Paper Citation Record · LEDGER

Physics-Informed Neural Networks with Hard Nonlinear Equality and Inequality Constraints

As of 18 August 2026, this Paper Citation Record lists 45 of 45 outbound references and 3 inbound Pith citation observations for arXiv:2507.08124.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2507.08124 v2

Coverage vector

measured 45 of 45 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T18:35:11.777746Z

measured 48 of 48 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-17T06:30:58.91139+00:00

measured 3 of 3 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-15T16:46:02.893660Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: arxiv_reference, observed 2026-07-04T06:29:37.389850Z

Reference resolution

45 of 45 outbound references displayed

verified exact0
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation f3e38b69-70c8-4c5d-b9a1-06b00c63e97a · outbound

This paper cites Physics- informed machine learning.

Physics-Informed Neural Networks with Hard Nonlinear Equality and Inequality Constraints Physics- informed machine learning

Reference 1

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Observation e1f6e434-cf3e-4c0b-8689-40cae7444d91 · outbound

This paper cites M Faruque Hasan.

Physics-Informed Neural Networks with Hard Nonlinear Equality and Inequality Constraints M Faruque Hasan

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:35:12.258535Z

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Observation 52540902-5bc7-4b47-b851-fb6553985451 · outbound

This paper cites Physics-informed neural networks for solving reynolds-averaged navier–stokes equations.

Physics-Informed Neural Networks with Hard Nonlinear Equality and Inequality Constraints Physics-informed neural networks for solving reynolds-averaged navier–stokes equations

Reference 3

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Observation 58de0b9c-6c5a-468f-b686-87c22d77dba6 · outbound

This paper cites Theory-guided hard constraint projection (hcp): A knowledge-based data-driven scientific machine learning method.

Physics-Informed Neural Networks with Hard Nonlinear Equality and Inequality Constraints Theory-guided hard constraint projection (hcp): A knowledge-based data-driven scientific machine learning method

Reference 4

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Observation ffac6453-1eb5-4d16-91b9-4d30fc2b9ee8 · outbound

This paper cites Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations.

Physics-Informed Neural Networks with Hard Nonlinear Equality and Inequality Constraints Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:35:12.234772Z

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Observation b7a595d5-acbe-4924-b5ed-6a06c8dff76f · outbound

This paper cites Real-time optimal control via deep neural networks: study on landing problems.

Physics-Informed Neural Networks with Hard Nonlinear Equality and Inequality Constraints Real-time optimal control via deep neural networks: study on landing problems

Reference 6

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Observation bc1ccd66-0481-4720-b178-bffb7b485fd2 · outbound

This paper cites Industrial, large-scale model predictive control with structured neural networks.

Physics-Informed Neural Networks with Hard Nonlinear Equality and Inequality Constraints Industrial, large-scale model predictive control with structured neural networks

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:35:12.218884Z

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Observation 2662236f-857e-49cd-bbde-c8d7b15b870e · outbound

This paper cites Advances in surrogate based modeling, feasibility analysis, and optimization: A review.

Physics-Informed Neural Networks with Hard Nonlinear Equality and Inequality Constraints Advances in surrogate based modeling, feasibility analysis, and optimization: A review

Reference 8

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Physics-Informed Neural Networks with Hard Nonlinear Equality and Inequality Constraints Unresolved cited work

Reference 9

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Physics-Informed Neural Networks with Hard Nonlinear Equality and Inequality Constraints Unresolved cited work

Reference 10

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Observation 2a2ef76d-e6e3-486f-8335-6941eed8e0dd · outbound

This paper cites Overview of surrogate modeling in chemical process engineering.

Physics-Informed Neural Networks with Hard Nonlinear Equality and Inequality Constraints Overview of surrogate modeling in chemical process engineering

Reference 11

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Observation af4bdc42-50a5-4fce-af2a-967d567ee752 · outbound

This paper cites Formulating data-driven surrogate models for process optimization.

