Weak Physics Informed Neural Networks for Geometry Compatible Hyperbolic Conservation Laws on Manifolds | Paper Citation Record

Observation 69d3b002-3278-4864-9b37-47443828bdd3 · outbound

This paper cites Hyperbolic conservation laws on manifolds: Total variation estimates and the finite volume method.

Weak Physics Informed Neural Networks for Geometry Compatible Hyperbolic Conservation Laws on Manifolds Hyperbolic conservation laws on manifolds: Total variation estimates and the finite volume method

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:27:03.200940Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 9dba772c-00ff-4e74-9723-ba9f14c9fa78 · outbound

This paper cites Neural operator: Graph kernel network for partial differential equations.

Weak Physics Informed Neural Networks for Geometry Compatible Hyperbolic Conservation Laws on Manifolds Neural operator: Graph kernel network for partial differential equations

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:27:03.184434Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation ea465db2-1e7c-4419-b039-d58f1eafcd16 · outbound

This paper cites Bartlett.

Weak Physics Informed Neural Networks for Geometry Compatible Hyperbolic Conservation Laws on Manifolds Bartlett

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:27:03.165482Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 28dd5a12-7520-411d-a344-8dabac140edd · outbound

This paper cites Intrinsic finite element method for advection-diffusion-reaction equations on surfaces.

Weak Physics Informed Neural Networks for Geometry Compatible Hyperbolic Conservation Laws on Manifolds Intrinsic finite element method for advection-diffusion-reaction equations on surfaces

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:27:03.150243Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation c2045973-d033-4632-8341-65f07fcfbaf7 · outbound

This paper cites Local Rademacher complex- ities.

Weak Physics Informed Neural Networks for Geometry Compatible Hyperbolic Conservation Laws on Manifolds Local Rademacher complex- ities

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:27:03.133950Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 7b612318-f0e5-4212-a104-818e256942f8 · outbound

This paper cites Nearly-tight VC-dimension and pseudodimension bounds for piecewise linear neural networks.Journal of Machine Learning Research, 20(1):2285–2301, 2019.

Weak Physics Informed Neural Networks for Geometry Compatible Hyperbolic Conservation Laws on Manifolds Nearly-tight VC-dimension and pseudodimension bounds for piecewise linear neural networks.Journal of Machine Learning Research, 20(1):2285–2301, 2019

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:27:03.117549Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 3aaed020-06c1-4595-b3d8-3fb12466477c · outbound

This paper cites Physics-informed neural networks for shell structures.

Weak Physics Informed Neural Networks for Geometry Compatible Hyperbolic Conservation Laws on Manifolds Physics-informed neural networks for shell structures

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:27:03.101123Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 2a28a3a0-babc-4809-b9d6-34d10adce887 · outbound

This paper cites The quiet revolution of numerical weather prediction.

Weak Physics Informed Neural Networks for Geometry Compatible Hyperbolic Conservation Laws on Manifolds The quiet revolution of numerical weather prediction

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-07T14:27:01.739058Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2f017c4e-4b85-4219-9517-acb7ad5f0058 · outbound

This paper cites Hyperbolic conservation laws on the sphere.

Weak Physics Informed Neural Networks for Geometry Compatible Hyperbolic Conservation Laws on Manifolds Hyperbolic conservation laws on the sphere

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:27:03.074073Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation c47eedea-8bf5-4253-91bd-27c4f33b7938 · outbound

This paper cites an unresolved cited work.

Weak Physics Informed Neural Networks for Geometry Compatible Hyperbolic Conservation Laws on Manifolds Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-07T14:27:03.059272Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation c15f2db0-92a7-43f6-9851-d33b46a9e59a · outbound

This paper cites Navier–Stokes, fluid dy- namics, and image and video inpainting.

Weak Physics Informed Neural Networks for Geometry Compatible Hyperbolic Conservation Laws on Manifolds Navier–Stokes, fluid dy- namics, and image and video inpainting

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:27:03.042233Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation ffde39c7-e11b-4d44-a242-3c65919e7765 · outbound

This paper cites Error estimates for deep learning methods in fluid dynamics.

