Linearly Constrained Neural Networks

2020/02/05 by Johannes Hendriks, Carl Jidling, Hendriks, Johannes +5
Computer Science · Engineering · Physics and Astronomy · #Computational Physics (physics.comp-ph) #Control Systems and Identification #FOS: Computer and information sciences #FOS: Physical sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Model Reduction and Neural Networks #Neural Networks and Applications

paper · pdf · doi:10.48550/arxiv.2002.01600

openalex publication_date 2020/02/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• A General Framework for Structured Learning of Mechanical Systems
• Lagrangian Neural Networks

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• Neural Fields with Hard Constraints of Arbitrary Differential Order
• Vector Field Neural Networks
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• Learning Physical Constraints with Neural Projections