Linearly Constrained Neural Networks

We present an approach to designing neural network based models that will explicitly satisfy known linear constraints. To achieve this, the target function is modelled as a linear transformation of an underlying function. This transformation is chosen such that any prediction of the target function is guaranteed to satisfy the constraints and can be determined from known physics or, more generally, by following a constructive procedure that was previously presented for Gaussian processes. The approach is demonstrated on simulated and real-data examples.