A micro-diagnostic for step-to-step energy jitter in contact-heavy MuJoCo simulations

[ZC502]

Subject: A micro-diagnostic for step-to-step energy jitter in contact-heavy simulations

MuJoCo shows excellent long-term energy stability. However, I’ve noticed that total energy drift can hide high-frequency behavior at the per-step scale, especially in stiff contact or SDF-based setups.

Instead of long-term drift, I’m using a "Energy Jitter Index" (EJI) to look at short-term statistics:

Python
E = np.array(energies)
dE = np.diff(E)
　　# Captures high-frequency noise even if total drift is ~0
eji = np.std(dE) / (np.mean(np.abs(E)) + 1e-9)

Why this matters:
For SDF/Stiff Models: EJI becomes non-zero in setups where the solver averages out energy over time but exhibits step-level "chattering."
For MJX/RL: This jitter might introduce gradient noise in policies trained on per-step transitions, even if the physics remains "globally" conserved.

Question: Has anyone else used similar diagnostics for fine-grained stability? Could EJI be a useful metric (or even a reward penalty) to improve training smoothness in MJX?

[quagla]

Did you manage to solve it using damping?

[ZC502]

Adding damping is certainly the standard engineering fix to suppress oscillations, but it often masks the underlying numerical behavior rather than explaining it.

My goal with EJI isn't just to 'fix' a specific simulation, but to provide a quantitative audit tool for step-level physical consistency. Even if the jitter is damped out visually, the high-frequency numerical 'noise' still exists in the solver's manifold, which can subtly corrupt gradients in MJX.

I'm more interested in using this as a diagnostic baseline to evaluate how different collision kernels (like SDF) or solvers handle stiff constraints at a fundamental level.