Physics-Informed Neural Networks with Hard Nonlinear Equality and Inequality Constraints Formulating data-driven surrogate models for process optimization

Reference 12

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Observation caf1b96e-a537-4aa5-b45e-d23e9d7eea45 · outbound

This paper cites The alamo approach to machine learning.

Physics-Informed Neural Networks with Hard Nonlinear Equality and Inequality Constraints The alamo approach to machine learning

Reference 13

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Observation da6a7998-99b7-43ce-96bd-d3e7ceae54cc · outbound

This paper cites Learning surrogate models for simulation-based optimization.

Physics-Informed Neural Networks with Hard Nonlinear Equality and Inequality Constraints Learning surrogate models for simulation-based optimization

Reference 14

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Observation 31c8c441-0d5b-4686-9661-3dfe603e7598 · outbound

This paper cites Multilayer feedforward networks are universal approxi- mators.

Physics-Informed Neural Networks with Hard Nonlinear Equality and Inequality Constraints Multilayer feedforward networks are universal approxi- mators

Reference 15

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Observation 5b1ea3c7-5654-443a-833c-2956fa6b4d25 · outbound

This paper cites Imagenet classification with deep convolutional neural networks.

Physics-Informed Neural Networks with Hard Nonlinear Equality and Inequality Constraints Imagenet classification with deep convolutional neural networks

Reference 16

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Observation 0f2d222a-bf47-442b-8271-892b69d6239f · outbound

This paper cites Generative adversarial networks.

Physics-Informed Neural Networks with Hard Nonlinear Equality and Inequality Constraints Generative adversarial networks

Reference 17

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Observation b36c2e00-4d2e-4aa2-8de1-3e398eb4be18 · outbound

This paper cites Deep learning.

Physics-Informed Neural Networks with Hard Nonlinear Equality and Inequality Constraints Deep learning

Reference 18

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Observation 45b380dd-a8ef-40db-a1d9-10c1df320161 · outbound

This paper cites Attention is all you need.

Physics-Informed Neural Networks with Hard Nonlinear Equality and Inequality Constraints Attention is all you need

Reference 19

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Observation d2f3a7c1-d3f9-416a-a6eb-5273894c7496 · outbound

This paper cites A tutorial review of neural network modeling approaches for model predictive control.

Physics-Informed Neural Networks with Hard Nonlinear Equality and Inequality Constraints A tutorial review of neural network modeling approaches for model predictive control

Reference 20

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Observation 95ab552f-c3a4-4301-9846-c4e566afe2ff · outbound

This paper cites Physics-informed neural networks (pinns) for fluid mechanics: A review.

Physics-Informed Neural Networks with Hard Nonlinear Equality and Inequality Constraints Physics-informed neural networks (pinns) for fluid mechanics: A review

Reference 21

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Observation a6f75607-d62c-4fc0-8f28-18d13f1fa3ed · outbound

This paper cites Multiscale high-throughput screening of ionic liquid solvents for mixed-refrigerant separation.

Physics-Informed Neural Networks with Hard Nonlinear Equality and Inequality Constraints Multiscale high-throughput screening of ionic liquid solvents for mixed-refrigerant separation

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:35:12.116575Z

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Observation d8ec0c2c-0a84-4a4f-bfa7-96c929e99ebe · outbound

This paper cites Physics-informed machine learning: case studies for weather and climate modelling.

Physics-Informed Neural Networks with Hard Nonlinear Equality and Inequality Constraints Physics-informed machine learning: case studies for weather and climate modelling

Reference 23

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Observation f24bbe63-ddf4-47d0-beaf-004e51659ca4 · outbound

This paper cites Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations.

Physics-Informed Neural Networks with Hard Nonlinear Equality and Inequality Constraints Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

Reference 24

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Observation dd6d8cce-9774-463d-8bf8-b5d10d5b5ba5 · outbound

This paper cites Physics-informed neural networks for heat transfer problems.

Physics-Informed Neural Networks with Hard Nonlinear Equality and Inequality Constraints Physics-informed neural networks for heat transfer problems

Reference 25

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Observation 2aa125f1-40a4-4b3f-a75f-48f2b7a5b984 · outbound

This paper cites Physics-informed neural networks with hard linear equality constraints.