Weak Physics Informed Neural Networks for Geometry Compatible Hyperbolic Conservation Laws on Manifolds Error estimates for deep learning methods in fluid dynamics

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:27:03.027152Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation a37da196-1a69-430c-be0d-62c3675760d6 · outbound

This paper cites A divergence-conforming finite ele- ment method for the surface Stokes equation.

Weak Physics Informed Neural Networks for Geometry Compatible Hyperbolic Conservation Laws on Manifolds A divergence-conforming finite ele- ment method for the surface Stokes equation

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:27:03.011318Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation d8c870d1-65b5-4f43-abd1-6fa7f6d28cde · outbound

This paper cites The Mathematical Theory of Finite Element Methods.

Weak Physics Informed Neural Networks for Geometry Compatible Hyperbolic Conservation Laws on Manifolds The Mathematical Theory of Finite Element Methods

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:27:02.995442Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 36a966df-1263-41f5-a416-38bb345d37f9 · outbound

This paper cites Improving weak PINNs for hyperbolic conserva- tion laws: Dual norm computation, boundary conditions and systems.

Weak Physics Informed Neural Networks for Geometry Compatible Hyperbolic Conservation Laws on Manifolds Improving weak PINNs for hyperbolic conserva- tion laws: Dual norm computation, boundary conditions and systems

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:27:02.979728Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 8eecf6fc-0726-4e76-b46c-6cff8f35e428 · outbound

This paper cites A comparison study of deep Galerkin method and deep Ritz method for elliptic problems with different boundary conditions.

Weak Physics Informed Neural Networks for Geometry Compatible Hyperbolic Conservation Laws on Manifolds A comparison study of deep Galerkin method and deep Ritz method for elliptic problems with different boundary conditions

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:27:02.963359Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation f987eec9-9a00-4dd7-8013-8f1fae0b2b81 · outbound

This paper cites Efficient approximation of deep ReLU networks for functions on low dimensional manifolds.

Weak Physics Informed Neural Networks for Geometry Compatible Hyperbolic Conservation Laws on Manifolds Efficient approximation of deep ReLU networks for functions on low dimensional manifolds

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:27:02.948087Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 25ae88b0-7253-419b-8415-bd87097bb98b · outbound

This paper cites Nonparametric regression on low-dimensional manifolds using deep ReLU networks: Function approximation and statistical recovery.

Weak Physics Informed Neural Networks for Geometry Compatible Hyperbolic Conservation Laws on Manifolds Nonparametric regression on low-dimensional manifolds using deep ReLU networks: Function approximation and statistical recovery

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:27:02.933702Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation a802a77c-5656-4fc9-97b4-1b4826c83938 · outbound

This paper cites Physics-informed machine learning for reduced-order modeling of nonlinear problems.

Weak Physics Informed Neural Networks for Geometry Compatible Hyperbolic Conservation Laws on Manifolds Physics-informed machine learning for reduced-order modeling of nonlinear problems

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:27:02.918542Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 922298d3-317a-410c-bcbe-542de261a4e2 · outbound

This paper cites δ-PINNs: Physics- informed neural networks on complex geometries.

Weak Physics Informed Neural Networks for Geometry Compatible Hyperbolic Conservation Laws on Manifolds δ-PINNs: Physics- informed neural networks on complex geometries

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:27:02.902119Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 75fc8144-6228-4cf4-852d-c3577f74d737 · outbound

This paper cites Error estimates for physics- informed neural networks approximating the Navier–Stokes equations.

Weak Physics Informed Neural Networks for Geometry Compatible Hyperbolic Conservation Laws on Manifolds Error estimates for physics- informed neural networks approximating the Navier–Stokes equations

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:27:02.884998Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation a9f4cf5b-4fe5-4eef-bbd2-0a8a913eb3a6 · outbound

This paper cites On the approximation of functions by tanh neural networks.

Weak Physics Informed Neural Networks for Geometry Compatible Hyperbolic Conservation Laws on Manifolds On the approximation of functions by tanh neural networks

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:27:02.869636Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 22bc6308-17ef-486b-862f-71612f544cf2 · outbound

This paper cites Error analysis for physics-informed neural networks (PINNs) approximating kolmogorov PDEs.

