ode: The 'ode' class object

In KGode: Kernel Based Gradient Matching for Parameter Inference in Ordinary Differential Equations

The 'ode' class object

Description

This class provide all information about odes and methods for numerically solving odes.

Format

R6Class object.

Value

an R6Class object which can be used for gradient matching.

Methods

solve_ode(par_ode,xinit,tinterv)

This method is used to solve ode numerically.

optim_par(par,y_p,z_p)

This method is used to estimate ode parameters by standard gradient matching.

lossNODE(par,y_p,z_p)

This method is used to calculate the mismatching between gradient of interpolation and gradient from ode.

Public fields

ode_par

vector(of length n_p) containing ode parameters. n_p is the number of ode parameters.

ode_fun

function containing the ode function.

t

vector(of length n_o) containing time points of observations. n_o is the length of time points.

Methods

Public methods

• ode$new()

• ode$greet()

• ode$solve_ode()

• ode$rmsfun()

• ode$gradient()

• ode$lossNODE()

• ode$grlNODE()

• ode$loss32NODE()

• ode$grl32NODE()

• ode$optim_par()

• ode$clone()

---

Method new()

Usage

ode$new(
  sample = NULL,
  fun = NULL,
  grfun = NULL,
  t = NULL,
  ode_par = NULL,
  y_ode = NULL
)

---

Method greet()

Usage

ode$greet()

---

Method solve_ode()

Usage

ode$solve_ode(par_ode, xinit, tinterv)

---

Method rmsfun()

Usage

ode$rmsfun(par_ode, state, M1, true_par)

---

Method gradient()

Usage

ode$gradient(y_p, par_ode)

---

Method lossNODE()

Usage

ode$lossNODE(par, y_p, z_p)

---

Method grlNODE()

Usage

ode$grlNODE(par, y_p, z_p)

---

Method loss32NODE()

Usage

ode$loss32NODE(par, y_p, z_p)

---

Method grl32NODE()

Usage

ode$grl32NODE(par, y_p, z_p)

---

Method optim_par()

Usage

ode$optim_par(par, y_p, z_p)

---

Method clone()

The objects of this class are cloneable with this method.

Usage

ode$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.

Author(s)

Mu Niu, [e-mail]

Examples

noise = 0.1  ## set the variance of noise
SEED = 19537
set.seed(SEED)
## Define ode function, we use lotka-volterra model in this example. 
## we have two ode states x[1], x[2] and four ode parameters alpha, beta, gamma and delta.
LV_fun = function(t,x,par_ode){
  alpha=par_ode[1]
  beta=par_ode[2]
  gamma=par_ode[3]
  delta=par_ode[4]
  as.matrix( c( alpha*x[1]-beta*x[2]*x[1] , -gamma*x[2]+delta*x[1]*x[2] ) )
}
## Define the gradient of ode function against ode parameters 
## df/dalpha,  df/dbeta, df/dgamma, df/ddelta where f is the differential equation.
LV_grlNODE= function(par,grad_ode,y_p,z_p) { 
alpha = par[1]; beta= par[2]; gamma = par[3]; delta = par[4]
dres= c(0)
dres[1] = sum( -2*( z_p[1,]-grad_ode[1,])*y_p[1,]*alpha ) 
dres[2] = sum( 2*( z_p[1,]-grad_ode[1,])*y_p[2,]*y_p[1,]*beta)
dres[3] = sum( 2*( z_p[2,]-grad_ode[2,])*gamma*y_p[2,] )
dres[4] = sum( -2*( z_p[2,]-grad_ode[2,])*y_p[2,]*y_p[1,]*delta)
dres
}

## create a ode class object
kkk0 = ode$new(2,fun=LV_fun,grfun=LV_grlNODE)
## set the initial values for each state at time zero.
xinit = as.matrix(c(0.5,1))
## set the time interval for the ode numerical solver.
tinterv = c(0,6)
## solve the ode numerically using predefined ode parameters. alpha=1, beta=1, gamma=4, delta=1.
kkk0$solve_ode(c(1,1,4,1),xinit,tinterv) 

## Create another ode class object by using the simulation data from the ode numerical solver.
## If users have experiment data, they can replace the simulation data with the experiment data.
## set initial values for ode parameters.
init_par = rep(c(0.1),4)
init_yode = kkk0$y_ode
init_t = kkk0$t
kkk = ode$new(1,fun=LV_fun,grfun=LV_grlNODE,t=init_t,ode_par= init_par, y_ode=init_yode )

KGode documentation built on Aug. 19, 2022, 5:08 p.m.