Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-15T20:39:26.900038Z
Paper Citation Record · LEDGER
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers
As of 16 August 2026, this Paper Citation Record lists 74 of 74 outbound references and 2 inbound Pith citation observations for arXiv:2505.12556.
A citation records a reference. It does not transfer a finding from one paper to another.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-07T12:28:02.281195Z
A source-named dated measurement, never combined with another source.
Source: arxiv_reference, observed 2026-05-22T13:04:52.500747Z
Reference resolution
74 of 74 outbound references displayed
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External citation measurements
No source-named external measurement is stored.
Outbound references
Observation cc1e1fc1-ed83-4148-ad1d-cc2ccd401157 · outbound
This paper cites Making partial differential equations accessible to ecologists.Nature Reviews Biodiversity, 1(2):87–87, 2025.
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers Making partial differential equations accessible to ecologists.Nature Reviews Biodiversity, 1(2):87–87, 2025
Reference 1
- Resolution
- verified fuzzy
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Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation c31997e2-8ab3-4d27-884c-b6257d1111c5 · outbound
This paper cites an unresolved cited work.
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers Unresolved cited work
Reference 2
- Resolution
- unresolved
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Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation a727e6fc-be98-436f-8ffa-e3a211df7d7b · outbound
This paper cites Neural differential equation-based two-stage approach for generalization of beam dynamics.IEEE Transactions on Industrial Informatics, 2024.
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers Neural differential equation-based two-stage approach for generalization of beam dynamics.IEEE Transactions on Industrial Informatics, 2024
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T20:39:27.740530Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation d6f67959-f798-4832-9901-3c338e3e82d0 · outbound
This paper cites Springer Science & Business Media, 2008.
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers Springer Science & Business Media, 2008
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T20:39:27.726474Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 6aa4eec4-eebc-4d53-8bad-5be23271998e · outbound
This paper cites Cambridge university press, 2002.
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers Cambridge university press, 2002
Reference 5
- Resolution
- unresolved
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Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation c5a5bcb0-6aba-4f17-88b6-f8a9576d94ed · outbound
This paper cites Partial differential equations meet deep neural networks: A survey.IEEE Transactions on Neural Networks and Learning Systems, 2025.
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers Partial differential equations meet deep neural networks: A survey.IEEE Transactions on Neural Networks and Learning Systems, 2025
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T20:39:27.704459Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 442925f3-bf39-4cff-9594-463b7f9b5ddb · outbound
This paper cites Weak baselines and reporting biases lead to overoptimism in machine learning for fluid-related partial differential equations.Nature Machine Intelligence, 6(10):1256–1269, 2024.
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers Weak baselines and reporting biases lead to overoptimism in machine learning for fluid-related partial differential equations.Nature Machine Intelligence, 6(10):1256–1269, 2024
Reference 7
- Resolution
- unresolved
- no resolver link, observed 2026-08-15T20:39:26.610800Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation f7ff360b-0f3d-45c6-9502-40005991e8dd · outbound
This paper cites Physics-informed machine learning.Nature Reviews Physics, 3(6):422–440, 2021.
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers Physics-informed machine learning.Nature Reviews Physics, 3(6):422–440, 2021
Reference 8
- Resolution
- unresolved
- no resolver link, observed 2026-08-15T20:39:26.615323Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 1eba278c-ed7c-4921-8e49-4915c36e1d85 · outbound
This paper cites Neural operators for accelerating scientific simulations and design.
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers Neural operators for accelerating scientific simulations and design
Reference 9
- Resolution
- unresolved
- no resolver link, observed 2026-08-15T20:39:26.620117Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation e1d5820a-89f7-4415-a82a-16d1c43a15e0 · outbound
This paper cites An operator preconditioning perspective on training in physics-informed machine learning.
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers An operator preconditioning perspective on training in physics-informed machine learning
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T20:39:27.669116Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation df79ed12-f493-4040-acdf-63188b85570e · outbound
This paper cites Achieving high accuracy with PINNs via energy natural gradient descent.
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers Achieving high accuracy with PINNs via energy natural gradient descent
Reference 11
- Resolution
- unresolved
- no resolver link, observed 2026-08-15T20:39:26.629757Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 530c1789-395f-4f0f-b6e1-7d328e50f47d · outbound
This paper cites Fast training of accurate physics-informed neural networks without gradient descent.
