Reconstruction of torsion pendulum ground vibration response via fourier feature network

To address the signal reconstruction problem of high-Q torsion pendulum systems under ground seismic excitation in ordinary laboratory environments—pertinent to ground testing for space gravitational wave detection—a curriculum learning-driven Fourier feature network (FouCLNet) is proposed. Existing hardware isolation strategies impose stringent environmental requirements that are difficult to meet in ordinary ground laboratories. Traditional physics-informed neural networks suffer from spectral bias, gradient conflict, and an inherent tendency for outputs to decay toward zero in high-Q oscillatory systems. Log-spaced Fourier feature mapping is employed with frequency parameters uniformly distributed over the 0.003–0.02 Hz band to match the 0.007 Hz natural frequency of the pendulum. A four-layer fully connected network is constructed, and a hard amplitude constraint loss function is designed to prevent attenuation of micro-radian-scale signals. Through a three-stage curriculum learning strategy, weak physical constraints are progressively introduced with PDE residual weights annealed to the order of 1e-8. Using the torsional response under seismic noise excitation as the target physical quantity and fourth-order Runge-Kutta integration results as ground-truth labels, we randomly sample 80% of time points for training and 20% for in-distribution validation. Experimental results demonstrate that the proposed method achieves a correlation coefficient of 0.9988 on the training set, peak error below 0.4% full scale, 100% amplitude matching, and power spectral density agreement at the 0.007 Hz resonance peak. The in-distribution discrete validation set achieves a correlation coefficient of 0.9958, and the single-point inference latency is merely 0.524 ms. Ablation studies indicate that removing Fourier features or hard amplitude constraints leads to severe model degradation. The pure data-driven configuration achieves good accuracy on the discrete validation set, yet its correlation coefficient drops sharply to 0.511 in continuous-segment reconstruction, whereas the full method maintains 0.986, indicating that weak physical constraints stabilize continuous temporal consistency. Temporal extrapolation beyond the training domain yields a correlation coefficient of merely 0.019, accompanied by spurious low-frequency drift. Furthermore, the model fails to generalize to continuous unseen periods within the training domain (R ≈ 0.029). Consequently, the proposed method is unsuitable for predictive extrapolation beyond the temporal scope of the training data and should be strictly confined to interpolation scenarios within the established training domain. The method provides a high-fidelity in-distribution interpolation reconstruction reference for torsion pendulum systems in ordinary laboratory environments and offers guidance for developing causal real-time vibration suppression algorithms.