pinn-phase-neural-integrator

PINN-Phase Neural Time Integration

Description

This skill covers PINN-Phase-style neural time integration of curvature-driven multiphase-field evolution. A recurrent field model advances a discrete phase-field state autonomously from an initial condition. It is trained only on the physical residual of the discrete operator evaluated on its own predicted trajectory, with hard admissibility (bounds and unit sum) enforced in the state update.

The skill covers:

• the discrete operator and the bounded increment map;
• label-free trajectory training with truncated BPTT;
• permutation-equivariant grain handling;
• long-horizon rollout and error accumulation;
• extinction and topology changes;
• the difference between horizon extrapolation and initial-condition generalization;
• frozen-checkpoint prospective evaluation in 2D and 3D;
• fair runtime reporting and checkpoint provenance.

Invoke this skill when building, reproducing, or auditing such an integrator. It is based on a 2026 arXiv preprint.

Domain Context

Evidence status. PINN-Phase (Elfetni, Thinius, Seeberger & Tyrikos-Ergas, arXiv:2608.29413, v2 October 2026) is a preprint and has not been peer reviewed. All numbers below are attributed to it and are scoped to its benchmark families. The repository README's citation block omits the second author (S. Thinius); cite the arXiv author list.

Equation. The preprint integrates a projected multi-channel Allen–Cahn operator. This is the equal-parameter, isotropic member of the constrained multiphase Allen–Cahn family:

R(φ) = μσ · P_N[ ∇²φ − W′(φ)/η² ], W(φ) = φ²(1 − φ)² applied componentwise.

• P_N subtracts the phase mean, so the rate sums to zero.
• The Laplacian is the second-order central-difference stencil with periodic indexing, so validation is against direct integration of the same discrete operator.
• This is a different discrete model from the Steinbach-type obstacle-potential MPF used by PINNs-MPF. The two are not interchangeable references.
• The preprint's scalar benchmarks use a separate double-obstacle-type Allen–Cahn form with a bound-aware rate map, which is not the N = 1 limit of the multiphase operator.