nve_step

torch_sim.integrators.nve.nve_step(state, model, *, dt, **_kwargs)

Perform one complete NVE (microcanonical) integration step.

Implements the velocity Verlet algorithm for NVE dynamics, which provides energy-conserving, time-reversible integration of Hamilton’s equations of motion.

Equations (standard velocity Verlet):

\[\begin{split}\mathbf{p}_i(t + \Delta t/2) &= \mathbf{p}_i(t) + \frac{\Delta t}{2}\,\mathbf{F}_i(t) \\ \mathbf{r}_i(t + \Delta t) &= \mathbf{r}_i(t) + \Delta t\,\frac{\mathbf{p}_i(t + \Delta t/2)}{m_i} \\ \mathbf{F}_i(t + \Delta t) &= -\nabla_{\mathbf{r}_i} U\bigl( \mathbf{r}(t + \Delta t)\bigr) \\ \mathbf{p}_i(t + \Delta t) &= \mathbf{p}_i(t + \Delta t/2) + \frac{\Delta t}{2}\,\mathbf{F}_i(t + \Delta t)\end{split}\]

Variable mapping (equation -> code):

Equation symbol	Code variable
\(\mathbf{r}_i\) (positions)	state.positions
\(\mathbf{p}_i\) (momenta)	state.momenta
\(m_i\) (masses)	state.masses
\(\mathbf{F}_i\) (forces)	state.forces
\(\Delta t\) (timestep)	dt

Parameters:

• model (ModelInterface) – Neural network model that computes energies and forces. Must return a dict with ‘energy’ and ‘forces’ keys.

• state (MDState) – Current system state containing positions, momenta, forces

• dt (float | Tensor) – Integration timestep, either scalar or shape [n_systems]

• _kwargs (Any)

Returns:

Updated state after one complete NVE step with new positions,

momenta, forces, and energy

Return type:

MDState

Notes

• Symplectic, time-reversible integrator of second order accuracy O(dt^2)

• Conserves energy in the absence of numerical errors