# Sparse Identification of Nonlinear Dynamics

RI-SINDy removes known Hill-type regulatory terms from the sparse-regression library and solves each coefficient separately from a drift-balance condition, the near-zero time average of the derivative along a bounded trajectory, avoiding the ill-conditioning that arises when regulatory and polynomial terms are nearly collinear over an oscillation. On Hes1 experimental data it gives the lowest trajectory error among Traditional SINDy, SR3 and Nullcline Reconstruction; on synthetic Goodwin and NF-κB models it recovers the correct sparse structure, and in a Goodwin noise sweep it still finds all 6 active terms at 15% noise.

RI-SINDy removes known Hill-type regulatory terms from the sparse-regression library and solves each coefficient separately from a drift-balance condition, the near-zero time average of the derivative along a bounded trajectory, avoiding the ill-conditioning that arises when regulatory and polynomial terms are nearly collinear over an oscillation. On Hes1 experimental data it gives the lowest trajectory error among Traditional SINDy, SR3 and Nullcline Reconstruction; on synthetic Goodwin and NF-κB models it recovers the correct sparse structure, and in a Goodwin noise sweep it still finds all 6 active terms at 15% noise.

On an axial compressor-plenum-throttle simulation, UQ-ACE infers a posterior over local dynamics from closed-loop data and blocks candidates whose stability probability falls short, producing no unstable trajectories across 100 runs.

On an axial compressor-plenum-throttle simulation, UQ-ACE infers a posterior over local dynamics from closed-loop data and blocks candidates whose stability probability falls short, producing no unstable trajectories across 100 runs.

This survey systematically reviews methods that embed physics priors into robot learning and proposes a unified taxonomy classifying existing work by where physics is embedded—physics-guided inputs, data, and representations; physics-encoded model architectures; and physics-informed training losses—then reviews methods for robot dynamics learning, trajectory planning and prediction, control, and estimation together with the open-source software ecosystem, reporting that physics-encoded architectures account for 71% of surveyed methods, physics-guided 16%, and physics-informed 13%, while only 4% combine more than one embedding route.

This survey systematically reviews methods that embed physics priors into robot learning and proposes a unified taxonomy classifying existing work by where physics is embedded—physics-guided inputs, data, and representations; physics-encoded model architectures; and physics-informed training losses—then reviews methods for robot dynamics learning, trajectory planning and prediction, control, and estimation together with the open-source software ecosystem, reporting that physics-encoded architectures account for 71% of surveyed methods, physics-guided 16%, and physics-informed 13%, while only 4% combine more than one embedding route.