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How to train on a pre-evaluated sample

ZüNIS provides integrators which use pre-evaluated samples. This is especially useful when fine-tuning integration parameters for a function that is very costly to evaluate.

The functionality for using pre-evaluated samples are provided by the Fixed Sample Integrator.

Starting from the basic example, on can train on a sample defined as a PyTorch tensor:

import torch
from zunis.integration.fixed_sample_integrator import  FixedSampleSurveyIntegrator
from zunis.training.weighted_dataset.stateful_trainer import StatefulTrainer

device = torch.device("cuda")

d = 2

def f(x):
    return x[:,0]**2 + x[:,1]**2

trainer = StatefulTrainer(d=d, loss="variance", flow="pwquad", device=device)
integrator =  FixedSampleSurveyIntegrator(f,trainer, device=device, n_points_survey=5)

n_points = 100
# Uniformly sampled points
x = torch.rand(n_points,d,device=device)
# x.shape = (n_points,d)

px = torch.ones(n_points)
# px.shape = (n_points,)

# Function values
fx = f(x)


sample = x, px, fx
integrator.set_sample(sample)
result, uncertainty, history = integrator.integrate()

The sample have to be PyTorch tensors present on the same device in a 3-tuple, with the first containing the sampled points, the second containing the sampling distribution PDF values, and the last entry containing the function values, respectively of shapes (sample_size, d), (sample_size,) and (sample_size,)

Fixed sample integrators can also directly import a pickle file, containing a sample batch of the same structure:

import torch
import pickle
from zunis.integration.fixed_sample_integrator import  FixedSampleSurveyIntegrator
from zunis.training.weighted_dataset.stateful_trainer import StatefulTrainer

device = torch.device("cuda")

d = 2

def f(x):
    return x[:,0]**2 + x[:,1]**2

trainer = StatefulTrainer(d=d, loss="variance", flow="pwquad", device="cuda")
integrator =  FixedSampleSurveyIntegrator(f,trainer, device=device, n_points_survey=5)

data_x=[[0,4],[1,3],[2,2],[3,1],[4,0]]
data_px=[1.0,1.0,1.0,1.0,1.0]

sample=(torch.tensor(data_x, device="cuda"),torch.tensor(data_px, device="cuda"),f(torch.tensor(data_x, device="cuda")))
pickle.dump(sample, open("sample.p","wb"))

integrator.set_sample_pickle("sample.p",device="cuda")
result, uncertainty, history = integrator.integrate()

Finally , it is also possible to provide samples as a .csv file. This file has to have d+2 columns, with the first d columns containing the sampled points, the second the sampling distribution PDF values and the last the function value. For the above example, the .csv file would look like:

0, 4, 1, 16
1, 3, 1, 10
2, 2, 1, 8
3, 1, 1, 10
4, 0, 1, 16

This could be imported as a pre-evaluated example and used for integration in the following way:

import torch
import numpy as np
from zunis.integration.fixed_sample_integrator import  FixedSampleSurveyIntegrator
from zunis.training.weighted_dataset.stateful_trainer import StatefulTrainer

device = torch.device("cuda")

d = 2

trainer = StatefulTrainer(d=d, loss="variance", flow="pwquad", device=device)
integrator =  FixedSampleSurveyIntegrator(f,trainer, device=device, n_points_survey=5)


integrator.set_sample_csv("sample.csv",device="cuda",dtype=np.float32)
result, uncertainty, history = integrator.integrate()