mlsanityData to 14 Oct 2026

Linearly Constrained Neural Networks

arXiv 2002.01600 ↗First posted 5 Feb 2020stat.ML cs.LG physics.comp-phcited by 18

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Abstract (arXiv)

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.

Key facts. Cited by 18 papers in the map (data through 14 Oct 2026). First posted on arXiv 5 Feb 2020.

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 6; 2023: 4; 2024: 3; 2025: 3; 2026: 2.

18 papers.

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  1. 2022Learning differentiable solvers for systems with hard constraintscited by 34
  2. 2023RAYEN: Imposition of Hard Convex Constraints on Neural Networkscited by 30
  3. 2023A New Computationally Simple Approach for Implementing Neural Networks with Output Hard Constraintscited by 12
  4. 2024Learning to Optimize for Mixed-Integer Non-linear Programming with Feasibility Guaranteescited by 8
  5. 2022Deep Random Vortex Method for Simulation and Inference of Navier-Stokes Equationscited by 5
  6. 2023Neural Fields with Hard Constraints of Arbitrary Differential Ordercited by 5
  7. 2022Towards Scalable Physically Consistent Neural Networks: an Application to Data-driven Multi-zone Thermal Building Modelscited by 4
  8. 2022Incorporating Sum Constraints into Multitask Gaussian Processescited by 2
  9. 2024Gaussian Process Priors for Boundary Value Problems of Linear Partial Differential Equationscited by 2
  10. 2025Riemann Tensor Neural Networks: Learning Conservative Systems with Physics-Constrained Networkscited by 2
  11. 2022Harmonic (Quantum) Neural Networkscited by 1
  12. 2025Deep Generative Models with Hard Linear Equality Constraintscited by 1
6 more
  1. 2022Neuro-physical dynamic load modeling using differentiable parametric optimizationcited by 0
  2. 2023Zero Coordinate Shift: Whetted Automatic Differentiation for Physics-informed Operator Learningcited by 0
  3. 2024Scalable physical source-to-field inference with hypernetworkscited by 0
  4. 2025LaPON: A Lagrange's-mean-value-theorem-inspired operator network for solving PDEs and its application on NSEcited by 0
  5. 2026Temperature transferable Machine Learned Coarse Grained model for proteinscited by 0
  6. 2026Steering Neural Network Training through Interpretable Constraints Based on Partial Dependencecited by 0