mlsanityData to 7 Oct 2026

Physics-Informed Neural Networks with Hard Linear Equality Constraints

arXiv 2402.07251 ↗First posted 11 Feb 2024cs.LG math.OCcited by 30

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Abstract (arXiv)

Surrogate modeling is used to replace computationally expensive simulations. Neural networks have been widely applied as surrogate models that enable efficient evaluations over complex physical systems. Despite this, neural networks are data-driven models and devoid of any physics. The incorporation of physics into neural networks can improve generalization and data efficiency. The physics-informed neural network (PINN) is an approach to leverage known physical constraints present in the data, but it cannot strictly satisfy them in the predictions. This work proposes a novel physics-informed neural network, KKT-hPINN, which rigorously guarantees hard linear equality constraints through projection layers derived from KKT conditions. Numerical experiments on Aspen models of a continuous stirred-tank reactor (CSTR) unit, an extractive distillation subsystem, and a chemical plant demonstrate that this model can further enhance the prediction accuracy.

Key facts. Cited by 30 papers in the map (data through 7 Oct 2026). Builds on 19 of its 62 references that are in the map. First posted on arXiv 11 Feb 2024.

Builds on

19 of 62 references.

References · 19

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7 more
  1. 2018Global Deterministic Optimization with Artificial Neural Networks Embeddedcited by 32
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 1; 2025: 14; 2026: 15.

30 papers.

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  1. 2024HardNet: Hard-Constrained Neural Networks with Universal Approximation Guaranteescited by 29
  2. 2025ENFORCE: Nonlinear Constrained Learning with Adaptive-depth Neural Projectioncited by 15
  3. 2025Physics-Informed Neural Networks with Hard Nonlinear Equality and Inequality Constraintscited by 14
  4. 2025Enforcing Hard Linear Constraints in Deep Learning Models with Decision Rulescited by 10
  5. 2025End-to-End Probabilistic Framework for Learning with Hard Constraintscited by 8
  6. 2025Physics-Constrained Machine Learning for Chemical Engineeringcited by 5
  7. 2025Picard-KKT-hPINN: Enforcing Nonlinear Enthalpy Balances for Physically Consistent Neural Networkscited by 3
  8. 2025DAE-HardNet: A Physics Constrained Neural Network Enforcing Differential-Algebraic Hard Constraintscited by 3
  9. 2025Federated Learning from Molecules to Processes: A Perspectivecited by 2
  10. 2025ECO: Energy-Constrained Operator Learning for Chaotic Dynamics with Boundedness Guaranteescited by 2
  11. 2026HardNet++: Nonlinear Constraint Enforcement in Neural Networkscited by 2
  12. 2025Deep Generative Models with Hard Linear Equality Constraintscited by 1
18 more
  1. 2025Machine Learning for Physical Simulation Challenge Results and Retrospective Analysis: Power Grid Use Casecited by 1
  2. 2026SnareNet: Flexible Repair Layers for Neural Networks with Hard Constraintscited by 1
  3. 2026Learning with Embedded Linear Equality Constraints via Variational Bayesian Inferencecited by 1
  4. 2026AdamFLIP: Adaptive Momentum Feedback Linearization Optimization for Hard Constrained PINN Trainingcited by 1
  5. 2026Exact Fixed-Point Constraints in Neural-ODEs with Provable Universalitycited by 1
  6. 2025A condensing approach to multiple shooting neural ordinary differential equationcited by 0
  7. 2025A Neural Network Framework for Discovering Closed-form Solutions to Quadratic Programs with Linear Constraintscited by 0
  8. 2025Guaranteeing Conservation of Integrals with Projection in Physics-Informed Neural Networkscited by 0
  9. 2026Stochastic Dimension Implicit Functional Projections for Global Integral Conservation in High-Dimensional PINNscited by 0
  10. 2026NLPOpt-Net: A Learning Method for Nonlinear Optimization with Feasibility Guaranteescited by 0
  11. 2026CAffNet: Hard Constraint-Affine Neural Networkscited by 0
  12. 2026DisjunctiveNet: Neural Symbolic Learning via Differentiable Convexified Optimization Layerscited by 0
  13. 2026PL-KKT-hPINN: Enforcing Nonlinear Equality Constraints on Neural Networks via Piecewise-Linear Projectioncited by 0
  14. 2026Structure-Preserving Neural Surrogates with Tractable Uncertainty Quantificationcited by 0
  15. 2026Embedding Linear Equality Constraints in Probabilistic Neural Networks for Dynamic Modellingcited by 0
  16. 2026An Embedded RISC-V Evaluation of Kolmogorov--Arnold Networks in Hard-Constrained Recurrent Physics-Informed Modelscited by 0
  17. 2026SLP-ProbHard: Probabilistic Hard-Constrained Learning via Structural Latent Parameterizationcited by 0
  18. 2026Atoms to Processes: The Role of Artificial Intelligence and Machine Learning in Chemical Engineeringcited by 0