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers Fast training of accurate physics-informed neural networks without gradient descent
Reference 12
- Resolution
- unresolved
- no resolver link, observed 2026-08-15T20:39:26.634603Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 7db1a6e2-b924-4aca-9675-e888f30ed4d3 · outbound
This paper cites Reliance on metrics is a fundamental challenge for AI.
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers Reliance on metrics is a fundamental challenge for AI
Reference 13
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T20:39:27.649130Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation ad13565e-9041-418f-8d31-899e355f5534 · outbound
This paper cites Problems of monetary management: the uk experience in papers in monetary economics.Monetary Economics, 1, 1975.
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers Problems of monetary management: the uk experience in papers in monetary economics.Monetary Economics, 1, 1975
Reference 14
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T20:39:27.636688Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation b13a2552-02da-43fe-9301-dfb5532a9790 · outbound
This paper cites an unresolved cited work.
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers Unresolved cited work
Reference 15
- Resolution
- unresolved
- raw_fallback, observed 2026-08-15T20:39:27.623841Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 10aabe20-5f59-4a99-8245-8da4ee44c8d0 · outbound
This paper cites Pinnsformer: A transformer-based framework for physics-informed neural networks.
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers Pinnsformer: A transformer-based framework for physics-informed neural networks
Reference 16
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T20:39:27.611118Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation a0af366d-4da3-41f3-9c6b-a8245b174384 · outbound
This paper cites Separable physics-informed neural networks.Advances in Neural Information Processing Systems, 36:23761–23788, 2023.
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers Separable physics-informed neural networks.Advances in Neural Information Processing Systems, 36:23761–23788, 2023
Reference 17
- Resolution
- unresolved
- no resolver link, observed 2026-08-15T20:39:26.656884Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation c6e7cfc1-60b3-4e68-a11c-7506d7d806d7 · outbound
This paper cites Learning nonlinear operators via deeponet based on the universal approximation theorem of operators.
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers Learning nonlinear operators via deeponet based on the universal approximation theorem of operators
Reference 18
- Resolution
- unresolved
- no resolver link, observed 2026-08-15T20:39:26.661118Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation bc320427-1351-4d38-8574-1c9b5795fa19 · outbound
This paper cites Fourier neural operator for parametric partial differential equations.
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers Fourier neural operator for parametric partial differential equations
Reference 19
- Resolution
- unresolved
- no resolver link, observed 2026-08-15T20:39:26.665800Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 47b3613c-0956-4ffa-b880-8e1ad7f265c2 · outbound
This paper cites Convolutional neural operators for robust and accurate learning of PDEs.Advances in Neural Information Processing Systems, 36: 77187–77200, 2023.
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers Convolutional neural operators for robust and accurate learning of PDEs.Advances in Neural Information Processing Systems, 36: 77187–77200, 2023
Reference 20
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T20:39:27.574206Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation da3ac6cb-e1b6-458d-ac82-bda97c2db1be · outbound
This paper cites PdeBench: An extensive benchmark for scientific machine learning.Advances in Neural Information Processing Systems, 35:1596–1611, 2022.
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers PdeBench: An extensive benchmark for scientific machine learning.Advances in Neural Information Processing Systems, 35:1596–1611, 2022
Reference 21
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T20:39:27.561710Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 3aac9c5f-78bb-413a-af45-a4cad2fed1a5 · outbound
This paper cites The well: a large-scale collection of diverse physics simulations for machine learning.Advances in Neural Information Processing Systems, 37:44989–45037, 2024.
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers The well: a large-scale collection of diverse physics simulations for machine learning.Advances in Neural Information Processing Systems, 37:44989–45037, 2024
Reference 22
- Resolution
- unresolved
- no resolver link, observed 2026-08-15T20:39:26.679576Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 10eff792-3b7a-4267-8668-bf3a0293ec7b · outbound
This paper cites Automating embodied and operational carbon assessment in urban sustainable development.Automation in Construction, 176:106245, 2025.
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers Automating embodied and operational carbon assessment in urban sustainable development.Automation in Construction, 176:106245, 2025
Reference 23
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T20:39:27.541558Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation ba74eae2-6938-4fdf-9253-5df681e3bdc6 · outbound
This paper cites Estimates on the generalization error of physics- informed neural networks for approximating PDEs.IMA Journal of Numerical Analysis, 43(1): 1–43, 2023.
