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 |