Physics-Informed Neural Networks with Hard Nonlinear Equality and Inequality Constraints Physics-informed neural networks with hard linear equality constraints

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:35:12.087199Z

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Observation 4d974975-bfbf-4158-afe4-408aa2dc25f4 · outbound

This paper cites When and why pinns fail to train: A neural tangent kernel perspective.

Physics-Informed Neural Networks with Hard Nonlinear Equality and Inequality Constraints When and why pinns fail to train: A neural tangent kernel perspective

Reference 27

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Observation b08645f9-458d-4060-8f88-2b160f96e385 · outbound

This paper cites Data-driven strategies for optimization of integrated chemical plants.

Physics-Informed Neural Networks with Hard Nonlinear Equality and Inequality Constraints Data-driven strategies for optimization of integrated chemical plants

Reference 28

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Observation 1e58cd0b-eeb9-4e69-bf2b-a6c599abece7 · outbound

This paper cites Characterizing possible failure modes in physics-informed neural networks.

Physics-Informed Neural Networks with Hard Nonlinear Equality and Inequality Constraints Characterizing possible failure modes in physics-informed neural networks

Reference 29

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Observation 24aade2d-8bfd-43ea-be28-0f4d72575eb8 · outbound

This paper cites Is L2 physics-informed loss always suitable for training physics-informed neural networks? Advances in Neural Information Processing Systems , 35:8278–8290, 2022.

Physics-Informed Neural Networks with Hard Nonlinear Equality and Inequality Constraints Is L2 physics-informed loss always suitable for training physics-informed neural networks? Advances in Neural Information Processing Systems , 35:8278–8290, 2022

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:35:12.058007Z

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Observation 166dcdea-4742-41c5-b5e5-31647169243d · outbound

This paper cites Challenges in Training PINNs: A Loss Landscape Perspective.

Physics-Informed Neural Networks with Hard Nonlinear Equality and Inequality Constraints Challenges in Training PINNs: A Loss Landscape Perspective

Reference 31

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Observation 8f64f28d-77d0-4a82-8da5-cc59efb7986f · outbound

This paper cites Hard-constrained neural networks with universal approxi- mation guarantees.

Physics-Informed Neural Networks with Hard Nonlinear Equality and Inequality Constraints Hard-constrained neural networks with universal approxi- mation guarantees

Reference 32

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Observation 48a02015-368d-4a77-bf6e-656119e95be9 · outbound

This paper cites Imposing Hard Constraints on Deep Networks: Promises and Limitations.

Physics-Informed Neural Networks with Hard Nonlinear Equality and Inequality Constraints Imposing Hard Constraints on Deep Networks: Promises and Limitations

Reference 33

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Observation 55c9ad0e-e68c-43d9-96e9-c52e7cd46ec6 · outbound

This paper cites Enforcing analytic constraints in neural networks emulating physical systems.

Physics-Informed Neural Networks with Hard Nonlinear Equality and Inequality Constraints Enforcing analytic constraints in neural networks emulating physical systems

Reference 34

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Observation 831dde64-3b57-4dec-ab16-4b6656592d5b · outbound

This paper cites DC3: A learning method for optimization with hard constraints.

Physics-Informed Neural Networks with Hard Nonlinear Equality and Inequality Constraints DC3: A learning method for optimization with hard constraints

Reference 35

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Observation cf9ebfd9-d652-44f3-85f4-002bba4c5a7e · outbound

This paper cites Numerical optimization.

Physics-Informed Neural Networks with Hard Nonlinear Equality and Inequality Constraints Numerical optimization

Reference 36

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Observation 7a319e15-2bcd-467c-b57f-15a25da5a86f · outbound

This paper cites Optnet: Differentiable optimization as a layer in neural networks.

Physics-Informed Neural Networks with Hard Nonlinear Equality and Inequality Constraints Optnet: Differentiable optimization as a layer in neural networks

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:35:12.036323Z

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Observation 534b6bae-ab3c-4977-9daa-29a71cb25f11 · outbound

This paper cites Differentiable convex optimization layers.