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers Estimates on the generalization error of physics- informed neural networks for approximating PDEs.IMA Journal of Numerical Analysis, 43(1): 1–43, 2023
Reference 24
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T20:39:27.528843Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 3be953ba-f077-412a-aeee-872ef9650294 · outbound
This paper cites Poseidon: Efficient foundation models for PDEs.
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers Poseidon: Efficient foundation models for PDEs
Reference 25
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T20:39:27.516493Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 8d7d12d2-e9e6-4bfc-b6a3-1f12a29869eb · outbound
This paper cites Gaussian processes for machine learning.International journal of neural systems, 14(02):69–106, 2004.
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers Gaussian processes for machine learning.International journal of neural systems, 14(02):69–106, 2004
Reference 26
- Resolution
- unresolved
- no resolver link, observed 2026-08-15T20:39:26.697475Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation d398739b-913a-4bd8-b99d-5e080fc0890f · outbound
This paper cites Neural Processes.
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers Neural Processes
Reference 27
- Resolution
- unresolved
- no resolver link, observed 2026-08-15T20:39:26.702105Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 57effae9-c51a-403a-b137-f2942bbeb675 · outbound
This paper cites Deep learning.nature, 521(7553):436–444, 2015.
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers Deep learning.nature, 521(7553):436–444, 2015
Reference 28
- Resolution
- unresolved
- no resolver link, observed 2026-08-15T20:39:26.706545Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 6eb6bce6-db62-4c8d-8ea6-fb5fd7ea1d6a · outbound
This paper cites Discovering governing equations from data by sparse identification of nonlinear dynamical systems.Proceedings of the national academy of sciences, 113(15):3932–3937, 2016.
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers Discovering governing equations from data by sparse identification of nonlinear dynamical systems.Proceedings of the national academy of sciences, 113(15):3932–3937, 2016
Reference 29
- Resolution
- unresolved
- no resolver link, observed 2026-08-15T20:39:26.711239Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation a70a3327-7cdf-49b1-946d-e21f40f996b7 · outbound
This paper cites Tackling the curse of dimensionality with physics-informed neural networks.Neural Networks, 176:106369, 2024.
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers Tackling the curse of dimensionality with physics-informed neural networks.Neural Networks, 176:106369, 2024
Reference 30
- Resolution
- unresolved
- no resolver link, observed 2026-08-15T20:39:26.715608Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 4cdbed7b-b5bd-4e3a-9952-5c35062bef25 · outbound
This paper cites Physics informed neural networks for simulating radiative transfer.Journal of Quantitative Spectroscopy and Radiative Transfer, 270:107705, 2021.
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers Physics informed neural networks for simulating radiative transfer.Journal of Quantitative Spectroscopy and Radiative Transfer, 270:107705, 2021
Reference 31
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T20:39:27.474192Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 72618e51-8988-4c45-9def-a92aed419c48 · outbound
This paper cites On the morality of artificial intelligence [commentary].
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers On the morality of artificial intelligence [commentary]
Reference 32
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T20:39:27.460977Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 770d74a2-6d14-45ba-9779-3f6449ef282b · outbound
This paper cites Measuring the carbon intensity of AI in cloud instances.
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers Measuring the carbon intensity of AI in cloud instances
Reference 33
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T20:39:27.448964Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 5190c061-6725-4108-bc7a-8537b5ef70b9 · outbound
This paper cites Quantifying the Carbon Emissions of Machine Learning.
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers Quantifying the Carbon Emissions of Machine Learning
Reference 34
- Resolution
- unresolved
- no resolver link, observed 2026-08-15T20:39:26.732316Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 4b7ff188-e72a-4712-8697-d3a0c1e4eace · outbound
This paper cites Green AI.Communications of the ACM, 63(12):54–63, 2020.
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers Green AI.Communications of the ACM, 63(12):54–63, 2020
Reference 35
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T20:39:27.434196Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 08e1ba75-9ec9-4e02-8517-f0cbbffb8e28 · outbound
This paper cites Energy and carbon considerations of fine-tuning BERT.
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers Energy and carbon considerations of fine-tuning BERT
Reference 36
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T20:39:27.420322Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 0c201acb-fac4-43e4-89c8-6ecd5d6df2a1 · outbound
This paper cites Bloom: A 176B-parameter open-access multilingual language model, 2023.
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers Bloom: A 176B-parameter open-access multilingual language model, 2023
Reference 37
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T20:39:27.406766Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 776fe110-fa34-48b5-a71f-6b53f5790621 · outbound
This paper cites Estimating the carbon footprint of BLOOM, a 176B parameter language model.Journal of Machine Learning Research, 24(253):1–15, 2023.
