arby 0.1

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Arby

Model Order Reduction (MOR) is a technique for reducing the computational complexity of mathematical models in numerical simulations.

Arby is a fully data-driven Python module to construct reduced bases, empirical interpolants and surrogate models from training data.

Install

pip install arby

Quick Usage

Suppose we want to build a surrogate model for a family of real functions $f_\lambda(x)$ parametrized by a real number $\lambda\in[\lambda_{min},\lambda_{max}]$ and $x\in[a,b]$. We have discretizations of both domains in, say, 101 and 1001 points respectively,

lambda_params = np.linspace(lambda_min, lambda_max, 101)
x_samples = np.linspace(a, b, 1001)

The next step is to build a training set of functions associated to the discretizations.

training_data = [f(lambda, x_samples) for lambda in lambda_params]

This is an array of shape $(101,1001)$.

Then we can build a surrogate model with arby using:

from arby import ReducedOrderModeling as ROM
f_model = ROM(training_space=training_data,
              physical_interval=x_samples,
              parameter_interval=lambda_params)

With our f_model we can get function samples for any parameter $\lambda$ in the interval $\lambda\in[\lambda_{min},\lambda_{max}]$.

new_param = 0.554
f_model_new_param = f_model.surrogate(new_param)
plt.plot(x_samples, model_new_param)
plt.show()

License

MIT

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(c) 2020 Aaron Villanueva