Nonlinear Wavefield Dynamics as a Computational Substrate: Phase-to-Amplitude Conversion and Noise-Tolerant Information Processing in the Nonlinear Schrödinger Equation

Identifying the minimal physical conditions under which a sub- strate can robustly process information is a central question in Ar- tificial Life and unconventional computing. Here we investigate the computational properties of nonlinear Schrödinger equation (NLSE) wavefields by constructing a classification task where information is encoded exclusively in phase gradients, rendering it inaccessible to any static amplitude readout. We first establish a 260-dimensional feature vector extracted from the initial wavefield, which is identical in dimen- sionality to the evolved-state readout; we find it performs at chance level across all noise conditions, confirming that dynamical evolution is necessary for the phase-encoded information to become observable. We then compare the focusing NLSE against its linear counterpart (LSE) across a sweep of phase jitter. Both achieve near-perfect accu- racy at low noise, but diverge as jitter increases: beyond a crossover threshold, the NLSE achieves statistically significant superiority (Co- hen’s d ≈ 2.8), while the LSE decays more than twice as fast. A parameter sweep over nonlinearity strength g reveals threshold-driven acceleration (d2Acc/dg2 > 0), identifying the onset of a regime where nonlinear self-interaction preserves information that linear dispersion destroys. These findings demonstrate that the NLSE wavefield per- forms a specific computational operation: converting fragile phase structure into robust amplitude morphology via interference. In par- ticular, we find that the nonlinear term protects this conversion under noise. We discuss implications for the Artificial Life goal of identifying minimal, noise-tolerant physical computing substrates.