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arxiv: 2606.10873 · v1 · pith:Y5IQOCXDnew · submitted 2026-06-09 · 🧬 q-bio.QM

Spatial Model Selection and Uncertainty Quantification: Comparing Continuous and Discrete Wound Healing Models

John T. Nardini , Jana L. Gevertz This is my paper

Pith reviewed 2026-06-27 10:53 UTC · model grok-4.3

classification 🧬 q-bio.QM
keywords model selectionapproximate Bayesian computationwound healingpartial differential equationsagent-based modelsuncertainty quantificationspatial modelinginformation criteria
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The pith

Mean-field PDE models are often selected over true generative ABMs for spatial wound healing data.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces a model selection pipeline based on approximate Bayesian computation that performs parameter estimation, uncertainty quantification, and comparison between partial differential equation and agent-based models for spatial processes. Tests on artificial data generated by ABMs show similar parameter recovery across modalities but much lower uncertainty and over 1000 times faster computation for PDEs. Information criteria and forecasting accuracy frequently favor the mean-field PDE even when the ABM is the true source. On real public wound healing data the pipeline selects a PDE that includes cell pulling and a time delay, yet this model exhibits high parametric uncertainty. The work supplies a concrete method for choosing modeling modality when spatial biological data must be represented.

Core claim

We created a model selection pipeline that uses approximate Bayesian computations to perform parameter estimation, uncertainty quantification, and model selection using both information criteria and out-of-sample forecasting. Applying the pipeline to artificial datasets generated from ABMs reveals that while both modalities yield comparable parameter estimation performance, the ABM estimates exhibit higher uncertainty, and the PDE models compute more than 1,000× faster. Surprisingly, the mean-field PDE is often selected over the true generative ABM model using both information criteria and data forecasting. Applying the pipeline to public wound healing data indicates that a PDE model with ce

What carries the argument

The approximate Bayesian computation pipeline that estimates parameters, quantifies uncertainty, and ranks PDE versus ABM models via information criteria and out-of-sample forecasting.

If this is right

  • PDE and ABM modalities produce comparable parameter estimates on artificial data.
  • ABM parameter uncertainty is higher than PDE uncertainty for the same data.
  • PDE models run more than 1000 times faster than equivalent ABMs.
  • A PDE that includes cell pulling and a time delay is selected for public wound healing data.
  • The selected PDE model for wound data carries high parametric uncertainty.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The computational speed advantage of PDEs could allow routine exploration of larger spatial domains or longer time scales in biological modeling.
  • High parametric uncertainty in the best-ranked model suggests that additional experimental measurements at specific spatial locations would most effectively reduce ambiguity.
  • The pipeline could be applied to other spatial processes such as tumor invasion or bacterial colony growth to test whether the PDE preference is general.
  • Cases with high residual uncertainty may motivate development of hybrid models that retain discrete cell rules only where continuous approximations break down.

Load-bearing premise

Artificial data generated from ABMs are representative of real spatial biological processes and the pipeline compares the two modalities without systematic bias.

What would settle it

Re-running the pipeline on a fresh collection of ABM-generated artificial datasets and finding that information criteria and forecasting accuracy no longer favor the PDE would directly test whether the reported selection pattern holds.

Figures

Figures reproduced from arXiv: 2606.10873 by Jana L. Gevertz, John T. Nardini.

Figure 1
Figure 1. Figure 1: Model selection pipeline. Our ABC pipeline begins with the processed data, [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The scratch assay procedure (a) Schematic of the well population after the creation of an artificial [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Estimating cell density from an experimental image and subsequent ABM initialization. (a) To [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Uncertainty quantification for Artificial datasets 1-4. We compute 90% credible intervals (see [PITH_FULL_IMAGE:figures/full_fig_p014_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Uncertainty quantification for Artificial dataset 5. We compute marginal 90% credible intervals [PITH_FULL_IMAGE:figures/full_fig_p015_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Out-of-sample forecasting for the Artificial datasets using the [PITH_FULL_IMAGE:figures/full_fig_p019_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Out-of-sample forecasting for the Wound Healing datasets using the [PITH_FULL_IMAGE:figures/full_fig_p021_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Uncertainty quantification for the the Wound Healing datasets. We compute 90% credible intervals [PITH_FULL_IMAGE:figures/full_fig_p022_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Walltimes for 1,000 PDE and ABM model simulations. The shaded areas of the violin plot [PITH_FULL_IMAGE:figures/full_fig_p022_9.png] view at source ↗
read the original abstract

