Cause of boundary-collapse artifacts and premature penetration in U-Net roll-outs

Determine the mechanism responsible for the collapse of the liquid–solid interface at the left and right domain boundaries during fully auto-regressive U‑Net surrogate simulations of two-dimensional liquid‑metal dealloying phase‑field dynamics, which leads to excessive maximum penetration depth and premature arrival of the liquid at the bottom boundary; specifically assess whether misrepresentation of boundary‑condition effects by the U‑Net is the cause of this behavior.

Background

In fully auto-regressive evaluations, the U-Net surrogate tended to predict that the liquid penetrates too quickly through the metal, reaching the bottom boundary earlier than in high-fidelity simulations. The authors attribute this behavior to a collapse of the liquid–solid interface at the lateral boundaries observed specifically in U-Net roll-outs.

The paper suggests a possible explanation: the U-Net may inadequately capture the effects of the boundary conditions on the phase-field dynamics, unlike the proposed U-AFNO model, which better preserves global and local statistics and does not exhibit the same failure mode.

References

This is due to the fact that with the U-Net, the liquid-solid interface tends to collapse at both the right and left edges of the domain. It is not clear why this phenomena occurs, but a possible explanation is that the U-Net fails to accurately capture the effects of the boundary conditions on the field dynamics.

— Accelerating Phase Field Simulations Through a Hybrid Adaptive Fourier Neural Operator with U-Net Backbone (2406.17119 - Bonneville et al., 24 Jun 2024) in Section 5.3 (Results)