Neural ODE Representations for Hidden Perturbation Detection and Causal Characterization in Chaotic Three-Body Dynamics

Detecting unmodelled gravitational forces in chaotic three-body systems presents a fundamental challenge at the intersection of dynamical systems theory and scientific machine learning. We propose a compact Neural ODE Autoencoder (Neural ODE-AE, ~5,900 parameters) that jointly learns a continuous-time deterministic latent representation of three-body trajectories and a binary classifier for perturbation detection. The model is trained on 15,440 segments from 1,207 simulated trajectories under five perturbation categories — hidden mass, aerodynamic drag, time-varying gravitational constant, impulsive velocity kicks, and non-inverse-square gravity — using a strict file-level disjoint train/validation split to prevent data leakage. On a balanced held-out set of 1,000 segments, the Neural ODE-AE achieves AUROC = 0.708 ± 0.007 and F1 = 0.642 ± 0.036 (mean ± std over three random seeds), outperforming an MLP (AUROC 0.655), GRU (0.659), LSTM (0.647), a structurally identical linear-latent autoencoder (0.592), and an energy-drift physics baseline (0.516). The +0.116 AUROC margin over the linear-latent ablation isolates the contribution of continuous-time ODE dynamics. Per-perturbation analysis identifies impulse (AUROC 0.845) as the most detectable type and aerodynamic drag (0.564) as the hardest. Dynamic threshold optimisation via Youden's Index improves operational F1 to 0.698 at decision boundary p* = 0.46. A six-method exploratory causal analysis pipeline applied to the learned latent space reveals evidence of causal sensitivity: DoWhy backdoor estimation yields robust average treatment effects on 15 of 16 latent dimensions, surviving both placebo-treatment and random-common-cause refutation; PC-algorithm structure learning recovers 50 directed edges broadly consistent with the theoretical Structural Causal Model; and ANOVA intervention testing identifies latent_4 (F = 5.297, p = 0.0003) as sensitive to perturbation type. Perturbation signatures appear primarily as increased latent temporal variability rather than mean shifts. After physics-informed normalisation, the encoder maps NASA JPL Horizons Sun-Earth-Moon trajectories to within 0.14σ of the training centroid (MMD = 0.086), demonstrating preliminary encoder transferability to real astronomical data. Classifier miscalibration for the low-chaos quasi-periodic regime is identified as the primary barrier to real-world deployment and is reported transparently as a limitation. Code and data: https://github.com/AkshaanAngral/Three-Body-Causal-AI