Paper Citation Record · LEDGER

Implicit differentiation with second-order derivatives and benchmarks in finite-element-based differentiable physics

As of 17 August 2026, this Paper Citation Record lists 35 of 35 outbound references and 0 inbound Pith citation observations for arXiv:2505.12646.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2505.12646 v1

Coverage vector

measured 35 of 35 reference resolution

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Pith citing papers itemized under the disclosed page cap.

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Source: cited_works

Reference resolution

35 of 35 outbound references displayed

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External citation measurements

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Outbound references

Observation 79d71d14-2a47-4f28-b429-bf95e55dd908 · outbound

This paper cites The Elements of Differentiable Programming.

Implicit differentiation with second-order derivatives and benchmarks in finite-element-based differentiable physics The Elements of Differentiable Programming

Reference 1

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This paper cites Deep learning.

Implicit differentiation with second-order derivatives and benchmarks in finite-element-based differentiable physics Deep learning

Reference 2

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Observation 182a32a0-846b-4b5b-8715-2aac503ad514 · outbound

This paper cites Jax: composable transformations of python+ numpy programs.

Implicit differentiation with second-order derivatives and benchmarks in finite-element-based differentiable physics Jax: composable transformations of python+ numpy programs

Reference 3

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This paper cites PyTorch: An Imperative Style, High-Performance Deep Learning Library.

Implicit differentiation with second-order derivatives and benchmarks in finite-element-based differentiable physics PyTorch: An Imperative Style, High-Performance Deep Learning Library

Reference 4

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This paper cites Jax-fluids: A fully-differentiable high-order computational fluid dynamics solver for compressible two-phase flows.

Implicit differentiation with second-order derivatives and benchmarks in finite-element-based differentiable physics Jax-fluids: A fully-differentiable high-order computational fluid dynamics solver for compressible two-phase flows

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This paper cites Machine learning–accelerated computational fluid dynamics.Proceedings of the National Academy of Sciences, 118(21):e2101784118, 2021.

Implicit differentiation with second-order derivatives and benchmarks in finite-element-based differentiable physics Machine learning–accelerated computational fluid dynamics.Proceedings of the National Academy of Sciences, 118(21):e2101784118, 2021

Reference 6

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Observation f42b0cee-6ea8-4971-a309-10c658ac4f12 · outbound

This paper cites Jax md: a framework for differentiable physics.

Implicit differentiation with second-order derivatives and benchmarks in finite-element-based differentiable physics Jax md: a framework for differentiable physics

Reference 7

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Observation db174bb1-4bfd-47e1-900f-175b84e8ac63 · outbound

This paper cites Simplifying fft-based methods for solid mechanics with au- tomatic differentiation.

Implicit differentiation with second-order derivatives and benchmarks in finite-element-based differentiable physics Simplifying fft-based methods for solid mechanics with au- tomatic differentiation

Reference 8

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This paper cites Neural-integrated meshfree (nim) method: A differentiable programming-based hybrid solver for computational mechanics.

Implicit differentiation with second-order derivatives and benchmarks in finite-element-based differentiable physics Neural-integrated meshfree (nim) method: A differentiable programming-based hybrid solver for computational mechanics

Reference 9

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This paper cites Jax-bte: a gpu-accelerated differentiable solver for phonon boltzmann transport equations.

Implicit differentiation with second-order derivatives and benchmarks in finite-element-based differentiable physics Jax-bte: a gpu-accelerated differentiable solver for phonon boltzmann transport equations

Reference 10

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Observation 27a1e552-dffb-4313-be47-25d844582147 · outbound

This paper cites Adjoint sensitivity analysis for differential-algebraic equations: The adjoint DAE system and its numerical solution.

Implicit differentiation with second-order derivatives and benchmarks in finite-element-based differentiable physics Adjoint sensitivity analysis for differential-algebraic equations: The adjoint DAE system and its numerical solution

Reference 11

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Observation 0b9f7657-4f7d-4e67-be9a-1836828d9b8d · outbound

This paper cites Efficient and modular implicit differentia- tion.

Implicit differentiation with second-order derivatives and benchmarks in finite-element-based differentiable physics Efficient and modular implicit differentia- tion

Reference 12

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This paper cites Jax-fem: A differentiable gpu-accelerated 3d finite element solver for automatic inverse design and mechanistic data science.

Implicit differentiation with second-order derivatives and benchmarks in finite-element-based differentiable physics Jax-fem: A differentiable gpu-accelerated 3d finite element solver for automatic inverse design and mechanistic data science

Reference 13

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Observation 378a72fb-0c6f-4b23-8629-6e81efe7f736 · outbound

This paper cites The finite element method: linear static and dynamic finite element analysis.

Implicit differentiation with second-order derivatives and benchmarks in finite-element-based differentiable physics The finite element method: linear static and dynamic finite element analysis

Reference 14

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Observation 493b3435-75bb-4aa4-b3df-f2b83f8e6dfc · outbound

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Implicit differentiation with second-order derivatives and benchmarks in finite-element-based differentiable physics springer, 2019

Reference 15

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Observation aa61bdad-b7af-42ce-9767-110ff82f17d2 · outbound

This paper cites Meshfree methods: moving beyond the finite element method.

