  Traditional machine learning is generally treated as a black-box optimization
problem and does not typically produce interpretable functions that connect
inputs and outputs. However, the ability to discover such interpretable
functions is desirable. In this work, we propose GINN-LP, an interpretable
neural network to discover the form and coefficients of the underlying equation
of a dataset, when the equation is assumed to take the form of a multivariate
Laurent Polynomial. This is facilitated by a new type of interpretable neural
network block, named the "power-term approximator block", consisting of
logarithmic and exponential activation functions. GINN-LP is end-to-end
differentiable, making it possible to use backpropagation for training. We
propose a neural network growth strategy that will enable finding the suitable
number of terms in the Laurent polynomial that represents the data, along with
sparsity regularization to promote the discovery of concise equations. To the
best of our knowledge, this is the first model that can discover arbitrary
multivariate Laurent polynomial terms without any prior information on the
order. Our approach is first evaluated on a subset of data used in SRBench, a
benchmark for symbolic regression. We first show that GINN-LP outperforms the
state-of-the-art symbolic regression methods on datasets generated using 48
real-world equations in the form of multivariate Laurent polynomials. Next, we
propose an ensemble method that combines our method with a high-performing
symbolic regression method, enabling us to discover non-Laurent polynomial
equations. We achieve state-of-the-art results in equation discovery, showing
an absolute improvement of 7.1% over the best contender, by applying this
ensemble method to 113 datasets within SRBench with known ground-truth
equations.
