Paper Citation Record · LEDGER

Muti-Fidelity Prediction and Uncertainty Quantification with Laplace Neural Operators for Parametric Partial Differential Equations

As of 14 August 2026, this Paper Citation Record lists 43 of 43 outbound references and 1 inbound Pith citation observation for arXiv:2502.00550.

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pith.paper-citation-record.v1
2502.00550 v1

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measured 43 of 43 reference resolution

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Pith citing papers itemized under the disclosed page cap.

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Source: arxiv_reference, observed 2026-05-18T01:35:36.290475Z

Reference resolution

43 of 43 outbound references displayed

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Outbound references

Observation 561cd51f-e5d3-4208-966e-ff8ef11d31b9 · outbound

This paper cites The Finite Element Method: Linear Static and Dynamic Finite Element Analysis.

Muti-Fidelity Prediction and Uncertainty Quantification with Laplace Neural Operators for Parametric Partial Differential Equations The Finite Element Method: Linear Static and Dynamic Finite Element Analysis

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T18:38:03.535240Z

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Observation 4d6fec90-8f6b-4ba6-aacd-e2fd261e47b7 · outbound

This paper cites Finite Di fference Methods for Ordinary and Partial Di fferential Equations: Steady-State and Time-Dependent Problems.

Muti-Fidelity Prediction and Uncertainty Quantification with Laplace Neural Operators for Parametric Partial Differential Equations Finite Di fference Methods for Ordinary and Partial Di fferential Equations: Steady-State and Time-Dependent Problems

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T18:38:03.523290Z

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Observation 268ea26a-49f8-4aa8-bc99-f0fc44c8aac4 · outbound

This paper cites Physics-Informed Neural Networks: A Deep Learning Framework for Solving Forward and Inverse Problems Involving Nonlinear Partial Differential Equations.

Muti-Fidelity Prediction and Uncertainty Quantification with Laplace Neural Operators for Parametric Partial Differential Equations Physics-Informed Neural Networks: A Deep Learning Framework for Solving Forward and Inverse Problems Involving Nonlinear Partial Differential Equations

Reference 3

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Observation 5dc99b93-25de-4599-8bb9-088633e33f82 · outbound

This paper cites Physics-Informed Machine Learning.

Muti-Fidelity Prediction and Uncertainty Quantification with Laplace Neural Operators for Parametric Partial Differential Equations Physics-Informed Machine Learning

Reference 4

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Observation b82da314-94f8-4653-a122-e014a17a38bf · outbound

This paper cites Learning Nonlinear Operators via Deeponet Based on the Universal Approximation Theorem of Operators.

Muti-Fidelity Prediction and Uncertainty Quantification with Laplace Neural Operators for Parametric Partial Differential Equations Learning Nonlinear Operators via Deeponet Based on the Universal Approximation Theorem of Operators

Reference 5

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 9000794d-ee3b-4f1e-a92f-2f9cd667917d · outbound

This paper cites Deepxde: A Deep Learning Library for Solving Differential Equations.

Muti-Fidelity Prediction and Uncertainty Quantification with Laplace Neural Operators for Parametric Partial Differential Equations Deepxde: A Deep Learning Library for Solving Differential Equations

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T18:38:03.477825Z

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 364263ba-f5e3-49c7-b5ae-8206ad63b46c · outbound

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

Muti-Fidelity Prediction and Uncertainty Quantification with Laplace Neural Operators for Parametric Partial Differential Equations Fourier Neural Operator for Parametric Partial Differential Equations

Reference 7

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 7e936065-7917-49c4-9932-ca2ddf0e8041 · outbound

This paper cites Neural Operator: Learning Maps Between Function Spaces with Applications to PDEs.

Muti-Fidelity Prediction and Uncertainty Quantification with Laplace Neural Operators for Parametric Partial Differential Equations Neural Operator: Learning Maps Between Function Spaces with Applications to PDEs

Reference 8

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Observation bfd17c8f-6335-48de-930c-0aebd7784e88 · outbound

This paper cites Laplace Neural Operator for Solving Differential Equations.

Muti-Fidelity Prediction and Uncertainty Quantification with Laplace Neural Operators for Parametric Partial Differential Equations Laplace Neural Operator for Solving Differential Equations

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T18:38:03.443126Z

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Observation 0a42005b-3cd7-48db-94aa-564202e0951d · outbound

This paper cites Nonlocal Kernel Network (NKN): A Stable and Resolution-Independent Deep Neural Network.

Muti-Fidelity Prediction and Uncertainty Quantification with Laplace Neural Operators for Parametric Partial Differential Equations Nonlocal Kernel Network (NKN): A Stable and Resolution-Independent Deep Neural Network

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T18:38:03.431534Z

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Observation 92604c20-f92a-4aba-beef-e3d06bcc0f5c · outbound

This paper cites Pole-Residue Method for Numerical Dynamic Analysis.

