Pith. Sign in

RECORD

Consistent Point Data Assimilation in Firedrake and Icepack

PaperPDF from arXiv

data files

Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
X Bluesky LinkedIn Reddit Hacker News
Reuben W. Nixon-Hill, Daniel Shapero, Colin J. Cotter, David A. Ham

Mathematical Software · Submitted 12 Apr 2023

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We demonstrate, with examples in the fields of groundwater hydrology and glaciology, that a consistent formulation can increase the accuracy of results and aid discourse between modellers and observationalists.

how it is stated · asserted 0.99 read the record →

Comment (0) Read on arXiv ↗
Cite ▾
arXiv ID2304.06058 (version 5)
Pith IDA5OUD5BA, Pith's permanent record of this paper and its review
CitationColin J. Cotter, Daniel Shapero, David A. Ham, Reuben W. Nixon-Hill. "Consistent Point Data Assimilation in Firedrake and Icepack." arXiv:2304.06058 (2023). https://pith.science/paper/A5OUD5BA
Claim paper

The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Open the compiled record

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 7,656 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.12 · human participants 0.03 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.20 · mentions code or data availability 0.09.

The abstract, sentence by sentence

arXiv listing abstract v5. Results and the main claim are underlined; .

When estimating quantities and fields that are difficult to measure directly, such as the fluidity of ice, from point data sources, such as satellite altimetry, it is important to solve a numerical inverse problem that is formulated with Bayesian consistency. Otherwise, the resultant probability density function for the difficult to measure quantity or field will not be appropriately clustered around the truth. In particular, the inverse problem should be formulated by evaluating the numerical solution at the true point locations for direct comparison with the point data source. If the data are first fitted to a gridded or meshed field on the computational grid or mesh, and the inverse problem formulated by comparing the numerical solution to the fitted field, the benefits of additional point data values below the grid density will be lost. We demonstrate, with examples in the fields of groundwater hydrology and glaciology, that a consistent formulation can increase the accuracy of results and aid discourse between modellers and observationalists. To do this, we bring point data into the finite element method ecosystem as discontinuous fields on meshes of disconnected vertices. Point evaluation can then be formulated as a finite element interpolation operation (dual-evaluation). This new abstraction is well-suited to automation, including automatic differentiation. We demonstrate this through implementation in Firedrake, which generates highly optimised code for solving Partial Differential Equations (PDEs) with the finite element method. Our solution integrates with dolfin-adjoint/pyadjoint, allowing PDE-constrained optimisation problems, such as data assimilation, to be solved through forward and adjoint mode automatic differentiation.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 When estimating quantities and fields that are difficult to measure directly, such as the fluidity of ice, from point data sources, such as satellite altimetry, it is important to solve a numerical inverse problem that is formulated with Bayesian consistency. background 1.00 0.07 0.08 asserted 0.98
s1 Otherwise, the resultant probability density function for the difficult to measure quantity or field will not be appropriately clustered around the truth. background 0.96 0.07 0.06 asserted 0.95
s2 In particular, the inverse problem should be formulated by evaluating the numerical solution at the true point locations for direct comparison with the point data source. method 0.53 0.10 0.12 asserted 0.97
s3 If the data are first fitted to a gridded or meshed field on the computational grid or mesh, and the inverse problem formulated by comparing the numerical solution to the fitted field, the benefits of additional point data values below the grid density will be lost. background 0.79 0.10 0.10 asserted 0.94
s4 We demonstrate, with examples in the fields of groundwater hydrology and glaciology, that a consistent formulation can increase the accuracy of results and aid discourse between modellers and observationalists. result 0.56 0.92 0.70 asserted 0.99
s5 To do this, we bring point data into the finite element method ecosystem as discontinuous fields on meshes of disconnected vertices. method 0.86 0.92 0.08 asserted 1.00
s6 Point evaluation can then be formulated as a finite element interpolation operation (dual-evaluation). method 0.97 0.67 0.06 asserted 0.93
s7 This new abstraction is well-suited to automation, including automatic differentiation. contribution 0.39 0.63 0.06 asserted 1.00
s8 We demonstrate this through implementation in Firedrake, which generates highly optimised code for solving Partial Differential Equations (PDEs) with the finite element method. method 0.69 0.67 0.08 asserted 1.00
s9 Our solution integrates with dolfin-adjoint/pyadjoint, allowing PDE-constrained optimisation problems, such as data assimilation, to be solved through forward and adjoint mode automatic differentiation. method 0.76 0.86 0.09 asserted 1.00

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from simulation or computation 0.99.

What was examined, and what was not

sources read
  • arXiv listing abstract v5
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

When estimating quantities and fields that are difficult to measure directly, such as the fluidity of ice, from point data sources, such as satellite altimetry, it is important to solve a numerical inverse problem that is formulated with Bayesian consistency. Otherwise, the resultant probability density function for the difficult to measure quantity or field will not be appropriately clustered around the truth. In particular, the inverse problem should be formulated by evaluating the numerical solution at the true point locations for direct comparison with the point data source. If the data are first fitted to a gridded or meshed field on the computational grid or mesh, and the inverse problem formulated by comparing the numerical solution to the fitted field, the benefits of additional point data values below the grid density will be lost. We demonstrate, with examples in the fields of groundwater hydrology and glaciology, that a consistent formulation can increase the accuracy of results and aid discourse between modellers and observationalists. To do this, we bring point data into the finite element method ecosystem as discontinuous fields on meshes of disconnected vertices. Point evaluation can then be formulated as a finite element interpolation operation (dual-evaluation). This new abstraction is well-suited to automation, including automatic differentiation. We demonstrate this through implementation in Firedrake, which generates highly optimised code for solving Partial Differential Equations (PDEs) with the finite element method. Our solution integrates with dolfin-adjoint/pyadjoint, allowing PDE-constrained optimisation problems, such as data assimilation, to be solved through forward and adjoint mode automatic differentiation.

Human review

How Pith checks papers → · Full audit of this paper →

How the literature uses it

2 arXiv papers cite this in 2 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 1 sentence without a confident label

Uses its method or tool 1 paper

What it cites · 1 sentence without a confident label

Uses the method or tool of 3 papers
Cites as background 1 paper
  • We build our $P0DG$ finite element space on top of in the same way we would any other mesh.[Other mesh types in Firedrake use the DMPlex data structure rather than DMSWARM as explained in [ref] .

    Efficient mesh management in Firedrake using PETSc-DMPlex · Firedrake implementation · 0.85

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.