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers Estimating the carbon footprint of BLOOM, a 176B parameter language model.Journal of Machine Learning Research, 24(253):1–15, 2023
Reference 38
- Resolution
- unresolved
- no resolver link, observed 2026-08-15T20:39:26.748483Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 8b804581-7bc9-4513-b323-1d1ab8b1ddda · outbound
This paper cites GPT-4 Technical Report.
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers GPT-4 Technical Report
Reference 39
- Resolution
- unresolved
- no resolver link, observed 2026-08-15T20:39:26.752579Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation e3baa9a8-c87e-42b8-b605-c360ddc277a4 · outbound
This paper cites https://news.mit.edu/ 2025/explained-generative-ai-environmental-impact-0117, 2025.
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers https://news.mit.edu/ 2025/explained-generative-ai-environmental-impact-0117, 2025
Reference 40
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T20:39:27.385080Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 589b2d7f-725c-420a-ad63-230cddc5a273 · outbound
This paper cites The carbon impact of artificial intelligence.Nature Machine Intelligence, 2 (8):423–425, Aug 2020.
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers The carbon impact of artificial intelligence.Nature Machine Intelligence, 2 (8):423–425, Aug 2020
Reference 41
- Resolution
- unresolved
- no resolver link, observed 2026-08-15T20:39:26.760915Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation eaa4df26-c215-481b-a68e-2338dd987df5 · outbound
This paper cites A high-efficient hybrid physics-informed neural networks based on convolutional neural network.IEEE Transactions on Neural Networks and Learning Systems, 33(10):5514– 5526, 2021.
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers A high-efficient hybrid physics-informed neural networks based on convolutional neural network.IEEE Transactions on Neural Networks and Learning Systems, 33(10):5514– 5526, 2021
Reference 42
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T20:39:27.372292Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation cddf58ed-faf2-4e3d-b484-3d7be387af87 · outbound
This paper cites Gnot: A general neural operator transformer for operator learning.
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers Gnot: A general neural operator transformer for operator learning
Reference 43
- Resolution
- unresolved
- no resolver link, observed 2026-08-15T20:39:26.769723Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 83b9e569-73b7-4728-8251-8a9a25d8048b · outbound
This paper cites In-context operator learning with data prompts for differential equation problems.Proceedings of the National Academy of Sciences, 120(39):e2310142120, 2023.
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers In-context operator learning with data prompts for differential equation problems.Proceedings of the National Academy of Sciences, 120(39):e2310142120, 2023
Reference 44
- Resolution
- unresolved
- no resolver link, observed 2026-08-15T20:39:26.773603Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 0819bdce-85dc-4d0c-9324-be518ed67fce · outbound
This paper cites Alias-free Mamba neural operator.Advances in Neural Information Processing Systems, 37:52962–52995, 2024.
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers Alias-free Mamba neural operator.Advances in Neural Information Processing Systems, 37:52962–52995, 2024
Reference 45
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T20:39:27.344305Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 6bcf7e36-1f6a-4634-af14-6d33374c16fb · outbound
This paper cites Codecarbon: estimate and track carbon emissions from machine learning computing.Cited on, 20, 2021.
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers Codecarbon: estimate and track carbon emissions from machine learning computing.Cited on, 20, 2021
Reference 46
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T20:39:27.330061Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation c43beb56-ce64-4602-8e2f-86b6665676cf · outbound
This paper cites Carbontracker: Tracking and Predicting the Carbon Footprint of Training Deep Learning Models.
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers Carbontracker: Tracking and Predicting the Carbon Footprint of Training Deep Learning Models
Reference 47
- Resolution
- unresolved
- no resolver link, observed 2026-08-15T20:39:26.786114Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation a5162f50-3c45-464e-897e-3b374334bd89 · outbound
This paper cites Towards the systematic reporting of the energy and carbon footprints of machine learning.
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers Towards the systematic reporting of the energy and carbon footprints of machine learning
Reference 48
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T20:39:27.317187Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 1c0fb45c-d3a2-483d-9008-c83e1475be77 · outbound
This paper cites Eco2ai: carbon emissions tracking of machine learning models as the first step towards sustainable ai.
