Flexible continuous-time predictive adaptive optics with a lightweight liquid network for high-order Zernike aberration forecasting

The inherent latency of adaptive optics (AO) systems can amplify residual errors and limit correction bandwidth under rapidly varying turbulence. This work proposes a continuous-time predictive framework, LZCP-Net (Liquid Zernike Coefficient Prediction Network), which predicts future Zernike coefficients from a short history to pre-drive deformable mirrors for compensation. LZCP-Net integrates a 1-D temporal convolutional front-end with liquid time-constant (LTC) units featuring learnable and bounded time constants, enabling stable ODE-based dynamics that capture both short-term transients and long-term dependencies. Simulations show that LZCP-Net achieves up to 57% lower residual RMS than conventional AO under strong turbulence and reduced sampling, outperforming LSTM and Kalman predictors, especially in the prediction of mid and high-order Zernike mode turbulence. Trained with 10-frame input sequences, the model retains near-optimal accuracy even when using only seven frames, ensuring flexibility for real-time inference. Without any fine-tuning, it also generalizes across different Shack–Hartmann WFS configurations, demonstrating strong robustness to system variations. Experimental results confirm that a model trained solely on simulated data achieves 34.7% RMS reduction and 32.3% smaller EE80 radius, validating its real-world applicability. These results establish LZCP-Net as a lightweight and adaptive predictive module that enables adaptive optics systems to achieve high-precision, low-latency correction in both simulation and experimental settings.