Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization | Paper Citation Record

Observation 61db564f-4b31-4948-a852-e3c6ff103020 · outbound

This paper cites Active Learning Enhanced Surrogate Modeling of Jet Engines in JuliaSim.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Active Learning Enhanced Surrogate Modeling of Jet Engines in JuliaSim

Reference 1

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This paper cites Accelerating the convergence of Newton's method for nonlinear elliptic PDEs using Fourier neural operators.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Accelerating the convergence of Newton's method for nonlinear elliptic PDEs using Fourier neural operators

Reference 2

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This paper cites Solving inverse problems using conditional invertible neural networks.Journal of Computational Physics, 433:110194, May 2021.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Solving inverse problems using conditional invertible neural networks.Journal of Computational Physics, 433:110194, May 2021

Reference 3

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This paper cites Learning to learn by gradient descent by gradient descent.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Learning to learn by gradient descent by gradient descent

Reference 4

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This paper cites Gradient Enhanced Surrogate Models Based on Adjoint CFD Methods for the Design of a Counter Rotating Turbofan.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Gradient Enhanced Surrogate Models Based on Adjoint CFD Methods for the Design of a Counter Rotating Turbofan

Reference 5

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This paper cites A Deep Learning Surrogate Model for Topology Optimization.IEEE Transactions on Magnetics, 57(6):1–4, June 2021.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization A Deep Learning Surrogate Model for Topology Optimization.IEEE Transactions on Magnetics, 57(6):1–4, June 2021

Reference 6

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Observation 88957d28-3dc8-469c-adc8-b5be24f68c25 · outbound

This paper cites Bendsøe and Ole Sigmund.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Bendsøe and Ole Sigmund

Reference 7

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This paper cites Automated reverse engineering of nonlinear dynamical systems.Proceedings of the National Academy of Sciences of the United States of America, 104(24):9943–9948, June 2007.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Automated reverse engineering of nonlinear dynamical systems.Proceedings of the National Academy of Sciences of the United States of America, 104(24):9943–9948, June 2007

Reference 8

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This paper cites Convex optimization.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Convex optimization

Reference 9

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Observation 5b06f3c9-f1d5-4ac6-b748-87f710804e18 · outbound

This paper cites Message passing neural PDE solvers, March 2023.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Message passing neural PDE solvers, March 2023

Reference 10

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This paper cites Learning phase field mean curvature flows with neural networks.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Learning phase field mean curvature flows with neural networks

Reference 11

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Observation 2193f1e5-05d2-4e5b-acd7-43123fa97b94 · outbound

This paper cites A penalized Allen-Cahn equation for the mean curvature flow of thin structures.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization A penalized Allen-Cahn equation for the mean curvature flow of thin structures

Reference 12

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Observation 63ff9396-92fb-4f14-a1ea-3e61646e93f9 · outbound

This paper cites Brogan.Modern Control Theory.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Brogan.Modern Control Theory

Reference 13

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Observation b2856f19-250f-4ee2-b89c-41b0bb717184 · outbound

This paper cites Brunton, Joshua L.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Brunton, Joshua L

Reference 14

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This paper cites Hesthaven.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Hesthaven

Reference 15

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This paper cites Stable signal recovery from incomplete and inaccurate measurements.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Stable signal recovery from incomplete and inaccurate measurements

Reference 16

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Observation 744825c7-0c6f-4051-b81a-1fef07295aa8 · outbound

This paper cites LNO: Laplace Neural Operator for Solving Differential Equations.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization LNO: Laplace Neural Operator for Solving Differential Equations

Reference 17

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This paper cites Nathan Kutz, and Steven L.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Nathan Kutz, and Steven L

Reference 18

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This paper cites Sign projected gradient flow: A continuous-time approach to convex optimization with linear equality constraints.Automatica, 120:109156, October 2020.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Sign projected gradient flow: A continuous-time approach to convex optimization with linear equality constraints.Automatica, 120:109156, October 2020

Reference 19

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Observation 48b81294-3833-4341-aed7-2c7ca5d8ad81 · outbound

This paper cites Neural Ordinary Differential Equations.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Neural Ordinary Differential Equations

Reference 20

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Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Unresolved cited work

Reference 21

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Observation f0c96595-4833-4faf-b2f8-163247e99aa0 · outbound

This paper cites Accelerated optimization in deep learning with a proportional-integral-derivative controller.Nature Communications, 15(1):10263, November 2024.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Accelerated optimization in deep learning with a proportional-integral-derivative controller.Nature Communications, 15(1):10263, November 2024

