Eulerian Parameter Inference (EPI) is a powerful and novel method for inverse model parameter inference. The eulerpi package provides an implementation of the EPI algorithm, which takes observed data and a model as input and returns a parameter distribution consistent with the observed data by solving the inverse problem directly. In case the model describes a one-to-one mapping between parameters and simulation results, the inferred parameter distribution is the true underlying distribution.

Documentation

The full documentation of this software, including a detailed tutorial on how to use EPI and the api documentation, can be found under Documentation.

Features

EPI supports

• SBML ode models
• User provided models
• Models with automatic differentiation using jax

Installation

The package is available on pypi and can be installed with:

pip install eulerpi

or

pip install eulerpi[sbml]

for the support of sbml models.

Make sure that you have the following C++ libraries installed

sudo apt install -y swig libblas-dev libatlas-base-dev libhdf5-dev

You can also build the library from the latest source code by following the Development Quickstart Guide.

Using the library

To use EPI, derive your model from the BaseModel class and implement the abstract functions. Here's an example code snippet:

# my_model.py

import jax.numpy as jnp

from eulerpi.core.models import BaseModel

class MyModel(BaseModel):

    param_dim = N # The dimension of a parameter point
    data_dim = M # The dimension of a data point

    def forward(self, param):
        return jnp.array(...)

    def jacobian(self, param):
        return jnp.array(...)

To evaluate the model and infer the parameter distribution, call:

from eulerpi.sampling import inference

from my_model import MyModel

# This line is needed for multiprocessing in python
if __name__ == "__main__":
    central_param = np.array([0.5, -1.5, ...])
    param_limits = np.array([[0.0, 1.0], [-3.0, 0.0], ...])

    model = MyModel(central_param, param_limits)
    inference(model=model, data="my_data.csv")

The data argument can be a numpy-2d-array or a PathLike object that points to a CSV file. In the example shown above, the CSV file my_data.csv should contain the data in the following format:

datapoint_dim1, datapoint_dim2, datapoint_dim3, ..., datapoint_dimN
datapoint_dim1, datapoint_dim2, datapoint_dim3, ..., datapoint_dimN
datapoint_dim1, datapoint_dim2, datapoint_dim3, ..., datapoint_dimN
...
datapoint_dim1, datapoint_dim2, datapoint_dim3, ..., datapoint_dimN

This corresponds to a matrix with the shape nSamples x data_dim. For more available options and parameters for the inference method, please refer to the api documentation. Note that the inference can be done with grid-based methods (dense grids, sparse grids) or sampling methods (mcmc).

The results are stored in the following location:

• ./Applications/<ModelName>/.../OverallParams.csv
• ./Applications/<ModelName>/.../OverallSimResults.csv
• ./Applications/<ModelName>/.../OverallDensityEvals.csv

These files contain the sampled parameters, the corresponding data points obtained from the model forward pass, and the corresponding density evaluation.