Molecular dynamics is a workhorse of modern computational condensed matter physics. It is frequently used to simulate materials to observe how small scale interactions can give rise to complex large-scale phenomenology. Most molecular dynamics packages (e.g. HOOMD Blue or LAMMPS) are complicated, specialized pieces of code that are many thousands of lines long. They typically involve significant code duplication to allow for running simulations on CPU and GPU. Additionally, large amounts of code is often devoted to taking derivatives of quantities to compute functions of interest (e.g. gradients of energies to compute forces).

However, recent work in machine learning has led to significant software developments that might make it possible to write more concise molecular dynamics simulations that offer a range of benefits. Here we target JAX, which allows us to write python code that gets compiled to XLA and allows us to run on CPU, GPU, or TPU. Moreover, JAX allows us to take derivatives of python code. Thus, not only is this molecular dynamics simulation automatically hardware accelerated, it is also end-to-end differentiable. This should allow for some interesting experiments that we're excited to explore.

JAX, MD is a research project that is currently under development. Expect sharp edges and possibly some API breaking changes as we continue to support a broader set of simulations.

To get started playing around with JAX, MD check out the following colab notebooks on Google Cloud without needing to install anything.

• Minimization
• NVE Simulation
• NVT Simulation

Alternatively, you can install JAX, MD by first following the JAX's installation instructions. Then installing JAX, MD should be as easy as,

git clone https://github.com/google/jax-md
pip install -e jax-md

There are several aspects of the library.

In general we must have a way of computing the pairwise distance between atoms. We must also have efficient strategies for moving atoms in some space that may or may not be globally isomorphic to R^N. For example, periodic boundary conditions are commonplace in simulations and must be respected. This part of the code implements these functions.

Example:

box_size = 25.0
displacement_fn, shift_fn = periodic(box_size)

In the simplest case, molecular dynamics calculations are often based on a pair potential that is defined by a user. This then is used to compute a total energy whose negative gradient gives forces. One of the very nice things about JAX is that we get forces for free! The second part of the code is devoted to computing energies. We provide a Soft Sphere potential and a Lennard Jones potential. We also offer a convenience wrapper to compute the force.

Example:

N = 1000
spatial_dimension = 2
key = random.PRNGKey(0)
R = random.uniform(key, (N, spatial_dimension), minval=0.0, maxval=1.0)
energy_fn = energy.lennard_jones_pairwise(displacement)
print('E = {}'.format(energy(R)))
force_fn = quantity.force(energy_fn)
print('Total Squared Force = {}'.format(np.sum(force_fn(R) ** 2)))

Given an energy function and a system, there are a number of dynamics are useful to simulate. The simulation code is based on the structure of the optimizers found in JAX. In particular, each simulation function returns an initialization function and an update function. The initialization function takes a set of positions and creates the necessary dynamical state variables. The update function does a single step of dynamics to the dynamical state variables and returns an updated state.

We include a several different kinds of dynamics. However, there is certainly room to add more for e.g. constaint strain simulations.

It is often desirable to find an energy minimum of the system. We provide two methods to do this. We provide simple gradient descent minimization. This is mostly for pedagogical purposes, since it often performs poorly. We additionally include the FIRE algorithm which often sees significantly faster convergence.

Moreover a common experiment to run in the context of molecular dynamics is to simulate a system with a fixed volume and temperature. We provide the function nvt_nose_hoover to do this.

Example:

temperature = 1.0
dt = 1e-3
init, update = nvt_nose_hoover(energy, wrap_fn, dt, temperature)
state = init(R)
for _ in range(100):
  state = update(state)
R = state.positions