Paper Citation Record · LEDGER

Loss Terms and Operator Forms of Koopman Autoencoders

As of 14 August 2026, this Paper Citation Record lists 60 of 60 outbound references and 3 inbound Pith citation observations for arXiv:2412.04578.

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pith.paper-citation-record.v1
2412.04578 v1

Coverage vector

measured 60 of 60 reference resolution

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measured 3 of 3 inbound itemization

Pith citing papers itemized under the disclosed page cap.

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measured 0 of 1 external citation measurements

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Source: arxiv_reference, observed 2026-07-04T10:29:45.019267Z

Reference resolution

60 of 60 outbound references displayed

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Outbound references

Observation 996eccc2-4718-4f94-8df1-a2698375fb89 · outbound

This paper cites Operator Learning: Algorithms and Analysis.

Loss Terms and Operator Forms of Koopman Autoencoders Operator Learning: Algorithms and Analysis

Reference 1

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This paper cites A Mathematical Guide to Operator Learning.

Loss Terms and Operator Forms of Koopman Autoencoders A Mathematical Guide to Operator Learning

Reference 2

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Observation f9da118b-c7be-4118-8951-0436a2561fc3 · outbound

This paper cites NeuralNetworkApproximationstoSolutionOperatorsforPartialDifferential Equations.

Loss Terms and Operator Forms of Koopman Autoencoders NeuralNetworkApproximationstoSolutionOperatorsforPartialDifferential Equations

Reference 3

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This paper cites A survey on the methods and results of data-driven koopman analysis in the visualization of dynamical systems.

Loss Terms and Operator Forms of Koopman Autoencoders A survey on the methods and results of data-driven koopman analysis in the visualization of dynamical systems

Reference 4

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Observation b9a2ef79-b4af-4a03-9f46-c0d2936ca70d · outbound

This paper cites Learning data-driven stable Koopman operators.

Loss Terms and Operator Forms of Koopman Autoencoders Learning data-driven stable Koopman operators

Reference 5

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Observation f101bfab-e78c-4d85-823e-f3d5db301a2e · outbound

This paper cites Data-driven nonlinear stabilization using koop- man operator.

Loss Terms and Operator Forms of Koopman Autoencoders Data-driven nonlinear stabilization using koop- man operator

Reference 6

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Observation a16284b1-b40f-4911-84a1-cd07ff48fce8 · outbound

This paper cites Data-driven approximation of the Koopman generator: Model reduc- tion, system identification, and control.

Loss Terms and Operator Forms of Koopman Autoencoders Data-driven approximation of the Koopman generator: Model reduc- tion, system identification, and control

Reference 7

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Observation 6b5ca25a-f626-46be-ae65-d212ab3f9608 · outbound

This paper cites Koopman invariant subspaces and finite linear representations of nonlinear dynamical systems for control.

Loss Terms and Operator Forms of Koopman Autoencoders Koopman invariant subspaces and finite linear representations of nonlinear dynamical systems for control

Reference 8

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Observation e2b2b91e-d491-467b-9113-2f91d384f92b · outbound

This paper cites Applied koopmanism.

Loss Terms and Operator Forms of Koopman Autoencoders Applied koopmanism

Reference 9

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Observation 447faa8d-7f15-44c0-9151-e81fdfbe2c88 · outbound

This paper cites Multiresolution dynamic mode decomposi- tion.

Loss Terms and Operator Forms of Koopman Autoencoders Multiresolution dynamic mode decomposi- tion

Reference 10

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Observation 312bb172-f4de-4f73-971c-a699232b39a4 · outbound

This paper cites Learning Koopman invariant sub- spaces for dynamic mode decomposition.

Loss Terms and Operator Forms of Koopman Autoencoders Learning Koopman invariant sub- spaces for dynamic mode decomposition

Reference 11

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Loss Terms and Operator Forms of Koopman Autoencoders Unresolved cited work

Reference 12

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Observation e654ad05-d5b2-49b8-a0af-44f677b7bb12 · outbound

This paper cites Learning Compositional Koopman Operators for Model-Based Control.

Loss Terms and Operator Forms of Koopman Autoencoders Learning Compositional Koopman Operators for Model-Based Control

Reference 13

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This paper cites Data-driven approximations of dy- namical systems operators for control.

