Recovering Physical Dynamics from Discrete Observations via Intrinsic Differential Consistency

Recovering continuous-time dynamics from discrete observations is difficult because local supervision loses fidelity as the observation interval grows. We replace local supervision with a global structural constraint: any flow representing autonomous dynamics must satisfy the semi-group property under time translation. We train a time-conditioned secant velocity field whose deviation from this property---which we call Symmetry Rupture---serves two roles: as a training regularizer it confines the hypothesis space to flows that compose consistently across temporal scales; as an inference oracle it guides an adaptive solver to select the largest step size that preserves internal consistency, without relying on local truncation error estimates. On the diffusion-reaction and Navier-Stokes benchmarks, our method achieves the lowest rollout RMSE among all evaluated methods using ≤ 3 function evaluations per step. On the near-conservative shallow water benchmark, our method matches or exceeds competing flow-based methods at far lower computational cost; the strongest Neural ODE baseline achieves lower absolute RMSE but at the expense of >100 function evaluations per step. In the direct auto-regressive setting, our solver maintains stable long-horizon rollouts where flow-matching baselines diverge and Neural ODE requires up to 12× more function evaluations. The core contribution is a model that internalizes temporal consistency, removing the need for high-order external solvers to compensate for structural bias.