Muti-Fidelity Prediction and Uncertainty Quantification with Laplace Neural Operators for Parametric Partial Differential Equations Pole-Residue Method for Numerical Dynamic Analysis

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T18:38:03.420248Z

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Observation e66a2f65-99a5-4a4c-ad11-526e390b5477 · outbound

This paper cites Extraction of Mechanical Properties of Materials Through Deep Learning from Instrumented Indentation.

Muti-Fidelity Prediction and Uncertainty Quantification with Laplace Neural Operators for Parametric Partial Differential Equations Extraction of Mechanical Properties of Materials Through Deep Learning from Instrumented Indentation

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T18:38:03.408697Z

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Observation cf7c5aed-97f9-4f08-a612-0d350263b9e2 · outbound

This paper cites Multifidelity Deep Neural Operators for Efficient Learning of Partial Differential Equations with Applica- tion to Fast Inverse Design of Nanoscale Heat Transport.

Muti-Fidelity Prediction and Uncertainty Quantification with Laplace Neural Operators for Parametric Partial Differential Equations Multifidelity Deep Neural Operators for Efficient Learning of Partial Differential Equations with Applica- tion to Fast Inverse Design of Nanoscale Heat Transport

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T18:38:03.397170Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 8e60cbd9-233a-4f38-9893-d4ab2ca3a510 · outbound

This paper cites Review of Multi-fidelity Models.

Muti-Fidelity Prediction and Uncertainty Quantification with Laplace Neural Operators for Parametric Partial Differential Equations Review of Multi-fidelity Models

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T18:38:03.386099Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 4d1a0a6e-b789-4904-b492-001627e45ae7 · outbound

This paper cites A Composite Neural Network That Learns from Multi-fidelity Data: Application to Function Approximation and Inverse PDE Problems.

Muti-Fidelity Prediction and Uncertainty Quantification with Laplace Neural Operators for Parametric Partial Differential Equations A Composite Neural Network That Learns from Multi-fidelity Data: Application to Function Approximation and Inverse PDE Problems

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T18:38:03.374236Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 71426fc3-a44e-4cc5-bcba-5c11196e8d25 · outbound

This paper cites Multifidelity deep operator networks for data-driven and physics-informed problems.

Muti-Fidelity Prediction and Uncertainty Quantification with Laplace Neural Operators for Parametric Partial Differential Equations Multifidelity deep operator networks for data-driven and physics-informed problems

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T18:38:03.363106Z

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation b6313053-c42e-4f6e-988a-f8adec978070 · outbound

This paper cites Gaussian Processes for Regression.

Muti-Fidelity Prediction and Uncertainty Quantification with Laplace Neural Operators for Parametric Partial Differential Equations Gaussian Processes for Regression

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T18:38:03.351206Z

Source-reported events for the cited work

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Observation 674b0107-265a-40c0-8dea-709ea89424d3 · outbound

This paper cites Neural-Net-Induced Gaussian Process Regression for Function Approximation and Pde Solution.

Muti-Fidelity Prediction and Uncertainty Quantification with Laplace Neural Operators for Parametric Partial Differential Equations Neural-Net-Induced Gaussian Process Regression for Function Approximation and Pde Solution

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T18:38:03.339809Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation f82fb47d-da63-44af-a666-6ae2b239b766 · outbound

This paper cites Multi-fidelity Bayesian Neural Networks: Algorithms and Applications.

Muti-Fidelity Prediction and Uncertainty Quantification with Laplace Neural Operators for Parametric Partial Differential Equations Multi-fidelity Bayesian Neural Networks: Algorithms and Applications

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T18:38:03.328522Z

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Observation 0643e38f-1d0b-4937-9ba5-40d0d53b68ff · outbound

This paper cites MCMC Using Hamiltonian Dynamics.

Muti-Fidelity Prediction and Uncertainty Quantification with Laplace Neural Operators for Parametric Partial Differential Equations MCMC Using Hamiltonian Dynamics

Reference 20

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 23d0555f-332c-4b67-bf10-fe5cc8468150 · outbound

This paper cites Stochastic Gradient Hamiltonian Monte Carlo.

Muti-Fidelity Prediction and Uncertainty Quantification with Laplace Neural Operators for Parametric Partial Differential Equations Stochastic Gradient Hamiltonian Monte Carlo

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T18:38:03.305762Z

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Observation 3658609e-08bb-4687-88d2-afcc4f51b167 · outbound

This paper cites The No-U-Turn Sampler: Adaptively Setting Path Lengths in Hamiltonian Monte Carlo.