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers Eco2ai: carbon emissions tracking of machine learning models as the first step towards sustainable ai
Reference 49
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T20:39:27.304511Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 64946d65-9710-49d4-8821-e163d2583d74 · outbound
This paper cites Green algorithms: quantifying the carbon footprint of computation.Advanced science, 8(12):2100707, 2021.
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers Green algorithms: quantifying the carbon footprint of computation.Advanced science, 8(12):2100707, 2021
Reference 50
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T20:39:27.291337Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation fe0a3791-a7b7-4984-8095-457e5a852621 · outbound
This paper cites Neural-network-based approximations for solving partial differential equations.communications in Numerical Methods in Engineering, 10(3):195–201, 1994.
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers Neural-network-based approximations for solving partial differential equations.communications in Numerical Methods in Engineering, 10(3):195–201, 1994
Reference 51
- Resolution
- unresolved
- no resolver link, observed 2026-08-15T20:39:26.802684Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation b9446841-8144-47ef-855c-c073d1aefe82 · outbound
This paper cites Artificial neural networks for solving ordinary and partial differential equations.IEEE transactions on neural networks, 9(5): 987–1000, 1998.
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers Artificial neural networks for solving ordinary and partial differential equations.IEEE transactions on neural networks, 9(5): 987–1000, 1998
Reference 52
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T20:39:27.270284Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation d77202e5-9aba-4a54-9139-45dc7443406d · outbound
This paper cites Learning the solution operator of parametric partial differential equations with physics-informed DeepONets.Science advances, 7(40): eabi8605, 2021.
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers Learning the solution operator of parametric partial differential equations with physics-informed DeepONets.Science advances, 7(40): eabi8605, 2021
Reference 53
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T20:39:27.256570Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 1691d063-3823-48b4-acda-eb00693897b8 · outbound
This paper cites Physics-informed deep neural operator networks.
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers Physics-informed deep neural operator networks
Reference 54
- Resolution
- unresolved
- no resolver link, observed 2026-08-15T20:39:26.815719Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation c5e338d0-5f13-476c-85ee-52e03255d429 · outbound
This paper cites https://github.com/ taniyakapoor/PINNs_beam/tree/master, 2023.
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers https://github.com/ taniyakapoor/PINNs_beam/tree/master, 2023
Reference 55
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T20:39:27.234148Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 34835cf2-9541-49da-9783-cb62a605add4 · outbound
This paper cites https://github.com/AdityaLab/ pinnsformer, 2024.
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers https://github.com/AdityaLab/ pinnsformer, 2024
Reference 56
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T20:39:27.221128Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 3d9c7997-a908-4353-9402-51ce07f451a6 · outbound
This paper cites https://github.com/stnamjef/SPINN, 2023.
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers https://github.com/stnamjef/SPINN, 2023
Reference 57
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T20:39:27.207284Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 41ac5d55-7634-4fd7-8320-b364449b4f46 · outbound
This paper cites https://github.com/raj-brown/ APMA2070, 2020.
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers https://github.com/raj-brown/ APMA2070, 2020
Reference 58
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T20:39:27.193115Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 51169ce7-5e0f-4e7d-bd03-46850971353f · outbound
This paper cites — github.com.
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers — github.com
Reference 59
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T20:39:27.178261Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation e526a5e0-d44e-4496-a3d8-70919c3ab9dc · outbound
This paper cites an unresolved cited work.
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers Unresolved cited work
Reference 60
- Resolution
- unresolved
- raw_fallback, observed 2026-08-15T20:39:27.165421Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 124b2f99-eca1-484a-8afe-61e21c822286 · outbound
This paper cites Automatic differentiation in pytorch.
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers Automatic differentiation in pytorch
Reference 61
- Resolution
- unresolved
- no resolver link, observed 2026-08-15T20:39:26.849943Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 4395f320-3a82-4052-94c0-73f2453e25e2 · outbound
This paper cites JAX: composable transformations of Python+NumPy programs, 2018.
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers JAX: composable transformations of Python+NumPy programs, 2018
Reference 62
- Resolution
- unresolved
- no resolver link, observed 2026-08-15T20:39:26.853767Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation c897f33a-34f1-4605-a41b-3e09851f0f09 · outbound
This paper cites Matplotlib: A 2d graphics environment computing in science & engineering 9 (3), 90–95.Publisher: IEEE COMPUTER SOC, 2007.