Reference 22

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This paper cites Learning to Optimize: A Primer and A Benchmark.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Learning to Optimize: A Primer and A Benchmark

Reference 23

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This paper cites Flow map learning for unknown dynamical systems: Overview, implementation, and benchmarks, 2023.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Flow map learning for unknown dynamical systems: Overview, implementation, and benchmarks, 2023

Reference 24

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This paper cites Dunton, Lluís Jofre, Gianluca Iaccarino, and Alireza Doostan.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Dunton, Lluís Jofre, Gianluca Iaccarino, and Alireza Doostan

Reference 25

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This paper cites Deterministic matrix sketches for low-rank compression of high-dimensional simulation data.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Deterministic matrix sketches for low-rank compression of high-dimensional simulation data

Reference 26

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This paper cites The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems

Reference 27

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Observation 3473d09c-ed63-4838-a757-e888680b7a8b · outbound

This paper cites Ebers, Katherine M.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Ebers, Katherine M

Reference 28

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Observation b7f85cf2-b07e-4504-b814-836b7c539c12 · outbound

This paper cites Using surrogate models to accelerate load step methods for nonlinear finite element problems in hyperelasticity.PAMM, 24(3):e202400081, 2024.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Using surrogate models to accelerate load step methods for nonlinear finite element problems in hyperelasticity.PAMM, 24(3):e202400081, 2024

Reference 29

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Observation 55cb1720-8def-4e0f-bfcd-27ba3800134d · outbound

This paper cites Explicit and data-Efficient Encoding via Gradient Flow.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Explicit and data-Efficient Encoding via Gradient Flow

Reference 30

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Observation 1137a91e-c6f9-4b8e-bb1b-cb87d80fb56f · outbound

This paper cites Gradient flows and proximal splitting methods: A unified view on accelerated and stochastic optimization.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Gradient flows and proximal splitting methods: A unified view on accelerated and stochastic optimization

Reference 31

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This paper cites Fixed-Time Stable Gradient Flows: Applications to Continuous-Time Opti- mization.IEEE Transactions on Automatic Control, 66(5):2002–2015, May 2021.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Fixed-Time Stable Gradient Flows: Applications to Continuous-Time Opti- mization.IEEE Transactions on Automatic Control, 66(5):2002–2015, May 2021

Reference 32

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This paper cites A surrogate model for topology optimisation of elastic structures via parametric autoencoders, July 2025.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization A surrogate model for topology optimisation of elastic structures via parametric autoencoders, July 2025

Reference 33

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This paper cites Simultaneous identification and denoising of dynamical systems.SIAM Journal on Scientific Computing, 2022.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Simultaneous identification and denoising of dynamical systems.SIAM Journal on Scientific Computing, 2022

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Observation e90b3ad2-a451-452c-a430-9f253d8b6f68 · outbound

This paper cites Neural Tangent Kernel: Convergence and Generalization in Neural Networks.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Neural Tangent Kernel: Convergence and Generalization in Neural Networks

Reference 35

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Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Unresolved cited work

Reference 36

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Observation b34aa107-0b7b-4fe8-8092-5195cc3b9022 · outbound

This paper cites Nathan Kutz, and Steven L.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Nathan Kutz, and Steven L

Reference 37

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Observation c78e9ac5-447d-40b4-a01e-c44c8b76843b · outbound

This paper cites Kaptanoglu, Brian M.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Kaptanoglu, Brian M

Reference 38

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This paper cites Kingma and Jimmy Ba.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Kingma and Jimmy Ba

Reference 39

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Observation f5db94c8-5a9f-41c8-95df-d78b7ed52140 · outbound

This paper cites Adam: A Method for Stochastic Optimization.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Adam: A Method for Stochastic Optimization

Reference 40

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This paper cites Adam: A method for stochastic optimization.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Adam: A method for stochastic optimization

Reference 41

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This paper cites Urbán, Jérôme Darbon, and George Em Karniadakis.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Urbán, Jérôme Darbon, and George Em Karniadakis

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This paper cites Continuous Time Analysis of Momentum Methods.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Continuous Time Analysis of Momentum Methods

Reference 43

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Observation 4e253698-59c0-4077-ae58-72e69a3b5bbf · outbound

This paper cites Full waveform inversion with random shot selection using adaptive gradient descent.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Full waveform inversion with random shot selection using adaptive gradient descent

Reference 44

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Observation 31bbb7ca-e3b2-4999-ae6c-aae6c105f204 · outbound

This paper cites Towards Understanding Gradient Flow Dynamics of Homogeneous Neural Networks Beyond the Origin.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Towards Understanding Gradient Flow Dynamics of Homogeneous Neural Networks Beyond the Origin

