The paper tackles the challenge of solving three-phase flows with phase change using phase-field formulations within physics-informed neural networks, where traditional PINNs struggle with gradient conflicts and artificially thick interfaces. It introduces discontinuity-aware residual-adaptive networks (DPINN) with Fourier embeddings, a learnable activation gate, and a localized artificial viscosity to resolve sharp interfaces in the energy-stable AC–CH–NS system without data. Key contributions include automatic detection of sharp interfaces, stability near steep gradients, and adaptive time-marching with gradient-based loss balancing, enabling accurate phase-change dynamics and high-contrast material properties, as demonstrated on two-phase benchmarks and a three-phase droplet icing case. The work advances AI-based multiphase-flow modeling by delivering a data-free, high-fidelity solver suitable for design, optimization, and control tasks where repeated simulations are required.

Abstract

Physics-informed neural networks (PINNs) have proved to be a promising method for modeling multiphase flows. However, due to the gradient-direction conflict during the optimization of the coupled strongly nonlinear Allen-Cahn, Cahn-Hilliard, and Navier-Stokes equations, phase-field-based PINNs have not been extended to three-phase flows with phase change. Furthermore, the interface thickness is known to be artificially magnified, whether in numerical or artificial intelligence-based simulations, reducing accuracy. To mitigate these limitations, this study presents a discontinuity-aware physics-informed neural network (DPINN) that solves an energy-stable phase-field model for three-phase flows. It incorporates a discontinuity-aware residual-adaptive architecture to mitigate spectral bias and to automatically detect and model sharp interfaces, and a learnable local artificial-viscosity term to stabilize the algorithm near steep gradients. During optimization, adaptive time-marching and loss-balancing strategies are introduced to reduce long-term error accumulation and to mitigate gradient conflicts in multi-objective training, respectively. In numerical experiments on the two-phase reversed single-vortex and bubble-rising problems, the proposed method accurately resolves sharp interfacial dynamics that conventional PINNs fail to converge. It also extends to a three-phase droplet-icing case with viscosity and density ratios exceeding 7 and 3 orders of magnitude, accurately capturing the phase-change dynamics and the formation of the pointy tip.

Figures (8)

• Figure 1: (a) Flowchart of the DPINN method applied to a 2D unsteady three-phase flow with phase change. (b) Model architecture of DPINN.
• Figure 2: Evolution of the loss function with training epochs.
• Figure 3: Interface evolution simulated by the PINN and DPINN at $t=0$ and $t=1$, shown from left to right. (a) and (b) present the PINN and DPINN results, respectively, for $\xi_\phi=0.01$, while (c) and (d) present the corresponding results for $\xi_\phi=0.001$.
• Figure 4: Phase-field evolution at $t=0$, $1.5$, and $3$ (left to right). (a), (c), and (e) show the PINN solutions for $\xi_\phi=0.01$, $0.005$, and $0.0025$, respectively, while (b), (d), and (f) show the corresponding DPINN solutions.
• Figure 5: Comparison of three benchmark quantities for the PINN and DPINN solutions at different $\xi_\phi$: (a) center of mass, (b) circularity, and (c) rising velocity.