Paper Citation Record · LEDGER

Energy Manifold Natural Gradient Descent: Riemannian Optimization for Neural PDE Solvers

As of 8 August 2026, this Paper Citation Record lists 20 of 20 outbound references and 0 inbound Pith citation observations for arXiv:2607.22004.

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pith.paper-citation-record.v1
2607.22004 v1

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measured 20 of 20 reference resolution

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measured 0 of 1 external citation measurements

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Reference resolution

20 of 20 outbound references displayed

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Outbound references

Observation 1869e1e6-8cd3-41db-a885-8f262af4c360 · outbound

This paper cites On the Promise of the Stochastic Generalized Gauss-Newton Method for Training DNNs.

Energy Manifold Natural Gradient Descent: Riemannian Optimization for Neural PDE Solvers On the Promise of the Stochastic Generalized Gauss-Newton Method for Training DNNs

Reference 7

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Observation 0a726314-6133-47c7-a9b2-d03222323f11 · outbound

This paper cites Greedy Training Algorithms for Neural Networks and Applications to PDEs.

Energy Manifold Natural Gradient Descent: Riemannian Optimization for Neural PDE Solvers Greedy Training Algorithms for Neural Networks and Applications to PDEs

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-01T06:09:01.596181Z

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Observation 1bc946e1-0e5c-449e-9bd5-5daf4353a5f4 · outbound

This paper cites Gauss-Newton Natural Gradient Descent for Physics-Informed Computational Fluid Dynamics.

Energy Manifold Natural Gradient Descent: Riemannian Optimization for Neural PDE Solvers Gauss-Newton Natural Gradient Descent for Physics-Informed Computational Fluid Dynamics

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-01T06:09:01.657091Z

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Observation d96393df-bfcd-4b91-8e9f-fdfd67b063a9 · outbound

This paper cites Zongyi Li, Nikola Borislavov Kovachki, Kamyar Azizzadenesheli, Burigede liu, Kaushik Bhat- tacharya, Andrew Stuart, and Anima Anandkumar.

Energy Manifold Natural Gradient Descent: Riemannian Optimization for Neural PDE Solvers Zongyi Li, Nikola Borislavov Kovachki, Kamyar Azizzadenesheli, Burigede liu, Kaushik Bhat- tacharya, Andrew Stuart, and Anima Anandkumar

Reference 11

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Source-reported events for the cited work

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Observation 40d4027c-a72b-4e83-a772-71ce23753718 · outbound

This paper cites Johannes M¨ uller and Marius Zeinhofer.

Energy Manifold Natural Gradient Descent: Riemannian Optimization for Neural PDE Solvers Johannes M¨ uller and Marius Zeinhofer

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-01T06:09:02.167737Z

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Observation e768f406-bd75-4471-b4c1-54b743fac6c2 · outbound

This paper cites Efficient Natural Gradient Descent Methods for Large-Scale PDE-Based Optimization Problems.

Energy Manifold Natural Gradient Descent: Riemannian Optimization for Neural PDE Solvers Efficient Natural Gradient Descent Methods for Large-Scale PDE-Based Optimization Problems

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-01T06:09:02.323721Z

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Observation b8bf84bf-13b7-467c-9f02-48e9ac52c085 · outbound

This paper cites Efficient Subsampled Gauss-Newton and Natural Gradient Methods for Training Neural Networks.

Energy Manifold Natural Gradient Descent: Riemannian Optimization for Neural PDE Solvers Efficient Subsampled Gauss-Newton and Natural Gradient Methods for Training Neural Networks

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-01T06:09:02.401966Z

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Observation f9c82938-2943-4c69-ab02-517b5662fcd0 · outbound

This paper cites ¨Uber eine neue Methode zur L¨ osung gewisser Variationsprobleme der mathe- matischen Physik.Journal f¨ ur die reine und angewandte Mathematik (Crelles Journal), 1909(135):1–61,.

Energy Manifold Natural Gradient Descent: Riemannian Optimization for Neural PDE Solvers ¨Uber eine neue Methode zur L¨ osung gewisser Variationsprobleme der mathe- matischen Physik.Journal f¨ ur die reine und angewandte Mathematik (Crelles Journal), 1909(135):1–61,

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-01T06:09:02.489927Z

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Observation 6b0f9da8-f10f-4acb-8625-0f9d99d8a8c7 · outbound

This paper cites Respecting causality is all you need for training physics-informed neural networks.

Energy Manifold Natural Gradient Descent: Riemannian Optimization for Neural PDE Solvers Respecting causality is all you need for training physics-informed neural networks

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-01T06:09:02.605898Z

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Observation 5b5fcd9a-26d3-4b70-9a8e-24fb2975490c · outbound

This paper cites Competitive physics informed networks.