Loss Terms and Operator Forms of Koopman Autoencoders Data-driven approximations of dy- namical systems operators for control

Reference 14

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This paper cites Deep learning of Koopman representation for control.

Loss Terms and Operator Forms of Koopman Autoencoders Deep learning of Koopman representation for control

Reference 15

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This paper cites Koopman-based control of a soft continuum manipulator under variable loading conditions.

Loss Terms and Operator Forms of Koopman Autoencoders Koopman-based control of a soft continuum manipulator under variable loading conditions

Reference 16

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Observation 4e9e69d6-6064-416c-b6aa-9c40d78c302f · outbound

This paper cites Modeling and Control of Soft Robots Using the Koopman Operator and Model Predictive Control.

Loss Terms and Operator Forms of Koopman Autoencoders Modeling and Control of Soft Robots Using the Koopman Operator and Model Predictive Control

Reference 17

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This paper cites A data-driven koopman model predictive control framework for nonlinear partial differential equations.

Loss Terms and Operator Forms of Koopman Autoencoders A data-driven koopman model predictive control framework for nonlinear partial differential equations

Reference 18

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This paper cites Model-Based Control Using Koopman Operators.

Loss Terms and Operator Forms of Koopman Autoencoders Model-Based Control Using Koopman Operators

Reference 19

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Observation c70f120a-9a4c-4d16-b34d-8f89e4291411 · outbound

This paper cites LearningnonlinearoperatorsviaDeepONetbasedontheuniversalapproximation theorem of operators.

Loss Terms and Operator Forms of Koopman Autoencoders LearningnonlinearoperatorsviaDeepONetbasedontheuniversalapproximation theorem of operators

Reference 20

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This paper cites Error estimates for deep- onets: A deep learning framework in infinite dimensions.

Loss Terms and Operator Forms of Koopman Autoencoders Error estimates for deep- onets: A deep learning framework in infinite dimensions

Reference 21

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Loss Terms and Operator Forms of Koopman Autoencoders A physics-informed variational DeepONet for predicting crack path in quasi-brittle materials

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Loss Terms and Operator Forms of Koopman Autoencoders Novel DeepONet architecture to predict stresses in elastoplastic structures with variable complex geometries and loads

Reference 23

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Observation e82d9163-2c62-4b6d-9848-5f161036dc70 · outbound

This paper cites Learning time-dependent PDE via graph neural networks and deep operator network for robust accuracy on irregular grids.

Loss Terms and Operator Forms of Koopman Autoencoders Learning time-dependent PDE via graph neural networks and deep operator network for robust accuracy on irregular grids

Reference 24

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This paper cites A comprehensive and fair comparison of two neural operators (with practical extensions) based on fair data.

Loss Terms and Operator Forms of Koopman Autoencoders A comprehensive and fair comparison of two neural operators (with practical extensions) based on fair data

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Loss Terms and Operator Forms of Koopman Autoencoders Fourier Neural Operator for Parametric Partial Differential Equations

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Loss Terms and Operator Forms of Koopman Autoencoders Toward a Better Understanding of Fourier Neural Operators from a Spectral Perspective

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Loss Terms and Operator Forms of Koopman Autoencoders Fourier neural operator with learned deformations for pdes on general ge- ometries

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Loss Terms and Operator Forms of Koopman Autoencoders Lie point symmetry data aug- mentation for neural PDE solvers

Reference 29

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Loss Terms and Operator Forms of Koopman Autoencoders On universal approximation and error bounds for Fourier neural operators

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Loss Terms and Operator Forms of Koopman Autoencoders Factorized Fourier Neural Operators

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Loss Terms and Operator Forms of Koopman Autoencoders Fourier features let networks learn high frequency functions in low di- mensionaldomains

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Loss Terms and Operator Forms of Koopman Autoencoders Hamiltonian systems and transformation in Hilbert space

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Loss Terms and Operator Forms of Koopman Autoencoders Modern Koopman Theory for Dynamical Systems

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Loss Terms and Operator Forms of Koopman Autoencoders What is the Koopman operator? a simplified treatment for discrete-time systems

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Loss Terms and Operator Forms of Koopman Autoencoders Understanding quantum physics: A user’s manual

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Loss Terms and Operator Forms of Koopman Autoencoders Griffiths

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Loss Terms and Operator Forms of Koopman Autoencoders Deep learning for universal linear embeddings of nonlinear dynamics