Weak Physics Informed Neural Networks for Geometry Compatible Hyperbolic Conservation Laws on Manifolds Error analysis for physics-informed neural networks (PINNs) approximating kolmogorov PDEs

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:27:02.855410Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 98074ced-bc35-4f42-b584-b816cc3d3dcf · outbound

This paper cites Generic bounds on the approximation error for physics-informed (and) operator learning.

Weak Physics Informed Neural Networks for Geometry Compatible Hyperbolic Conservation Laws on Manifolds Generic bounds on the approximation error for physics-informed (and) operator learning

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:27:02.840131Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation e5514333-e06a-47d8-b778-2bcc575450d1 · outbound

This paper cites Numerical analysis of physics-informed neural networks and related models in physics-informed machine learning.

Weak Physics Informed Neural Networks for Geometry Compatible Hyperbolic Conservation Laws on Manifolds Numerical analysis of physics-informed neural networks and related models in physics-informed machine learning

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:27:02.822925Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation bb834763-45e2-4a3a-93ec-765ff1a333b7 · outbound

This paper cites wPINNs: Weak physics in- formed neural networks for approximating entropy solutions of hyperbolic conservation laws.

Weak Physics Informed Neural Networks for Geometry Compatible Hyperbolic Conservation Laws on Manifolds wPINNs: Weak physics in- formed neural networks for approximating entropy solutions of hyperbolic conservation laws

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:27:02.805177Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 2b26398c-72c4-4a0c-b940-e5f13a79059f · outbound

This paper cites Reproducing kernel Hilbert spaces on manifolds: Sobolev and diffusion spaces.

Weak Physics Informed Neural Networks for Geometry Compatible Hyperbolic Conservation Laws on Manifolds Reproducing kernel Hilbert spaces on manifolds: Sobolev and diffusion spaces

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:27:02.788332Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 3409dd0e-c906-45ec-a760-b0155fb757cd · outbound

This paper cites The deep Ritz method: A deep learning-based numerical algo- rithm for solving variational problems.

Weak Physics Informed Neural Networks for Geometry Compatible Hyperbolic Conservation Laws on Manifolds The deep Ritz method: A deep learning-based numerical algo- rithm for solving variational problems

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:27:02.772099Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 947eb365-eef4-4bb7-8ff9-4d19e38a368d · outbound

This paper cites The shallow water equations and their application to realistic cases.

Weak Physics Informed Neural Networks for Geometry Compatible Hyperbolic Conservation Laws on Manifolds The shallow water equations and their application to realistic cases

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:27:02.755646Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation bddcb356-74f8-4c04-9f13-95b4deeb4ea7 · outbound

This paper cites A combined PDE and texture synthesis approach to inpainting.

Weak Physics Informed Neural Networks for Geometry Compatible Hyperbolic Conservation Laws on Manifolds A combined PDE and texture synthesis approach to inpainting

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:27:02.740818Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 23d3cb0b-7359-403e-aac2-513f904d271a · outbound

This paper cites Error bounds for approximations with deep ReLU neural networks in W s,p norms.

Weak Physics Informed Neural Networks for Geometry Compatible Hyperbolic Conservation Laws on Manifolds Error bounds for approximations with deep ReLU neural networks in W s,p norms

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:27:02.721807Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 4e96c7ea-0798-48cc-b506-349b6e26a450 · outbound

This paper cites Pre-training strategy for solving evolution equations based on physics-informed neural networks.

Weak Physics Informed Neural Networks for Geometry Compatible Hyperbolic Conservation Laws on Manifolds Pre-training strategy for solving evolution equations based on physics-informed neural networks

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:27:02.700835Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 5e9a6814-055f-4f69-902f-0730d2fd8f08 · outbound

This paper cites Numerical Prediction and Dynamic Meteorology.

Weak Physics Informed Neural Networks for Geometry Compatible Hyperbolic Conservation Laws on Manifolds Numerical Prediction and Dynamic Meteorology

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:27:02.681814Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 4c26e247-7715-426e-8e6f-f6bead9925b6 · outbound

This paper cites Error analysis of higher order trace finite element methods for the surface Stokes equation.

Weak Physics Informed Neural Networks for Geometry Compatible Hyperbolic Conservation Laws on Manifolds Error analysis of higher order trace finite element methods for the surface Stokes equation

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:27:02.663038Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 4ce93252-00ed-4f8f-9edb-87eb5a9fe90c · outbound

This paper cites Neural operator: Learning maps between function spaces with applications to PDEs.

