2026-10-14T14:41:55Z https://www.scidb.cn/oai

10.57760/sciencedb.37520 2026-05-18T09:37:33Z

2026-05-18 Data set for Study of the Dynamical Behavior of Solitons Crossing Barriers/Traps in One-Dimensional Nonlinear Schrödinger Equation Based on Physics-Informed Neural Networks doi:10.57760/sciencedb.37520 en This dataset contains all CSV files generated by the accompanying numerical code, serving as the complete data source for every figure (Figure 1 through Figure 28) presented in the Bachelor's Thesis titled "Study of the Dynamical Behavior of Solitons Crossing Barriers/Traps in One-Dimensional Nonlinear Schrödinger Equation Based on Physics-Informed Neural Networks“. The files document the entire computational workflow, including training loss evolution, adaptive weights, PINN-predicted wavefunction fields (amplitude, density, real part, imaginary part, phase), SSFM reference solutions, error heatmaps and time histories, scatter comparisons, spectra, phase portraits, conservation-law verification (mass, energy, momentum, periodic consistency, kurtosis), transmission/reflection/capture coefficients, dynamical phase maps, potential-well capture curves, inverse-problem parameter‐retrieval errors, and PDE residual distributions. Each CSV corresponds directly to a specific figure in the thesis, thereby ensuring full reproducibility of all reported quantitative analyses and visualizations.Figure CSV file DescriptionFigure 1 training_loss.csv Total loss function versus training epoch.Figure 2 training_loss_components.csv Individual loss components (L_ic, L_bc, L_pde, L_mass, L_energy) versus epoch.Figure 3 adaptive_weights.csv Adaptive loss weights (λ_ic, λ_bc, λ_pde, λ_mass, λ_energy) versus adaptation step.Figure 4 potential_profile.csv Spatial profile of the Gaussian barrier V(x).Figure 5 heatmap_amp_values.csv Spatiotemporal heatmap of PINN-predicted wavefunction amplitude |u|.Figure 6 heatmap_den_values.csv Spatiotemporal heatmap of PINN-predicted density |u|².Figure 7 heatmap_real_values.csv Spatiotemporal heatmap of PINN-predicted real part Re(u).Figure 8 heatmap_imag_values.csv Spatiotemporal heatmap of PINN-predicted imaginary part Im(u).Figure 9 heatmap_phase_values.csv Spatiotemporal heatmap of PINN-predicted phase (range [−π, π]).Figure 10 ssfm_heatmap_amp_values.csv Spatiotemporal heatmap of the SSFM reference amplitude |u|.Figure 11 error_heatmap_diff.csv Spatiotemporal absolute amplitude error |u_PINN − u_SSFM|.Figure 12 error_metrics_time.csv Relative L² error and L∞ error as functions of time t.Figure 13 scatter_pinn_vs_ssfm.csv Scatter-plot data: PINN-predicted versus SSFM reference amplitude at randomly selected space–time points.Figure 14 spectrum_tfinal.csv Fourier spectrum |Û(k)| at the final time, from both PINN and SSFM.Figure 15 phase_portrait_tfinal.csv Phase portrait in the complex plane at the final time (Re(u), Im(u), |u|).Figure 16 probability_over_time.csv Total mass P(t) = ∫|u|² dx versus time (mass conservation verification).Figure 17 energy_over_time.csv Total energy H(t) versus time (energy conservation verification).Figure 18 momentum_over_time.csv Momentum P(t) versus time.Figure 19 periodic_consistency.csv Periodic boundary-condition consistency: |Δu| and |Δu_x| across the boundaries versus time.Figure 20 kurtosis_over_time.csv Kurtosis coefficient K(t) versus time.Figure 21 trans_reflect_capture.csv Time evolution of the transmission T, reflection R, capture C coefficients and their sum T+R+C.Figure 22 T_R_C_vs_V0_data.csvT_vs_V0_fit.csv Raw final-transmission data points for different barrier heights V0 (first file); dense points on the logistic fit curve (second file).Figure 23 phase_map_data.csv Dynamical phase-map data: transmission T from (V0, v) parameter scans (also used for Figure 24).Figure 24 (same) phase_map_data.csv The label field classifies the dynamics (transmission, reflection, capture, splitting) for the classification phase map.Figure 25 well_trans_reflect_capture.csv Time evolution of T, R, C for the potential-well case (capture coefficient C(t) is highlighted in the thesis).Figure 26 inverse_errors_vs_Nobs.csv Inversion errors (mean ± std) for V0, w, xc versus the number of observation points N_obs, including failure rate.Figure 27 residual_cloud.csv Scatter data of PDE residual magnitude at training collocation points (x, t, res).Figure 28 residual_bin_heatmap.csv Binned average PDE residual heatmap over the space–time domain (t, x, value). soliton; PINN; nonlinear Schrödinger equation Yuxin Wang Peng Yue PUBLIC https://creativecommons.org/licenses/by/4.0/ dataset Science Data Bank