Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-05-12T01:19:06.747356Z
Paper Citation Record · LEDGER
Posterior Concentration of Bayesian Physics-Informed Neural Networks for Elliptic PDEs
As of 6 August 2026, this Paper Citation Record lists 12 of 12 outbound references and 1 inbound Pith citation observation for arXiv:2605.08672.
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 2026-08-06T06:34:29.942622+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-02T01:33:36.766201Z
A source-named dated measurement, never combined with another source.
Source: cited_works
Reference resolution
12 of 12 outbound references displayed
- verified exact6
- verified fuzzy4
- unresolved1
- parse uncertain0
- malformed identifier0
- metadata mismatch1
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 09f87c19-6345-4c97-94b8-f563d89c138b · outbound
This paper cites A rate of convergence of Physics Informed Neural Networks for the linear second order elliptic PDEs.
Posterior Concentration of Bayesian Physics-Informed Neural Networks for Elliptic PDEs A rate of convergence of Physics Informed Neural Networks for the linear second order elliptic PDEs
Reference 1
- Resolution
- verified exact
- arxiv_id, observed 2026-05-12T08:06:28.506448Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.
Observation 1add3770-4cc8-4397-9cd6-3ec401dfabe7 · outbound
This paper cites Posterior contraction for sparse neural networks in besov spaces with intrinsic dimensionality.arXiv preprint arXiv:2506.19144.
Posterior Concentration of Bayesian Physics-Informed Neural Networks for Elliptic PDEs Posterior contraction for sparse neural networks in besov spaces with intrinsic dimensionality.arXiv preprint arXiv:2506.19144
Reference 2
- Resolution
- verified exact
- arxiv_id, observed 2026-05-12T08:06:28.616347Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.
Observation 144b2457-b578-4186-9373-6790c9178cdf · outbound
This paper cites Machine Learning For Elliptic PDEs: Fast Rate Generalization Bound, Neural Scaling Law and Minimax Optimality.
Posterior Concentration of Bayesian Physics-Informed Neural Networks for Elliptic PDEs Machine Learning For Elliptic PDEs: Fast Rate Generalization Bound, Neural Scaling Law and Minimax Optimality
Reference 3
- Resolution
- verified exact
- arxiv_id, observed 2026-05-12T08:06:28.639356Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.
Observation 338d0c1c-b585-48c9-81c8-5b503461e2d2 · outbound
This paper cites Raissi, P.
Posterior Concentration of Bayesian Physics-Informed Neural Networks for Elliptic PDEs Raissi, P
Reference 4
- Resolution
- metadata mismatch
- doi, observed 2026-05-12T01:21:17.767157Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.
Observation cfb90968-ee8a-4de3-b377-13832193b843 · outbound
This paper cites Uncertainty Quantification in PINNs for Turbulent Flows: Bayesian Inference and Repulsive Ensembles.
Posterior Concentration of Bayesian Physics-Informed Neural Networks for Elliptic PDEs Uncertainty Quantification in PINNs for Turbulent Flows: Bayesian Inference and Repulsive Ensembles
Reference 5
- Resolution
- verified exact
- local_arxiv, observed 2026-05-12T08:06:28.572368Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.
Observation 55acd4b0-5cd6-46f3-8938-518a789d3c9c · outbound
This paper cites On the estimation rate of Bayesian PINN for inverse problems.
Posterior Concentration of Bayesian Physics-Informed Neural Networks for Elliptic PDEs On the estimation rate of Bayesian PINN for inverse problems
Reference 6
- Resolution
- verified exact
- arxiv_id, observed 2026-05-12T08:06:28.540376Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.
Observation 8b16b523-33e7-4cf2-8fc6-dfa3b31ffe02 · outbound
This paper cites Tim Van Erven and Peter Harremos.
Posterior Concentration of Bayesian Physics-Informed Neural Networks for Elliptic PDEs Tim Van Erven and Peter Harremos
Reference 7
- Resolution
- verified exact
- doi, observed 2026-05-12T01:21:17.755669Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.
Observation 6d2cc174-67ac-4a8f-9c47-c975f5bcdbec · outbound
This paper cites Z F \Fn p(n) u p(n) u∗ q(n) u q(n) u∗ dΠ(u) # =.
Posterior Concentration of Bayesian Physics-Informed Neural Networks for Elliptic PDEs Z F \Fn p(n) u p(n) u∗ q(n) u q(n) u∗ dΠ(u) # =
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-14T07:45:03.334383Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.
Observation af867cd5-fd98-4fed-8f82-912319a346e2 · outbound
This paper cites To see this, E[˜h2] =E |E[h]−h| 2 |E[h] +r| 2 ≤ ∥h∥∞E[h] 2E[h]r ≤ C1 r =: σ2, Let U= max{σ, 2C|Ω| r }= max{ q C1 r , C1 r } ≥σ.
Posterior Concentration of Bayesian Physics-Informed Neural Networks for Elliptic PDEs To see this, E[˜h2] =E |E[h]−h| 2 |E[h] +r| 2 ≤ ∥h∥∞E[h] 2E[h]r ≤ C1 r =: σ2, Let U= max{σ, 2C|Ω| r }= max{ q C1 r , C1 r } ≥σ
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-14T07:45:03.327046Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.
Observation f27fcdc4-0dba-460c-ad71-c506c15dc70e · outbound
This paper cites an unresolved cited work.
Posterior Concentration of Bayesian Physics-Informed Neural Networks for Elliptic PDEs Unresolved cited work
Reference 10
- Resolution
- unresolved
- raw_fallback, observed 2026-05-14T07:45:03.330660Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.
Observation 780156ae-6ad5-4939-ae8f-05cb0b54978d · outbound
This paper cites sup f∈F 1 n nX i=1 f(X i) # + √2vnt n + U t 3n , where vn = 2UE.
Posterior Concentration of Bayesian Physics-Informed Neural Networks for Elliptic PDEs sup f∈F 1 n nX i=1 f(X i) # + √2vnt n + U t 3n , where vn = 2UE
Reference 11
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-14T07:45:03.328886Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.
Observation bafa973b-f159-4b2a-84c3-b31fab79f526 · outbound
This paper cites sup f∈F nX i=1 f(X i) # t+ √ 2nσ2t≤E.
Posterior Concentration of Bayesian Physics-Informed Neural Networks for Elliptic PDEs sup f∈F nX i=1 f(X i) # t+ √ 2nσ2t≤E
Reference 12
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-14T07:45:03.332287Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.
Pith citing papers
Observation d5950491-c95e-4dea-86f2-5eaee8eae0e7 · inbound
Operator-Split Bayesian Learning for Elliptic PDEs with Unequal Interior and Boundary Data cites this paper.
Operator-Split Bayesian Learning for Elliptic PDEs with Unequal Interior and Boundary Data Posterior Concentration of Bayesian Physics-Informed Neural Networks for Elliptic PDEs
Reference 47
- Resolution
- unresolved
- no resolver link, observed 2026-08-02T01:33:36.766201Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.