Energy Manifold Natural Gradient Descent: Riemannian Optimization for Neural PDE Solvers Competitive physics informed networks

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-01T06:09:02.680956Z

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Observation eeb4939a-a03e-4a91-aa8c-d7e2a6accdfa · outbound

This paper cites Neural Operator: Learning Maps Between Function Spaces.

Energy Manifold Natural Gradient Descent: Riemannian Optimization for Neural PDE Solvers Neural Operator: Learning Maps Between Function Spaces

Reference 2001

Resolution: unresolved; no resolver link, observed 2026-08-01T06:09:01.761928Z

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Observation d68738c7-759e-4b46-9d55-77616d0e2c07 · outbound

This paper cites An iteration count estimate for a mesh-dependent steepest descent method based on finite elements and Riesz inner product representation.

Energy Manifold Natural Gradient Descent: Riemannian Optimization for Neural PDE Solvers An iteration count estimate for a mesh-dependent steepest descent method based on finite elements and Riesz inner product representation

Reference 2002

Resolution: unresolved; no resolver link, observed 2026-08-01T06:09:02.550455Z

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Observation 64ca3141-9710-4dcb-80be-feb831c82555 · outbound

This paper cites An overview on deep learning-based approximation methods for partial differential equations.

Energy Manifold Natural Gradient Descent: Riemannian Optimization for Neural PDE Solvers An overview on deep learning-based approximation methods for partial differential equations

Reference 2003

Resolution: unresolved; no resolver link, observed 2026-08-01T06:09:00.997699Z

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Observation 66bc3707-0610-4b1b-8068-108d49cb21bc · outbound

This paper cites Geometry and convergence of natural policy gradi- ents.MPI MiS Preprint 31/2022,.

Energy Manifold Natural Gradient Descent: Riemannian Optimization for Neural PDE Solvers Geometry and convergence of natural policy gradi- ents.MPI MiS Preprint 31/2022,

Reference 2008

Resolution: unresolved; no resolver link, observed 2026-08-01T06:09:02.071860Z

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Observation c68d25f1-5815-4713-9477-ebfe1b02c012 · outbound

This paper cites Gram-Gauss-Newton Method: Learning Overparameterized Neural Networks for Regression Problems.

Energy Manifold Natural Gradient Descent: Riemannian Optimization for Neural PDE Solvers Gram-Gauss-Newton Method: Learning Overparameterized Neural Networks for Regression Problems

Reference 2018

Resolution: unresolved; no resolver link, observed 2026-08-01T06:09:01.051615Z

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Observation 8fa8b88c-7da8-402f-8607-8aeaa20cbc6f · outbound

This paper cites Empowering deep neural quantum states through efficient optimization.

Energy Manifold Natural Gradient Descent: Riemannian Optimization for Neural PDE Solvers Empowering deep neural quantum states through efficient optimization

Reference 2019

Resolution: unresolved; no resolver link, observed 2026-08-01T06:09:01.120423Z

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Observation 663aed9b-9146-48be-8aed-cef216736b9a · outbound

This paper cites Nystr\"om Approximation on Manifolds.

Energy Manifold Natural Gradient Descent: Riemannian Optimization for Neural PDE Solvers Nystr\"om Approximation on Manifolds

Reference 2021

Resolution: unresolved; no resolver link, observed 2026-08-01T06:09:02.240209Z

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Observation ce1ab534-97b7-478d-9d79-127345d03b71 · outbound

This paper cites Mitigating Propagation Failures in Physics-informed Neural Networks using Retain-Resample-Release (R3) Sampling.

Energy Manifold Natural Gradient Descent: Riemannian Optimization for Neural PDE Solvers Mitigating Propagation Failures in Physics-informed Neural Networks using Retain-Resample-Release (R3) Sampling

Reference 2022

Resolution: unresolved; no resolver link, observed 2026-08-01T06:09:01.431933Z

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Observation dfe00422-fe04-461a-8cac-1d2351d2024f · outbound

This paper cites Kronecker-Factored Approximate Curvature for Physics-Informed Neural Networks.

Energy Manifold Natural Gradient Descent: Riemannian Optimization for Neural PDE Solvers Kronecker-Factored Approximate Curvature for Physics-Informed Neural Networks

Reference 2023

Resolution: unresolved; no resolver link, observed 2026-08-01T06:09:01.226078Z

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Observation be03a5c2-b598-46b2-8ba8-9fd89a12b5ef · outbound

This paper cites PSO-PINN: Physics-Informed Neural Networks Trained with Particle Swarm Optimization.

Energy Manifold Natural Gradient Descent: Riemannian Optimization for Neural PDE Solvers PSO-PINN: Physics-Informed Neural Networks Trained with Particle Swarm Optimization

Reference 2024

Resolution: unresolved; no resolver link, observed 2026-08-01T06:09:01.344971Z

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Pith citing papers

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