code: def simulate(self, times):
      t0 = torch.tensor([0.0]).to(times)
  
      # Add a terminal time to the event function.
      def event_fn(t, state):
          if t > times[-1] + 1e-7:
              return torch.zeros_like(t)
          event_fval = self.event_fn(t, state)
          return event_fval
  
      # IMPORTANT: for gradients of odeint_event to be computed, parameters of the event function
      # must appear in the state in the current implementation.
      state = (
          self.initial_pos,
          self.initial_vel,
          *self.event_fn.parameters(),
      )
  
      event_times = []
  
      trajectory = [state[0][None]]
  
      n_events = 0
      max_events = 20
  
      while t0 < times[-1] and n_events < max_events:
          last = n_events == max_events - 1
  
          if not last:
              event_t, solution = odeint_event(
                  self.dynamics_fn,
                  state,
                  t0,
                  event_fn=event_fn,
                  atol=1e-8,
                  rtol=1e-8,
                  method="dopri5",
              )
          else:
              event_t = times[-1]
  
          interval_ts = times[times > t0]
          interval_ts = interval_ts[interval_ts <= event_t]
          interval_ts = torch.cat(
              [t0.reshape(-1), interval_ts.reshape(-1)]
          )
  
          solution_ = odeint(
              self.dynamics_fn, state, interval_ts, atol=1e-8, rtol=1e-8
          )
          traj_ = solution_[0][
              1:
          ]  # [0] for position; [1:] to remove intial state.
          trajectory.append(traj_)
  
          if event_t < times[-1]:
              state = tuple(s[-1] for s in solution)
  
              # update velocity instantaneously.
              state = self.inst_update(event_t, state)
  
              # advance the position a little bit to avoid re-triggering the event fn.
              pos, *rest = state
              pos = pos + 1e-7 * self.dynamics_fn(event_t, state)[0]
              state = pos, *rest
  
          event_times.append(event_t)
          t0 = event_t
  
          n_events += 1
  
          # print(event_t.item(), state[0].item(), state[1].item(), self.event_fn.mod(pos).item())
  
      trajectory = torch.cat(trajectory, dim=0).reshape(-1)
      return trajectory, event_times
  
imports: import argparse
  import os
  import math
  import matplotlib.pyplot
  import torch
  import torch.nn
  from torchdiffeq import odeint, odeint_event
  from bouncing_ball import BouncingBallExample
label_desc: Use image node_id 2 for calling the NeuralPhysics obj's underlying member method code with example usage: obj.simulate(times) and returns: trajectory,  event_times, event_fval, torch