Recovering Physical Dynamics from Discrete Observations via Intrinsic Differential Consistency
Researchers Yuxiang Luo and Andrew Perrault have introduced a novel method for recovering continuous-time physical dynamics from discrete observations, addressing the fidelity loss associated with local supervision as observation intervals grow. Published on arXiv, the study replaces local constraints with a global structural constraint based on the semi-group property of autonomous dynamics under time translation. The authors train a time-conditioned secant velocity field, utilizing a metric called 'Symmetry Rupture' to measure deviation from this property. This approach serves dual purposes: acting as a training regularizer to ensure consistent flow composition across temporal scales, and functioning as an inference oracle that allows solvers to select optimal step sizes based on internal consistency rather than local truncation error. Experimental results on diffusion-reaction benchmarks demonstrate an 87% reduction in rollout RMSE while using five times fewer function evaluations compared Neural ODE baselines. Furthermore, in direct auto-regressive settings, the adaptive solver effectively allocates compute based on geometric complexity, maintaining stability and accuracy where baseline models often diverge or require significantly more resources.
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Recovering Physical Dynamics from Discrete Observations via Intrinsic Differential Consistency
Researchers Yuxiang Luo and Andrew Perrault have introduced a novel method for recovering continuous-time physical dynamics from discrete observations, addressing the fidelity loss associated with local supervision as observation intervals grow. Published on arXiv, the study replaces local constraints with a global structural constraint based on the semi-group property of autonomous dynamics under time translation. The authors train a time-conditioned secant velocity field, utilizing a metric called 'Symmetry Rupture' to measure deviation from this property. This approach serves dual purposes: acting as a training regularizer to ensure consistent flow composition across temporal scales, and functioning as an inference oracle that allows solvers to select optimal step sizes based on internal consistency rather than local truncation error. Experimental results on diffusion-reaction benchmarks demonstrate an 87% reduction in rollout RMSE while using five times fewer function evaluations compared Neural ODE baselines. Furthermore, in direct auto-regressive settings, the adaptive solver effectively allocates compute based on geometric complexity, maintaining stability and accuracy where baseline models often diverge or require significantly more resources.
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