Muti-Fidelity Prediction and Uncertainty Quantification with Laplace Neural Operators for Parametric Partial Differential Equations The No-U-Turn Sampler: Adaptively Setting Path Lengths in Hamiltonian Monte Carlo

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T18:38:03.294423Z

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Observation a6eb92d5-4a2c-46b5-9ac2-3b0f9f4f1eee · outbound

This paper cites Non-convex Learning via Replica Exchange Stochastic Gradient MCMC.

Muti-Fidelity Prediction and Uncertainty Quantification with Laplace Neural Operators for Parametric Partial Differential Equations Non-convex Learning via Replica Exchange Stochastic Gradient MCMC

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T18:38:03.282994Z

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 1754f341-ddab-4b6c-93eb-452ae3b5658d · outbound

This paper cites Exploring Non-Convex Discrete Energy Landscapes: A Langevin-Like Sampler with Replica Exchange.

Muti-Fidelity Prediction and Uncertainty Quantification with Laplace Neural Operators for Parametric Partial Differential Equations Exploring Non-Convex Discrete Energy Landscapes: A Langevin-Like Sampler with Replica Exchange

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T18:38:03.271696Z

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 937fcea3-aa8b-4444-86be-6f7e5a193913 · outbound

This paper cites Riemann Manifold Langevin and Hamiltonian Monte Carlo Methods.

Muti-Fidelity Prediction and Uncertainty Quantification with Laplace Neural Operators for Parametric Partial Differential Equations Riemann Manifold Langevin and Hamiltonian Monte Carlo Methods

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T18:38:03.260473Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation ae01487c-997e-4aa2-83fd-0591d5e8e255 · outbound

This paper cites Preconditioned Stochas- tic Gradient Langevin Dynamics for Deep Neural Networks.

Muti-Fidelity Prediction and Uncertainty Quantification with Laplace Neural Operators for Parametric Partial Differential Equations Preconditioned Stochas- tic Gradient Langevin Dynamics for Deep Neural Networks

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T18:38:03.248842Z

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 49b4a16f-1e17-4291-918f-bf2ef07b39a2 · outbound

This paper cites An Adaptive Empirical Bayesian Method for Sparse Deep Learning.

Muti-Fidelity Prediction and Uncertainty Quantification with Laplace Neural Operators for Parametric Partial Differential Equations An Adaptive Empirical Bayesian Method for Sparse Deep Learning

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T18:38:03.237427Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 4db5f154-7676-49ad-9104-9f9e39ef71da · outbound

This paper cites Underdamped Langevin MCMC: A Non-asymptotic Analysis.

Muti-Fidelity Prediction and Uncertainty Quantification with Laplace Neural Operators for Parametric Partial Differential Equations Underdamped Langevin MCMC: A Non-asymptotic Analysis

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T18:38:03.225832Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation e867a229-179f-4258-8aaa-8dcfabc0bfad · outbound

This paper cites Improved Discretization Analysis for Underdamped Langevin Monte Carlo.

Muti-Fidelity Prediction and Uncertainty Quantification with Laplace Neural Operators for Parametric Partial Differential Equations Improved Discretization Analysis for Underdamped Langevin Monte Carlo

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T18:38:03.214544Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 659bc844-f691-4a9a-91af-c7708de4b695 · outbound

This paper cites Accelerating Approximate Thompson Sampling with Underdamped Langevin Monte Carlo.

Muti-Fidelity Prediction and Uncertainty Quantification with Laplace Neural Operators for Parametric Partial Differential Equations Accelerating Approximate Thompson Sampling with Underdamped Langevin Monte Carlo

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T18:38:03.203153Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 56babb45-a6e0-476b-afaf-9240a2081419 · outbound

This paper cites Cyclical Stochastic Gradient MCMC for Bayesian Deep Learning.

Muti-Fidelity Prediction and Uncertainty Quantification with Laplace Neural Operators for Parametric Partial Differential Equations Cyclical Stochastic Gradient MCMC for Bayesian Deep Learning

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T18:38:03.191383Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation ae138958-8134-424c-9c28-6205e1472d06 · outbound

This paper cites A Complete Recipe for Stochastic Gradient MCMC.

Muti-Fidelity Prediction and Uncertainty Quantification with Laplace Neural Operators for Parametric Partial Differential Equations A Complete Recipe for Stochastic Gradient MCMC

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T18:38:03.179630Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 154b285e-a9b7-44ab-b671-039413fe7b1e · outbound

This paper cites Log-Concave Sampling: Metropolis-Hastings Algorithms Are Fast.