Implicit differentiation with second-order derivatives and benchmarks in finite-element-based differentiable physics Meshfree methods: moving beyond the finite element method

Reference 16

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Observation 78317ade-f3ab-4477-8b05-7298abe66564 · outbound

This paper cites Optimal solvers for pde-constrained optimization.

Implicit differentiation with second-order derivatives and benchmarks in finite-element-based differentiable physics Optimal solvers for pde-constrained optimization

Reference 17

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Observation 37bfb910-3a6f-4fd4-bb80-cc21a4ad8a0a · outbound

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Implicit differentiation with second-order derivatives and benchmarks in finite-element-based differentiable physics Function minimization by conjugate gradients

Reference 18

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Implicit differentiation with second-order derivatives and benchmarks in finite-element-based differentiable physics Newton-type minimization via the lanczos method

Reference 19

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Implicit differentiation with second-order derivatives and benchmarks in finite-element-based differentiable physics A reduced hessian method for large-scale constrained optimization

Reference 20

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Implicit differentiation with second-order derivatives and benchmarks in finite-element-based differentiable physics Numerical optimization

Reference 21

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This paper cites Fractional pde constrained optimization: An optimize- then-discretize approach with l-bfgs and approximate inverse preconditioning.

Implicit differentiation with second-order derivatives and benchmarks in finite-element-based differentiable physics Fractional pde constrained optimization: An optimize- then-discretize approach with l-bfgs and approximate inverse preconditioning

Reference 22

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Observation fa8bc6cc-4e5e-44be-80e3-5f7a49642747 · outbound

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Implicit differentiation with second-order derivatives and benchmarks in finite-element-based differentiable physics Discretize then optimize

Reference 23

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This paper cites A computational framework for infinite-dimensional bayesian inverse problems part i: The linearized case, with application to global seismic inversion.

Implicit differentiation with second-order derivatives and benchmarks in finite-element-based differentiable physics A computational framework for infinite-dimensional bayesian inverse problems part i: The linearized case, with application to global seismic inversion

Reference 24

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Observation e3be7835-9081-4b43-9710-56d2d85ea49d · outbound

This paper cites hippylib: An extensible software framework for large-scale inverse problems governed by pdes: Part i: Deterministic inversion and linearized bayesian inference.

Implicit differentiation with second-order derivatives and benchmarks in finite-element-based differentiable physics hippylib: An extensible software framework for large-scale inverse problems governed by pdes: Part i: Deterministic inversion and linearized bayesian inference

Reference 25

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This paper cites dolfin-adjoint 2018.1: automated ad- joints for fenics and firedrake.

Implicit differentiation with second-order derivatives and benchmarks in finite-element-based differentiable physics dolfin-adjoint 2018.1: automated ad- joints for fenics and firedrake

Reference 26

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Implicit differentiation with second-order derivatives and benchmarks in finite-element-based differentiable physics Adjoint optimization of pressurized membrane structures using automatic differentiation tools

Reference 27

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Observation 1f3b1e0d-af33-4eb0-bdc0-720ab3f7247f · outbound

This paper cites Mapped shape optimization method for the rational design of cellular mechanical metamaterials under large deformation.

Implicit differentiation with second-order derivatives and benchmarks in finite-element-based differentiable physics Mapped shape optimization method for the rational design of cellular mechanical metamaterials under large deformation

Reference 28

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Observation 567f7a0f-c6ba-4f20-803e-771b5055c4c5 · outbound

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Implicit differentiation with second-order derivatives and benchmarks in finite-element-based differentiable physics Principles of mathematical analysis

Reference 29

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Observation d13d8175-8617-4da2-b972-b48c7c5726c5 · outbound

This paper cites Sparser, Better, Faster, Stronger: Sparsity Detection for Efficient Automatic Differentiation.

Implicit differentiation with second-order derivatives and benchmarks in finite-element-based differentiable physics Sparser, Better, Faster, Stronger: Sparsity Detection for Efficient Automatic Differentiation

Reference 30

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Implicit differentiation with second-order derivatives and benchmarks in finite-element-based differentiable physics Algorithm 778: L-bfgs-b: Fortran subroutines for large-scale bound-constrained optimization

Reference 31

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Observation a075c673-6ff4-4d34-a0ea-306de3023c44 · outbound

This paper cites Scipy 1.0: fundamental algorithms for scientific computing in python.Nature methods, 17(3):261–272, 2020.

Implicit differentiation with second-order derivatives and benchmarks in finite-element-based differentiable physics Scipy 1.0: fundamental algorithms for scientific computing in python.Nature methods, 17(3):261–272, 2020

Reference 32

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This paper cites Non-contact reconstitution of the traction distribution using in- complete deformation measurements: Methodology and experimental validation.

Implicit differentiation with second-order derivatives and benchmarks in finite-element-based differentiable physics Non-contact reconstitution of the traction distribution using in- complete deformation measurements: Methodology and experimental validation

Reference 33

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Observation f8c8b446-0cef-4b37-8a61-3dadcc8d5a9e · outbound

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Implicit differentiation with second-order derivatives and benchmarks in finite-element-based differentiable physics Non-linear elastic deformations

Reference 34

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Observation 38bdfabc-a467-44da-8952-7b74e5fc380b · outbound

This paper cites Topology optimization: theory, methods, and appli- cations.

Implicit differentiation with second-order derivatives and benchmarks in finite-element-based differentiable physics Topology optimization: theory, methods, and appli- cations

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:35:27.981689Z

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