Weak Physics Informed Neural Networks for Geometry Compatible Hyperbolic Conservation Laws on Manifolds Neural operator: Learning maps between function spaces with applications to PDEs

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:27:02.646342Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 233621b7-11c2-447e-bb81-ae544483f3e4 · outbound

This paper cites First order quasilinear equations in several independent variables.

Weak Physics Informed Neural Networks for Geometry Compatible Hyperbolic Conservation Laws on Manifolds First order quasilinear equations in several independent variables

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:27:02.626243Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 921162c8-8e2d-4301-8960-1cf661a684c2 · outbound

This paper cites Low dimensional approximation and generalization of mul- tivariate functions on smooth manifolds using deep ReLU neural networks.

Weak Physics Informed Neural Networks for Geometry Compatible Hyperbolic Conservation Laws on Manifolds Low dimensional approximation and generalization of mul- tivariate functions on smooth manifolds using deep ReLU neural networks

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:27:02.607077Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation a8423f95-b84c-4f0c-95bc-2c7ff27e2d74 · outbound

This paper cites Deep learning.

Weak Physics Informed Neural Networks for Geometry Compatible Hyperbolic Conservation Laws on Manifolds Deep learning

Reference 38

Resolution: unresolved; no resolver link, observed 2026-08-07T14:27:01.900112Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c8c6208c-5fb0-4cf0-bf89-b35c649992d6 · outbound

This paper cites Probability in Banach Spaces: Isoperimetry and Processes.

Weak Physics Informed Neural Networks for Geometry Compatible Hyperbolic Conservation Laws on Manifolds Probability in Banach Spaces: Isoperimetry and Processes

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:27:02.578257Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 2c55c21d-9806-4525-b1a1-e1f37ea96e64 · outbound

This paper cites an unresolved cited work.

Weak Physics Informed Neural Networks for Geometry Compatible Hyperbolic Conservation Laws on Manifolds Unresolved cited work

Reference 40

Resolution: unresolved; raw_fallback, observed 2026-08-07T14:27:02.557842Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 604165fd-4f38-462d-b9b6-9a51e9d40df0 · outbound

This paper cites Solving PDEs on spheres with physics-informed convolutional neural networks.Applied and Computational Harmonic Analysis, 74:101714, 2025.

Weak Physics Informed Neural Networks for Geometry Compatible Hyperbolic Conservation Laws on Manifolds Solving PDEs on spheres with physics-informed convolutional neural networks.Applied and Computational Harmonic Analysis, 74:101714, 2025

Reference 41

Resolution: unresolved; no resolver link, observed 2026-08-07T14:27:01.915107Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d1815591-f799-45a2-8d28-1eb5aa9065d8 · outbound

This paper cites Fourier neural operator for parametric partial differential equations.

Weak Physics Informed Neural Networks for Geometry Compatible Hyperbolic Conservation Laws on Manifolds Fourier neural operator for parametric partial differential equations

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:27:02.528982Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation cf4cb2fb-e5b7-4182-b03e-ce47a325735b · outbound

This paper cites Physics-informed neural operator for learning partial differential equations.

Weak Physics Informed Neural Networks for Geometry Compatible Hyperbolic Conservation Laws on Manifolds Physics-informed neural operator for learning partial differential equations

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:27:02.511558Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 8afe2c84-4baa-4262-8526-2ae773da1f04 · outbound

This paper cites Higher- order quasi-Monte Carlo training of deep neural networks.

Weak Physics Informed Neural Networks for Geometry Compatible Hyperbolic Conservation Laws on Manifolds Higher- order quasi-Monte Carlo training of deep neural networks

Reference 44

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:27:02.495635Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 8141ac37-3ea1-44d6-8978-fa2885aa6ad5 · outbound

This paper cites Deep network approxima- tion for smooth functions.

Weak Physics Informed Neural Networks for Geometry Compatible Hyperbolic Conservation Laws on Manifolds Deep network approxima- tion for smooth functions

Reference 45

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:27:02.477975Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 980b0b03-ad8e-4cdd-aaef-a3731738b0c7 · outbound

This paper cites Learning nonlinear operators via DeepONet based on the universal approximation theo- rem of operators.