Physics-Informed Neural Networks with Hard Nonlinear Equality and Inequality Constraints Differentiable convex optimization layers

Reference 38

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Observation 1d7b26aa-b63e-4068-a524-f38f59a40376 · outbound

This paper cites ENFORCE: Nonlinear Constrained Learning with Adaptive-depth Neural Projection.

Physics-Informed Neural Networks with Hard Nonlinear Equality and Inequality Constraints ENFORCE: Nonlinear Constrained Learning with Adaptive-depth Neural Projection

Reference 39

Resolution: unresolved; no resolver link, observed 2026-08-06T18:35:11.762175Z

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Observation 010b3f7d-cf44-4b0c-92d5-0de3fdf565e8 · outbound

This paper cites Smoothed fischer-burmeister equation methods for the complementarity problem.

Physics-Informed Neural Networks with Hard Nonlinear Equality and Inequality Constraints Smoothed fischer-burmeister equation methods for the complementarity problem

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:35:12.022607Z

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Observation a637a36d-0272-43e6-9047-c3bbef054a36 · outbound

This paper cites PyTorch: An Imperative Style, High-Performance Deep Learning Library.

Physics-Informed Neural Networks with Hard Nonlinear Equality and Inequality Constraints PyTorch: An Imperative Style, High-Performance Deep Learning Library

Reference 41

Resolution: unresolved; no resolver link, observed 2026-08-06T18:35:11.767280Z

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Observation dd155dec-8d9d-48aa-a187-abedbefc3053 · outbound

This paper cites Adam: A Method for Stochastic Optimization.

Physics-Informed Neural Networks with Hard Nonlinear Equality and Inequality Constraints Adam: A Method for Stochastic Optimization

Reference 42

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Observation 571a235a-1726-4483-a33c-428877433de6 · outbound

This paper cites The moore–penrose pseudoinverse: A tutorial review of the theory.

Physics-Informed Neural Networks with Hard Nonlinear Equality and Inequality Constraints The moore–penrose pseudoinverse: A tutorial review of the theory

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:35:12.014519Z

Source-reported events for the cited work

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Observation cb2cc66d-e0b4-4179-94a4-7c05d4364c39 · outbound

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Physics-Informed Neural Networks with Hard Nonlinear Equality and Inequality Constraints Unresolved cited work

Reference 44

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Observation e9eee677-567d-495f-a277-855482513d3c · outbound

This paper cites Handbook of test problems in local and global optimization, volume 33.

Physics-Informed Neural Networks with Hard Nonlinear Equality and Inequality Constraints Handbook of test problems in local and global optimization, volume 33

Reference 45

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:35:11.998320Z

Source-reported events for the cited work

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Pith citing papers

Observation e8f62098-412d-4ca7-a5bc-bdf4577dd0f5 · inbound

Molecular Machine Learning in Chemical Process Design cites this paper.

Molecular Machine Learning in Chemical Process Design Physics-Informed Neural Networks with Hard Nonlinear Equality and Inequality Constraints

Reference 75

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Observation 40a9ec72-a7d9-47d9-a8d0-2785a64d6826 · inbound

Physics-Constrained Machine Learning for Chemical Engineering cites this paper.

Physics-Constrained Machine Learning for Chemical Engineering Physics-Informed Neural Networks with Hard Nonlinear Equality and Inequality Constraints

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-05T15:00:21.844489Z

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Observation ad1b3955-e971-4942-8227-a083ead9bb70 · inbound

Embedding Linear Equality Constraints in Probabilistic Neural Networks for Dynamic Modelling cites this paper.

Embedding Linear Equality Constraints in Probabilistic Neural Networks for Dynamic Modelling Physics-Informed Neural Networks with Hard Nonlinear Equality and Inequality Constraints

Reference 12

Resolution: verified exact; arxiv_id, observed 2026-07-04T06:29:37.391195Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.