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Loss Terms and Operator Forms of Koopman Autoencoders Deep Koopman operator with control for nonlinear systems

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Loss Terms and Operator Forms of Koopman Autoencoders Deep learning nonlinear multiscale dynamic problems using Koopman operator

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Loss Terms and Operator Forms of Koopman Autoencoders Astudyondata-driveniden- tification and representation of nonlinear dynamical systems with a physics-integrated deep learning approach: Koopman operators and nonlinear normal modes

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Loss Terms and Operator Forms of Koopman Autoencoders Matrix analysis.CambridgeuniversitypressCambridge, 1985

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Loss Terms and Operator Forms of Koopman Autoencoders Representer theorem for learning Koopman operators

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Loss Terms and Operator Forms of Koopman Autoencoders SIAM, 2022

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Loss Terms and Operator Forms of Koopman Autoencoders Forecasting sequential data using consistent koopman autoencoders

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Loss Terms and Operator Forms of Koopman Autoencoders Physics-Informed Koopman Network for time-series prediction of dynamical systems

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This paper cites Analyzing Koopman approaches to physics-informed machine learning for long-term sea-surface temperature forecasting.

Loss Terms and Operator Forms of Koopman Autoencoders Analyzing Koopman approaches to physics-informed machine learning for long-term sea-surface temperature forecasting

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Loss Terms and Operator Forms of Koopman Autoencoders Finite difference methods for ordinary and partial differential equations: steady-state and time-dependent problems

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Loss Terms and Operator Forms of Koopman Autoencoders A hierarchy of low-dimensional models for the transient and post- transient cylinder wake

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Loss Terms and Operator Forms of Koopman Autoencoders Springer Nature, 2017

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Loss Terms and Operator Forms of Koopman Autoencoders Interaction of “solitons

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Loss Terms and Operator Forms of Koopman Autoencoders Automatic differentiation in PyTorch

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Loss Terms and Operator Forms of Koopman Autoencoders Programming pytorch for deep learning: Creating and deploying deep learning applications

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Loss Terms and Operator Forms of Koopman Autoencoders UvA Deep Learning Tutorials

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Observation 5f80984c-3aba-45f4-b7f1-81c0249a5581 · outbound

This paper cites url: https://github.com/Lightning-AI/pytorch-lightning.

Loss Terms and Operator Forms of Koopman Autoencoders url: https://github.com/Lightning-AI/pytorch-lightning

Reference 58

Resolution: unresolved; no resolver link, observed 2026-08-11T21:27:26.471641Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 67fc76f3-8bf1-414b-9be8-fd47666d0137 · outbound

This paper cites Hydra - A framework for elegantly configuring complex applications.

Loss Terms and Operator Forms of Koopman Autoencoders Hydra - A framework for elegantly configuring complex applications

Reference 59

Resolution: unresolved; no resolver link, observed 2026-08-11T21:27:26.474035Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8f751371-3f27-48a2-b5d5-2da9fe49d1eb · outbound

This paper cites an unresolved cited work.

Loss Terms and Operator Forms of Koopman Autoencoders Unresolved cited work

Reference 2019

Resolution: unresolved; raw_fallback, observed 2026-08-11T21:27:26.570287Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Pith citing papers

Observation cb146f1e-f272-4cce-bb7b-e24128970e4b · inbound

Some Best Practices in Operator Learning cites this paper.

Some Best Practices in Operator Learning Loss Terms and Operator Forms of Koopman Autoencoders

Reference 2024

Resolution: unresolved; no resolver link, observed 2026-08-11T19:24:03.528996Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 40ade2c2-8611-46ed-9cc8-a60538a954d9 · inbound

Adversarial Autoencoders in Operator Learning cites this paper.

Adversarial Autoencoders in Operator Learning Loss Terms and Operator Forms of Koopman Autoencoders

Reference 2024

Resolution: unresolved; no resolver link, observed 2026-08-11T19:07:05.600534Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 88da66b4-fec1-44ec-b239-6ccf41ad35ad · inbound

Learning the Koopman Operator using Attention Free Transformers cites this paper.

Learning the Koopman Operator using Attention Free Transformers Loss Terms and Operator Forms of Koopman Autoencoders

Reference 57

Resolution: verified exact; arxiv_id, observed 2026-07-04T10:29:45.020816Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.