Weak Physics Informed Neural Networks for Geometry Compatible Hyperbolic Conservation Laws on Manifolds Learning nonlinear operators via DeepONet based on the universal approximation theo- rem of operators

Reference 46

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:27:02.461017Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 888907dd-d71f-4ed7-a2a0-d239e609d775 · outbound

This paper cites Machine learn- ing for elliptic PDEs: Fast rate generalization bound, neural scaling law and minimax optimality.

Weak Physics Informed Neural Networks for Geometry Compatible Hyperbolic Conservation Laws on Manifolds Machine learn- ing for elliptic PDEs: Fast rate generalization bound, neural scaling law and minimax optimality

Reference 47

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:27:02.441882Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation e1a87840-3525-4cca-ad7c-2dadbf159791 · outbound

This paper cites Deep learning observables in computa- tional fluid dynamics.

Weak Physics Informed Neural Networks for Geometry Compatible Hyperbolic Conservation Laws on Manifolds Deep learning observables in computa- tional fluid dynamics

Reference 48

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:27:02.421900Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation a0e7fb00-7e97-4e32-b0a4-ddbd232ff1c6 · outbound

This paper cites A few notes on statistical learning theory.

Weak Physics Informed Neural Networks for Geometry Compatible Hyperbolic Conservation Laws on Manifolds A few notes on statistical learning theory

Reference 49

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:27:02.398112Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation c14e729e-5d7c-4bc5-98f3-674e7553212a · outbound

This paper cites Miranda, Jr., D.

Weak Physics Informed Neural Networks for Geometry Compatible Hyperbolic Conservation Laws on Manifolds Miranda, Jr., D

Reference 50

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:27:02.380857Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation be741034-7dc2-4a4a-af74-4c96e7a54b3c · outbound

This paper cites Estimates on the generalization error of physics-informed neural networks for approximating a class of inverse problems for PDEs.

Weak Physics Informed Neural Networks for Geometry Compatible Hyperbolic Conservation Laws on Manifolds Estimates on the generalization error of physics-informed neural networks for approximating a class of inverse problems for PDEs

Reference 51

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:27:02.363542Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 192fc81f-d68a-4692-9036-63b8cb8abc60 · outbound

This paper cites Enhancing accuracy of deep learning algo- rithms by training with low-discrepancy sequences.SIAM Journal on Numerical Analysis, 59(3):1811–1834, 2021.

Weak Physics Informed Neural Networks for Geometry Compatible Hyperbolic Conservation Laws on Manifolds Enhancing accuracy of deep learning algo- rithms by training with low-discrepancy sequences.SIAM Journal on Numerical Analysis, 59(3):1811–1834, 2021

Reference 52

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:27:02.345700Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation b974b4aa-a05b-4b5f-beb3-ba9908a98ad4 · outbound

This paper cites The imbedding problem for Riemannian manifolds.

Weak Physics Informed Neural Networks for Geometry Compatible Hyperbolic Conservation Laws on Manifolds The imbedding problem for Riemannian manifolds

Reference 53

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:27:02.324951Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation ec9afe48-de51-437e-8188-2c3ff6ecce79 · outbound

This paper cites Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations.

Weak Physics Informed Neural Networks for Geometry Compatible Hyperbolic Conservation Laws on Manifolds Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

Reference 54

Resolution: unresolved; no resolver link, observed 2026-08-07T14:27:01.981265Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3d3531f9-1893-40f3-9e42-00e8845c2814 · outbound

This paper cites Deep ReLU network approximation of functions on a manifold.

Weak Physics Informed Neural Networks for Geometry Compatible Hyperbolic Conservation Laws on Manifolds Deep ReLU network approximation of functions on a manifold

Reference 55

Resolution: unresolved; no resolver link, observed 2026-08-07T14:27:01.986053Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1ce5da4a-a39a-404d-885d-9d2b8f91ea6b · outbound

This paper cites Nonparametric regression using deep neural networks with ReLU activation function.

Weak Physics Informed Neural Networks for Geometry Compatible Hyperbolic Conservation Laws on Manifolds Nonparametric regression using deep neural networks with ReLU activation function

Reference 56

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:27:02.294729Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 04de31c2-061e-4884-96bc-7ca8531c1de8 · outbound

This paper cites Deep network approximation characterized by number of neurons.

