Source code for pyro.ops.integrator

# Copyright (c) 2017-2019 Uber Technologies, Inc.
# SPDX-License-Identifier: Apache-2.0

from torch.autograd import grad

[docs]def velocity_verlet( z, r, potential_fn, kinetic_grad, step_size, num_steps=1, z_grads=None ): r""" Second order symplectic integrator that uses the velocity verlet algorithm. :param dict z: dictionary of sample site names and their current values (type :class:`~torch.Tensor`). :param dict r: dictionary of sample site names and corresponding momenta (type :class:`~torch.Tensor`). :param callable potential_fn: function that returns potential energy given z for each sample site. The negative gradient of the function with respect to ``z`` determines the rate of change of the corresponding sites' momenta ``r``. :param callable kinetic_grad: a function calculating gradient of kinetic energy w.r.t. momentum variable. :param float step_size: step size for each time step iteration. :param int num_steps: number of discrete time steps over which to integrate. :param torch.Tensor z_grads: optional gradients of potential energy at current ``z``. :return tuple (z_next, r_next, z_grads, potential_energy): next position and momenta, together with the potential energy and its gradient w.r.t. ``z_next``. """ z_next = z.copy() r_next = r.copy() for _ in range(num_steps): z_next, r_next, z_grads, potential_energy = _single_step_verlet( z_next, r_next, potential_fn, kinetic_grad, step_size, z_grads ) return z_next, r_next, z_grads, potential_energy
def _single_step_verlet(z, r, potential_fn, kinetic_grad, step_size, z_grads=None): r""" Single step velocity verlet that modifies the `z`, `r` dicts in place. """ z_grads = potential_grad(potential_fn, z)[0] if z_grads is None else z_grads for site_name in r: r[site_name] = r[site_name] + 0.5 * step_size * ( -z_grads[site_name] ) # r(n+1/2) r_grads = kinetic_grad(r) for site_name in z: z[site_name] = z[site_name] + step_size * r_grads[site_name] # z(n+1) z_grads, potential_energy = potential_grad(potential_fn, z) for site_name in r: r[site_name] = r[site_name] + 0.5 * step_size * (-z_grads[site_name]) # r(n+1) return z, r, z_grads, potential_energy
[docs]def potential_grad(potential_fn, z): """ Gradient of `potential_fn` w.r.t. parameters z. :param potential_fn: python callable that takes in a dictionary of parameters and returns the potential energy. :param dict z: dictionary of parameter values keyed by site name. :return: tuple of `(z_grads, potential_energy)`, where `z_grads` is a dictionary with the same keys as `z` containing gradients and potential_energy is a torch scalar. """ z_keys, z_nodes = zip(*z.items()) for node in z_nodes: node.requires_grad_(True) try: potential_energy = potential_fn(z) # deal with singular matrices except RuntimeError as e: if "singular" in str(e) or "input is not positive-definite" in str(e): grads = {k: v.new_zeros(v.shape) for k, v in z.items()} return grads, z_nodes[0].new_tensor(float("nan")) else: raise e grads = grad(potential_energy, z_nodes) for node in z_nodes: node.requires_grad_(False) return dict(zip(z_keys, grads)), potential_energy.detach()