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Overview¶

FormaK aims to combine symbolic modeling for fast, efficient system modelling with code generation to create performant code that is easy to use.

The values (in order) are:

• Easy to use
• Performant

The Five Key Elements the library provides to achieve this (see parent) are:

1. Python Interface to define models
2. Python implementation of the model and supporting tooling
3. Integration to scikit-learn to leverage the model selection and parameter tuning functions
4. C++ and Python to C++ interoperability for performance
5. C++ interfaces to support a variety of model uses

This design provides the initial implementation of third of the Five Keys "Integration to scikit-learn to leverage the model selection and parameter tuning functions". Scikit-learn is a common library who's interface is replicated many places (e.g. dask-ml for scaling up machine learning tasks) that's a good place to start with for an easy to use library.

Why is scikit-learn and machine learning relevant? Conceptually, a detailed, physical model derived from first principles describes both one complex model, as well as a space of models derived via simplifications, enhancements or even disconnected approximations from the original model. Using data from the system we hope to describe, we can select the appropriate model from the space. This process is analogous to a machine learning model, where we have one idea of how to approximate the system and want to select machine learning models (in a more algorithmic sense of the term models) and their parameters to best fit data.

The Dream¶

In the end, my hope is that the user can provide an arbitrarily complex description of the system as a model and provide data and auto-magically get a best fit approximation to their system. Providing a more complicated model provides more of a space for discovering improvements to the final system in the same way providing more data can improve the final system. The "auto-magic" doesn't come from anything magical; instead, it comes from accumulating knowledge and how to use it in one place where the final level (improved knowledge) can also improve the final system above and beyond that which could be achieved by the user alone. Scikit-learn makes some of this process easier, especially when it comes to comparing multiple candidate models.

What could this look like?¶

Scikit-learn offers helpful tooling for many things, including model selection, cross validation and building pipelines from estimators and transformers. By borrowing from scikit-learn's Pipeline documentation and Model Selection documentation we can build the code to compose a pipeline and validate the estimator:

from formak import py

from sklearn.decomposition import PCA
from sklearn.model_selection import train_test_split
from sklearn.pipeline import Pipeline

formak_model = py.Model(...)

estimators = [('reduce_dim', PCA()), ('formak model', formak_model)]
pipeline = Pipeline(estimators)

# ... load some data X, y...

X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.4, random_state=0)

pipeline.fit(X_train, y_train)

pipeline.score(X_test, y_test)

This is just a small part of what scikit-learn has to offer. For example, scikit-learn has additional functionality for detecting outliers and other unsupervised learning capabilities that are direclty useful to FormaK.