Weak Physics Informed Neural Networks for Geometry Compatible Hyperbolic Conservation Laws on Manifolds Deep network approximation characterized by number of neurons

Reference 57

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:27:02.275934Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 58e9f9c7-5e5d-4237-ba31-ccc735666a06 · outbound

This paper cites On the convergence of physics informed neural networks for linear second-order elliptic and parabolic type PDEs.

Weak Physics Informed Neural Networks for Geometry Compatible Hyperbolic Conservation Laws on Manifolds On the convergence of physics informed neural networks for linear second-order elliptic and parabolic type PDEs

Reference 58

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:27:02.259017Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 0b75d88b-5603-4ba7-8673-119efff7b074 · outbound

This paper cites Topics in Variational PDE Image Segmentation, Inpainting and Denoising.

Weak Physics Informed Neural Networks for Geometry Compatible Hyperbolic Conservation Laws on Manifolds Topics in Variational PDE Image Segmentation, Inpainting and Denoising

Reference 59

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:27:02.243018Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 3e6802bc-0604-4ce9-9d38-6fa04c106ab0 · outbound

This paper cites Singular Integrals and Differentiability Properties of Functions.

Weak Physics Informed Neural Networks for Geometry Compatible Hyperbolic Conservation Laws on Manifolds Singular Integrals and Differentiability Properties of Functions

Reference 60

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:27:02.226542Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 1f9a3153-5c68-4712-b98c-83a7aaf808db · outbound

This paper cites Generating textures on arbitrary surfaces using reaction-diffusion.

Weak Physics Informed Neural Networks for Geometry Compatible Hyperbolic Conservation Laws on Manifolds Generating textures on arbitrary surfaces using reaction-diffusion

Reference 61

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:27:02.210210Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 1ce8e383-77c1-49cb-9fff-b35522665978 · outbound

This paper cites A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks.

Weak Physics Informed Neural Networks for Geometry Compatible Hyperbolic Conservation Laws on Manifolds A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks

Reference 62

Resolution: unresolved; no resolver link, observed 2026-08-07T14:27:02.026494Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 41537494-d115-47ab-8b3e-8849e715e52a · outbound

This paper cites Nearly optimal VC-dimension and pseudo- dimension bounds for deep neural network derivatives.

Weak Physics Informed Neural Networks for Geometry Compatible Hyperbolic Conservation Laws on Manifolds Nearly optimal VC-dimension and pseudo- dimension bounds for deep neural network derivatives

Reference 63

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:27:02.183543Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 3ade8c1f-aed7-46a4-af56-2a9a919b4f21 · outbound

This paper cites Error bounds for approximations with deep ReLU networks.

Weak Physics Informed Neural Networks for Geometry Compatible Hyperbolic Conservation Laws on Manifolds Error bounds for approximations with deep ReLU networks

Reference 64

Resolution: unresolved; no resolver link, observed 2026-08-07T14:27:02.040239Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 69334752-cf6c-4e45-bebb-81f19dfb4666 · outbound

This paper cites Weak adversarial networks for high-dimensional partial differential equations.

Weak Physics Informed Neural Networks for Geometry Compatible Hyperbolic Conservation Laws on Manifolds Weak adversarial networks for high-dimensional partial differential equations

Reference 65

Resolution: unresolved; no resolver link, observed 2026-08-07T14:27:02.046279Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3ebf389e-7f19-4d9e-bf0c-64e35c122d68 · outbound

This paper cites Classification with deep neural networks and logistic loss.

Weak Physics Informed Neural Networks for Geometry Compatible Hyperbolic Conservation Laws on Manifolds Classification with deep neural networks and logistic loss

Reference 66

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:27:02.142003Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation b1675a8b-afd8-4699-bb38-940cb43d4d2f · outbound

This paper cites Deep distributed convolutional neural networks: Universality.

Weak Physics Informed Neural Networks for Geometry Compatible Hyperbolic Conservation Laws on Manifolds Deep distributed convolutional neural networks: Universality

Reference 67

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:27:02.121391Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Coverage vector

Reference resolution

Outbound references

Pith citing papers