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Observation d6709621-4c40-4e8d-84c0-f11b71478454 · outbound

This paper cites Derivative-free optimization methods.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Derivative-free optimization methods

Reference 46

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Observation 26907c34-e3d9-47f5-bbac-e18d5e2f3e1f · outbound

This paper cites Analysis of stochastic gradient descent in continuous time.Statistics and Computing, 31(4):39, May 2021.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Analysis of stochastic gradient descent in continuous time.Statistics and Computing, 31(4):39, May 2021

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Observation fa244028-61ff-472c-8287-90b7c7d8d22e · outbound

This paper cites Cauchy and the gradient method | EMS Press, 2012.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Cauchy and the gradient method | EMS Press, 2012

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Observation c72f6ce1-64c5-44e4-8e76-113a8ff7f480 · outbound

This paper cites Learning to Optimize.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Learning to Optimize

Reference 49

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Observation 2073eaca-5402-4569-ba0a-d6ea2861a26f · outbound

This paper cites Fourier Neural Operator for Parametric Partial Differential Equations.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Fourier Neural Operator for Parametric Partial Differential Equations

Reference 50

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Observation 71708b7f-d6eb-48ab-ba9d-1dd6df6dd96f · outbound

This paper cites A NONLINEAR EIGENV ALUE PROBLEM.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization A NONLINEAR EIGENV ALUE PROBLEM

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This paper cites Decoupled Weight Decay Regularization, January 2019.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Decoupled Weight Decay Regularization, January 2019

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Observation 573cfd00-0c02-49c0-9c9b-35e708183d7e · outbound

This paper cites DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators

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Observation d9200074-cec0-41c8-84e6-6356d3b4c21d · outbound

This paper cites Villaverde, and Julio R.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Villaverde, and Julio R

Reference 54

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This paper cites Designing full waveform inverse problems: a combined data and model approach.Geophysical Journal International, 241(3):1479–1494, June 2025.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Designing full waveform inverse problems: a combined data and model approach.Geophysical Journal International, 241(3):1479–1494, June 2025

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Observation 32860ef8-a95c-442f-801a-7a0005702e58 · outbound

This paper cites Weak SINDy For Partial Differential Equations.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Weak SINDy For Partial Differential Equations

Reference 56

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Observation 6d050b92-d4e0-4cce-a6af-a005f6d48433 · outbound

This paper cites Messenger and David M.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Messenger and David M

Reference 57

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Observation 3a44bcad-7c47-44d8-ae51-c5604b92cb65 · outbound

This paper cites Wright.Numerical Optimization.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Wright.Numerical Optimization

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This paper cites Continuous-time Models for Stochastic Optimization Algorithms, March.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Continuous-time Models for Stochastic Optimization Algorithms, March

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Observation 7f810ad3-a6fc-44bb-a4d1-a0ecfb2d5f56 · outbound

This paper cites Ozan and Luca Magri.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Ozan and Luca Magri

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This paper cites Raissi, P.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Raissi, P

Reference 61

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This paper cites Machine learning of linear differential equations using Gaussian processes.Journal of Computational Physics, 348:683–693, November 2017.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Machine learning of linear differential equations using Gaussian processes.Journal of Computational Physics, 348:683–693, November 2017

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Observation 9260f783-5208-488d-9a2e-d6fc33037d2d · outbound

This paper cites Reddi, Satyen Kale, and Sanjiv Kumar.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Reddi, Satyen Kale, and Sanjiv Kumar

Reference 63

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Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Unresolved cited work

Reference 64

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Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization On a continuous time model of gradient descent dynamics and instability in deep learning

Reference 65

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Observation 91e4dd8d-cab4-40a0-8024-c5693193c930 · outbound

This paper cites On the definition and importance of interpretability in scientific machine learning.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization On the definition and importance of interpretability in scientific machine learning

Reference 66

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This paper cites Solving engineering eigenvalue problems with neural networks using the Rayleigh quotient.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Solving engineering eigenvalue problems with neural networks using the Rayleigh quotient

Reference 67

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This paper cites Variational volume reconstruction with the Deep Ritz Method.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Variational volume reconstruction with the Deep Ritz Method

Reference 68

Resolution: unresolved; no resolver link, observed 2026-08-02T23:34:48.867421Z

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Observation f2693699-116e-447a-b01a-f150a01d286e · outbound

This paper cites Princeton University Press, 2006.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Princeton University Press, 2006

Reference 69

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Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Unresolved cited work

