@atomistics/gradient-descent

gradient-descent

Given a set of atomic positions and a potential energy calculator, provides a function that steps in the direction of the force.

npm i --save @atomistics/gradient-descent

Example

const LJ = require('@atomistics/lennard-jones-pairwise-js');
const pairwisePotential = require('@atomistics/pairwise-potential');
const gradientDescent = require('@atomistics/gradient-descent');

// Create a generic LJ potential.
const ljp = pairwisePotential(LJ());

// Initialize gradient descent with a particle at the origin and at 1.2 along x,
// our Lennard-Jones potential, and a timestep of 0.01.
const step = gradientDescent([0,0,0, 1.2,0,0], ljp, 0.01);

// Take ten steps, printing the energy and force at each step.
for (let i = 0; i < 10; i++) {
  const rfe = step();
  console.log(rfe.energy.toFixed(4), norm(rfe.force).toFixed(4));
}

/*  
    Prints the following:
    -0.6639 3.5784
    -0.7973 3.8020
    -0.9332 3.0937
    -0.9982 0.6909
    -0.9998 0.2555
    -1.0000 0.1175
    -1.0000 0.0505
    -1.0000 0.0224
    -1.0000 0.0098
    -1.0000 0.0043    
*/

API

const gradientDescent = require('@atomistics/gradient-descent');
const step = gradientDescent(positions, potential, timestep);

Parameter	Type	Description
positions	float array	An flat array of atomic positions in 3D
potential	function	A potential energy function

Option	Type	Default	Description
timestep	float	0.01	The coefficient by which the force is multiplied when calculating a distance to step along the negative gradient

Returns a function that when invoked performs a single iteration of the gradient descent algorithm. An internal state is maintained to track the progress of the algorithm.

const result = step();

Returns an object containing the updated energy, force, and positions of the system.

Name	Type	Description
result.energy	float	The energy of the system as of the most recent step
result.force	float array	A flat array of forces on each component of the system
result.positions	float array	A flat array of the updated atomic positions of the system