brencej
commented
1 year ago Hi!
We have recently changed the way ProGED is set up and have not yet updated all the examples and documentation. Most importantly, a pandas dataframes is expected, with column names matching variable names. Furthermore, rhs_vars and lhs_vars expect lists with variable names. Time should be called either "t" or "time".
We also built in better support of systems of equations. Now, Model represents a system of equations, represented as a list of expressions. Parameter estimation always fits all the components in the system. The generator generates each component independently by default. You could change this behavior by manually calling ProGED.generate.generate_models with system_size=1 for each component, and then composing the system yourself, for example, through cartesian product. Which approach is better is unclear at the moment.
The most comprehensive source of examples currently is test/test_core.py. (Note that at the moment, some tests will throw assertion errors for "wrong" results, but in fact, the code is running fine). Since there is no test for 2D ODEs with generation and estimation, I wrote an example below.
import numpy as np
import pandas as pd
import ProGED as pg
np.random.seed(2)
# Generate and prepare data
t = np.arange(0, 1, 0.1)
x = 3*np.exp(-2*t)
y = 5.1*np.exp(-1*t)
data = pd.DataFrame(np.vstack((t, x, y)).T, columns=['t', 'x', 'y'])
# Set up equation discovery
ED = pg.EqDisco(data = data,
task_type="differential", #either algebraic or differential
lhs_vars = ["x", "y"], # the variables on the left-hand side, the number should match system_size
rhs_vars = ["t", "x", "y"], # the variables that can appear on the right-hand side
sample_size = 3, # how many random candidate systems to generate
system_size = 2, # how many equations in the system of equations
generator_template_name = "polynomial", # the grammar to use; you can write your own
strategy_settings = {"max_repeat": 100}) # gives more attempts to generator, ensuring we get 3
print("Generating models...")
ED.generate_models()
print(ED.models)
print("Estimating parameters...")
ED.fit_models()
print("The best discovered model:")
print(ED.get_results())I hope this answers your questions. If you have any further issues, please do not hesitate to ask!
soerenab
Hi, thanks again for open sourcing your repository. Could you provide a simple example on how to apply your model for discovery of ODE systems (e.g. 2 variables). I had a look at the lorenz.py example but I get the following error:
(I am also guessing that the code has changed since the lorenz.py example was added.)
My fundamental question is the following: When I have a system of equations, do I need to run
fit()multiple times, once per component of the system (as specified bytarget_variable_index). If so, how do I deal with the fact that the equation discoverer usually outputs many candidates (=sample_size), i.e., I would get multiple candidates per component. What's the best way to combine the candidate of different components, is it just the cartesian product?Thanks a lot for you help!