Reference 70

Resolution: unresolved; no resolver link, observed 2026-08-02T23:34:49.086866Z

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This paper cites A Differential Equation for Modeling Nesterov's Accelerated Gradient Method: Theory and Insights.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization A Differential Equation for Modeling Nesterov's Accelerated Gradient Method: Theory and Insights

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Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Unresolved cited work

Reference 72

Resolution: unresolved; no resolver link, observed 2026-08-02T23:34:49.330103Z

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Observation 16e11481-3737-41d3-8277-316f624345cf · outbound

This paper cites Sukumar and Ankit Srivastava.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Sukumar and Ankit Srivastava

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Resolution: unresolved; no resolver link, observed 2026-08-02T23:34:49.523483Z

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Observation a1774b67-a173-4b4c-bd00-c59db5ea7ee2 · outbound

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Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization SciPy 1.0: Fundamental algorithms for scientific computing in python

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Resolution: unresolved; no resolver link, observed 2026-08-02T23:34:49.707816Z

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Observation 465505d2-f8c0-4a5b-a675-19f4d4a28540 · outbound

This paper cites Learning Adaptive Hydrodynamic Models Using Neural ODEs in Complex Conditions.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Learning Adaptive Hydrodynamic Models Using Neural ODEs in Complex Conditions

Reference 75

Resolution: unresolved; no resolver link, observed 2026-08-02T23:34:49.848297Z

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Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Unresolved cited work

Reference 76

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Observation faf129b2-ac61-4017-a918-a579d18d3160 · outbound

This paper cites Deep-Learning-Based Adjoint State Method: Methodology and Preliminary Application to Inverse Modeling.Water Resources Research, 57(2):e2020WR027400, 2021.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Deep-Learning-Based Adjoint State Method: Methodology and Preliminary Application to Inverse Modeling.Water Resources Research, 57(2):e2020WR027400, 2021

Reference 77

Resolution: verified exact; doi, observed 2026-08-02T23:38:21.600730Z

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Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Unresolved cited work

Reference 78

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This paper cites Machine learning for adjoint vector in aerodynamic shape optimization.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Machine learning for adjoint vector in aerodynamic shape optimization

Reference 79

Resolution: unresolved; no resolver link, observed 2026-08-02T23:34:50.499327Z

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Observation 9a7bf62f-2c8c-4d64-9f31-056e4313765d · outbound

This paper cites Learning to Optimize: Where Deep Learning Meets Optimization and Inverse Problems | SIAM, December 2022.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Learning to Optimize: Where Deep Learning Meets Optimization and Inverse Problems | SIAM, December 2022

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Resolution: unresolved; no resolver link, observed 2026-08-02T23:34:50.638919Z

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Observation f2008069-6591-4bcc-8f3a-3f41cedf2caf · outbound

This paper cites Young, Yaël Balbastre, Bruce Fischl, Polina Golland, and Juan Eugenio Iglesias.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Young, Yaël Balbastre, Bruce Fischl, Polina Golland, and Juan Eugenio Iglesias

Reference 81

Resolution: unresolved; no resolver link, observed 2026-08-02T23:34:50.782342Z

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Observation c0598aba-7e53-4d6c-8a76-5393ac0ad085 · outbound

This paper cites Non-Linear Topology Optimization Via Neural Representations and Material Point Method Part I: Quasi-Static Problem, May 2024.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Non-Linear Topology Optimization Via Neural Representations and Material Point Method Part I: Quasi-Static Problem, May 2024

Reference 82

Resolution: unresolved; no resolver link, observed 2026-08-02T23:34:50.918770Z

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Observation c6553d88-9c25-46c5-9218-fd00655f1630 · outbound

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Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Unresolved cited work

Reference 83

Resolution: verified exact; doi, observed 2026-08-02T23:38:21.446047Z

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Observation 551caa93-a15d-4ad2-92ed-c7eeccbe9b8d · outbound

This paper cites an unresolved cited work.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Unresolved cited work

Reference 2019

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Observation 92b0bc9c-b59d-4974-8ad2-adc5c877f78c · outbound

This paper cites Continuous-time Models for Stochastic Optimization Algorithms.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Continuous-time Models for Stochastic Optimization Algorithms

Reference 2020

Resolution: unresolved; no resolver link, observed 2026-08-02T23:34:47.609304Z

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This paper cites Discrepancy Modeling Framework: Learning missing physics, modeling systematic residuals, and disambiguating between deterministic and random effects.

Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization Discrepancy Modeling Framework: Learning missing physics, modeling systematic residuals, and disambiguating between deterministic and random effects

Reference 2023

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