Muti-Fidelity Prediction and Uncertainty Quantification with Laplace Neural Operators for Parametric Partial Differential Equations Log-Concave Sampling: Metropolis-Hastings Algorithms Are Fast

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T18:38:03.168072Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation d6a4a8ab-a7a1-4214-bfad-8414b3174b7f · outbound

This paper cites Optimal Dimension Dependence of the Metropolis-Adjusted Langevin Algorithm.

Muti-Fidelity Prediction and Uncertainty Quantification with Laplace Neural Operators for Parametric Partial Differential Equations Optimal Dimension Dependence of the Metropolis-Adjusted Langevin Algorithm

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T18:38:03.155091Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation e7c6bb25-3468-40ed-899c-d96f791739e6 · outbound

This paper cites Stochastic Gradient Langevin Dynamics with Adaptive Drifts.

Muti-Fidelity Prediction and Uncertainty Quantification with Laplace Neural Operators for Parametric Partial Differential Equations Stochastic Gradient Langevin Dynamics with Adaptive Drifts

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T18:38:03.142953Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 601d3f0a-9eb8-4ebc-8844-6de47bf18b30 · outbound

This paper cites Provable and Practical: Efficient Exploration in Reinforcement Learning via Langevin Monte Carlo.

Muti-Fidelity Prediction and Uncertainty Quantification with Laplace Neural Operators for Parametric Partial Differential Equations Provable and Practical: Efficient Exploration in Reinforcement Learning via Langevin Monte Carlo

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T18:38:03.130148Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 3dc2ccf1-3c12-473e-b7ec-cfe468be38b5 · outbound

This paper cites Replica Exchange for Non-Convex Optimization.

Muti-Fidelity Prediction and Uncertainty Quantification with Laplace Neural Operators for Parametric Partial Differential Equations Replica Exchange for Non-Convex Optimization

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T18:38:03.117905Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 1cc2e1ca-92ff-43e7-9a65-65467bf65803 · outbound

This paper cites Accelerating Convergence of Replica Exchange Stochastic Gradient Mcmc via Variance Reduction.

Muti-Fidelity Prediction and Uncertainty Quantification with Laplace Neural Operators for Parametric Partial Differential Equations Accelerating Convergence of Replica Exchange Stochastic Gradient Mcmc via Variance Reduction

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T18:38:03.105982Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 0cd803cf-6a74-4a4a-91ca-fc98f16b3683 · outbound

This paper cites Bayesian Learning via Stochastic Gradient Langevin Dynamics.

Muti-Fidelity Prediction and Uncertainty Quantification with Laplace Neural Operators for Parametric Partial Differential Equations Bayesian Learning via Stochastic Gradient Langevin Dynamics

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T18:38:03.092535Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 41af3758-ba6f-4cf0-87a5-700ef9092962 · outbound

This paper cites Stochastic Gradient Hamiltonian Monte Carlo.

Muti-Fidelity Prediction and Uncertainty Quantification with Laplace Neural Operators for Parametric Partial Differential Equations Stochastic Gradient Hamiltonian Monte Carlo

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T18:38:03.079463Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 8ff8d051-c6bc-4b3b-a824-e1955d8cb3c0 · outbound

This paper cites Non-reversible Parallel Tempering for Deep Posterior Approximation.

Muti-Fidelity Prediction and Uncertainty Quantification with Laplace Neural Operators for Parametric Partial Differential Equations Non-reversible Parallel Tempering for Deep Posterior Approximation

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T18:38:03.066831Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation f6d64283-5247-416a-91f0-a2f65b6376ca · outbound

This paper cites Constrained Explo- ration via Reflected Replica Exchange Stochastic Gradient Langevin Dynamics.

Muti-Fidelity Prediction and Uncertainty Quantification with Laplace Neural Operators for Parametric Partial Differential Equations Constrained Explo- ration via Reflected Replica Exchange Stochastic Gradient Langevin Dynamics

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T18:38:03.054426Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation b56c1b61-32ba-4601-861f-7310701c3d4d · outbound

This paper cites Delving Deep into Rectifiers: Surpassing Human-Level Performance on Imagenet Classification.

Muti-Fidelity Prediction and Uncertainty Quantification with Laplace Neural Operators for Parametric Partial Differential Equations Delving Deep into Rectifiers: Surpassing Human-Level Performance on Imagenet Classification

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T18:38:03.041353Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Pith citing papers

Observation b914edfc-e90e-4f0d-86b5-a6237afb6036 · inbound

NOWS: Neural Operator Warm Starts for Accelerating Iterative Solvers cites this paper.

NOWS: Neural Operator Warm Starts for Accelerating Iterative Solvers Muti-Fidelity Prediction and Uncertainty Quantification with Laplace Neural Operators for Parametric Partial Differential Equations

Reference 30

Resolution: verified exact; arxiv_id, observed 2026-05-18T01:35:36.294013Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.