Linearly Constrained Neural Networks

Abstract

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.

References in corpus (11)

• DGM: A deep learning algorithm for solving partial differential equations
• Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations
• Anatomically Constrained Neural Networks (ACNN): Application to Cardiac Image Enhancement and Segmentation
• Hamiltonian Neural Networks
• Symplectic ODE-Net: Learning Hamiltonian Dynamics with Control
• Lagrangian Neural Networks
• Tomographic Reconstruction of Two-Dimensional Residual Strain Fields from Bragg-Edge Neutron Imaging
• Linearly constrained Gaussian processes
• Algorithmic Linearly Constrained Gaussian Processes
• A General Framework for Structured Learning of Mechanical Systems
• Port-Hamiltonian Approach to Neural Network Training

Cited by in corpus (3)

• Nonlinear System Identification: Learning while respecting physical models using a sequential Monte Carlo method
• Physics-Guided Neural Networks for Feedforward Control: An Orthogonal Projection-Based Approach
• Deep Learning Alternative to Explicit Model Predictive Control for Unknown Nonlinear Systems