Linearly Constrained Neural Networks
This addresses the challenge of incorporating physical constraints into neural network models for applications in physics and engineering, representing an incremental improvement.
The authors tackled the problem of modeling vector fields from physical systems by introducing neural networks that explicitly satisfy known linear operator constraints, achieving guaranteed constraint satisfaction through a linear transformation of an underlying neural network potential field.
We present a novel approach to modelling and learning vector fields from physical systems using neural networks that explicitly satisfy known linear operator constraints. To achieve this, the target function is modelled as a linear transformation of an underlying potential field, which is in turn modelled by a neural network. This transformation is chosen such that any prediction of the target function is guaranteed to satisfy the constraints. The approach is demonstrated on both simulated and real data examples.