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.
翻译:为实现这一目标,目标功能以潜在领域线性转换为模型,而潜在领域又以神经网络为模型。选择这种转换是为了保证对目标功能的任何预测都能够满足这些限制。该方法在模拟和真实数据实例中均有体现。