A collection of basic routines for Molecular Dynamics simulations written in Julia. These include
- Euler–Maruyama (EM)
- Random Walk Metropolis (RWM)
- Metropolis Adjusted Langevin (MALA)
- Brünger, Brooks and Karplus (BBK)
- Grønbech-Jensen and Farago (GJF)
- ABOBA, BAOAB
- Verlet
- Hamiltonian/Hybrid Monte Carlo (HMC)
This is intended to be a collection for small scale problems and code development. Larger problems will best be handled with LAMMPS or OpenMM
This module has been significantly reorganized to better take advantage of
multiple dispatch. The older versions are still available in deprecated.jl as a part of the module OldJuBasicMD, if needed.
Each sampler is first initialized as
> sampler = RWM(V, β, Δt);
or
> sampler = HMC(V, gradV!, β, M, Δt, nΔt);
depending on the type of sampler that is chosen. Information about what is needed to define each sampler can be obtained in the REPL by calling ? with the sampler name (i.e., ?HMC).
Once a sampler is constructed, sampling is then performed with either sample_trajectory! or sample_trajectory. The former performs an in place transformation on the input state, while the latter records values along the trajectory:
sample_trajectory!(X, sampler, options=opts);
and
Xvals = sample_trajectory(X₀, sampler);
For Metropolis methods, the latter form also returns the running acceptance rate,
Xvals, avals = sample_trajectory(X₀, sampler);
The number of iterations performed is determined by the optional options
argument. This takes as its argument a data structure which is formatted using
the Options function:
opts = Options(n_iters=n_iters,n_save_iters=n_save_iters)
n_iters is the number of iterations performed by the sampler. n_save_iters
is the frequency with which samples are saved. If n_save_iters=1, every
iteration is saved. If n_save_iters=n_iters, only the final iteration is saved.
All of these methods have two versions, Integrator and Integrator!. The Integrator! routine performs an in place transformation on the starting position (and momentum, where appropriate), while Integrator copies over the initial condition. Integrator also accepts the optional argument return_trajectory=true/false, which will return the entire time series data.
Example codes include:
- 1D Harmonic potential
- 1D Double Well Potential
- 2D Muller Potential
- The code assumes that the state space is vector valued. Thus, even if the problem is one dimensional, you should have initial points and functions formatted appropriately, i.e.
> x0 = [1.0]
-
The mass matrix,
M, used in the inertial Langevin integrators and Hamiltonian methods must be diagonal and provided either as a scalar (in the isotropic case) or a vector (in the anisotropic case). This restriction is in place for performance purposes. -
BBK is currently implemented for a slightly different version of the Langevin SDE than ABOBA/BAOAB. BBK requires inverting the mass matrix while ABOBA/BAOAB require its square root.
-
GJF is implemented in (q,p) coordinates as opposed to (x,v) coordinates. Consequently, the mass term appears slightly differently than in the literature.
Both will sample the associated Boltzmann distribution, but the SDE trajectories will differ when M≂̸I.
Before reaching a 1.0, the goals are:
- Include GHMC samplers.
- Include reporter functions that allow for the computation of observables on at particular time intervals.