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers Matplotlib: A 2d graphics environment computing in science & engineering 9 (3), 90–95.Publisher: IEEE COMPUTER SOC, 2007
Reference 63
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T20:39:27.119349Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 4d419cf8-ce24-4ec1-9251-aad20860d6d2 · outbound
This paper cites Harris, K.
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers Harris, K
Reference 64
- Resolution
- unresolved
- no resolver link, observed 2026-08-15T20:39:26.861796Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 6205dd76-0e9b-4da9-96dd-dbcec9cfdc2f · outbound
This paper cites pandas-dev/pandas: Pandas, February 2020.
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers pandas-dev/pandas: Pandas, February 2020
Reference 65
- Resolution
- unresolved
- no resolver link, observed 2026-08-15T20:39:26.865843Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation d086dfbf-88d3-4367-9c78-955ad1d7798e · outbound
This paper cites Oliphant, Matt Haberland, Tyler Reddy, David Cournapeau, Evgeni Burovski, Pearu Peterson, Warren Weckesser, Jonathan Bright, Stéfan J.
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers Oliphant, Matt Haberland, Tyler Reddy, David Cournapeau, Evgeni Burovski, Pearu Peterson, Warren Weckesser, Jonathan Bright, Stéfan J
Reference 66
- Resolution
- unresolved
- no resolver link, observed 2026-08-15T20:39:26.870072Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 2434a36f-c673-45cd-84ac-7d616f961ed5 · outbound
This paper cites Lie Point Symmetry Data Augmentation for Neural PDE Solvers.
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers Lie Point Symmetry Data Augmentation for Neural PDE Solvers
Reference 67
- Resolution
- unresolved
- no resolver link, observed 2026-08-15T20:39:26.874151Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 28b2fb9b-f458-4d0d-a772-cb83d313c5c2 · outbound
This paper cites Lie Point Symmetry Data Augmentation for Neural PDE Solvers.
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers Lie Point Symmetry Data Augmentation for Neural PDE Solvers
Reference 68
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T20:39:27.087519Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 475a7bc4-e3a2-49a8-9bfb-f058afcab9cd · outbound
This paper cites Understanding the difficulty of training deep feedfor- ward neural networks.
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers Understanding the difficulty of training deep feedfor- ward neural networks
Reference 69
- Resolution
- unresolved
- no resolver link, observed 2026-08-15T20:39:26.882818Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 94aac2e2-031a-4f0d-9d13-ec7c782fd937 · outbound
This paper cites Adam: A Method for Stochastic Optimization.
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers Adam: A Method for Stochastic Optimization
Reference 70
- Resolution
- unresolved
- no resolver link, observed 2026-08-15T20:39:26.887001Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 0af08279-3a40-415a-a567-d91b0c6ed001 · outbound
This paper cites [Accessed 18-05-2025].
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers [Accessed 18-05-2025]
Reference 71
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T20:39:27.065360Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 2fb784b0-a508-4c14-b1bc-1ce43eaca358 · outbound
This paper cites Embodied Carbon.
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers Embodied Carbon
Reference 72
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T20:39:27.052138Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 6c53d8bc-4045-4a47-9b7b-d14890f22023 · outbound
This paper cites Xavier uniform initialization [69] is employed with a fixed seed for reproducibility.
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers Xavier uniform initialization [69] is employed with a fixed seed for reproducibility
Reference 128
- Resolution
- malformed identifier
- raw_fallback, observed 2026-08-15T20:39:27.037363Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 29080f3f-8e14-49c4-b4de-378989841be9 · outbound
This paper cites an unresolved cited work.
Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers Unresolved cited work
Reference 2023
- Resolution
- parse uncertain
- raw_fallback, observed 2026-08-15T20:39:27.152446Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Pith citing papers
Observation 25903808-025d-48e8-9c46-71a80b912bf1 · inbound
Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems cites this paper.
Neuro-Symbolic Operator for Interpretable and Generalizable Characterization of Complex Piezoelectric Systems Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers
Reference 27
- Resolution
- unresolved
- no resolver link, observed 2026-08-07T12:28:02.281195Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 82537de7-2709-4b65-a04d-ac9afa385d74 · inbound
Performance-Carbon Trade-Offs across Architectural Biases in Shear Flow Forecasting cites this paper.
Performance-Carbon Trade-Offs across Architectural Biases in Shear Flow Forecasting Beyond Accuracy: EcoL2 Metric for Sustainable Neural PDE Solvers
Reference 18
- Resolution
- verified exact
- arxiv_id, observed 2026-05-22T13:04:52.503873Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.