All data-driven modeling tasks (e.g., parameter estimation, uncertainty quantification, and data forecasting) require the selection of a mathematical model. An overlooked aspect of model selection is modality; for example, there are no guidelines on when to use a partial differential equation (PDE) model or an agent-based model (ABM) for spatial processes. To address this, we created a model selection pipeline that uses approximate Bayesian computations to perform parameter estimation, uncertainty quantification, and model selection (using both information criteria and out-of-sample forecasting). Applying the pipeline to artificial datasets (generated from ABMs) reveals that while both modalities yield comparable parameter estimation performance, the ABM estimates exhibit higher uncertainty, and the PDE models compute more than 1,000$\times$ faster. Surprisingly, the mean-field PDE is often selected over the true generative ABM model using both information criteria and data forecasting. Applying the pipeline to public wound healing data indicates that a PDE model with cell pulling and a time delay is the most appropriate model for this data, however, this model has high levels of parametric uncertainty. This methodology establishes a preliminary framework for selecting the appropriate modeling modality for spatial biological data.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The paper introduces an ABC-based pipeline for parameter estimation, uncertainty quantification, and modality selection (via information criteria and out-of-sample forecasting) between PDE and ABM models of spatial wound healing. On synthetic data generated from ABMs, it reports comparable parameter recovery but higher uncertainty and slower computation for ABMs, with the mean-field PDE frequently selected over the true generative ABM; on public wound-healing data it selects a PDE variant with cell pulling and time delay, albeit with high parametric uncertainty. The work positions this as a preliminary framework for choosing modeling modality in spatial biology.

Significance. If the comparability of the selection criteria between deterministic PDE and stochastic ABM modalities can be established, the pipeline would supply a concrete, reproducible method for modality choice that quantifies both predictive performance and computational cost, directly addressing an under-studied decision in spatial biological modeling.

major comments (2)
  1. [Model selection pipeline and Results on synthetic data] The headline result that the mean-field PDE is often selected over the true generative ABM (Abstract) rests on the unverified assumption that ABC-derived information criteria and forecasting scores place deterministic PDE and stochastic ABM likelihood approximations on a commensurate scale. Because ABM simulations retain intrinsic noise while PDE solutions are deterministic, any mismatch in how residual variability or effective degrees of freedom enter the ABC proxy likelihood or penalty terms could systematically favor the smoother PDE; the manuscript must demonstrate that this bias is absent or corrected before the “surprisingly” claim can be interpreted as evidence about biological modeling choice.
  2. [Methods and synthetic-data experiments] The artificial datasets are generated exclusively from ABMs (Abstract). While this tests recovery of the true modality, it leaves open whether the pipeline’s preference for PDE would persist if the data-generating process were itself a PDE with added observation noise; an additional cross-modality simulation study is required to confirm that the selection procedure does not embed an intrinsic modality bias.
minor comments (1)
  1. [Abstract and Results] The abstract states that PDE models compute “more than 1,000× faster,” but no corresponding timing table or hardware specification is referenced; a supplementary table reporting wall-clock times, number of ABC particles, and hardware would make the computational claim reproducible.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments, which help clarify the scope and limitations of our model selection pipeline. We address each major comment below and indicate the revisions we will make.

read point-by-point responses

  1. Referee: [Model selection pipeline and Results on synthetic data] The headline result that the mean-field PDE is often selected over the true generative ABM (Abstract) rests on the unverified assumption that ABC-derived information criteria and forecasting scores place deterministic PDE and stochastic ABM likelihood approximations on a commensurate scale. Because ABM simulations retain intrinsic noise while PDE solutions are deterministic, any mismatch in how residual variability or effective degrees of freedom enter the ABC proxy likelihood or penalty terms could systematically favor the smoother PDE; the manuscript must demonstrate that this bias is absent or corrected before the “surprisingly” claim can be interpreted as evidence about biological modeling choice.

    Authors: We agree that establishing commensurability of the ABC-based information criteria and forecasting scores between the deterministic PDE and stochastic ABM is essential for interpreting the modality selection results. Although both modalities are evaluated under the identical ABC framework (using simulation-based likelihood approximations for parameter estimation, WAIC-style criteria, and out-of-sample prediction error), the intrinsic noise in ABM trajectories versus the deterministic PDE solutions could indeed affect the scale of the approximated likelihoods and penalty terms. In the revision we will add an explicit discussion of this issue, together with sensitivity analyses that vary the ABC tolerance and summary statistics to test whether the observed preference for PDEs persists under different noise-handling regimes. These additions will qualify the “surprisingly” claim and provide the required demonstration that the selection is not an artifact of scale mismatch. revision: yes

  2. Referee: [Methods and synthetic-data experiments] The artificial datasets are generated exclusively from ABMs (Abstract). While this tests recovery of the true modality, it leaves open whether the pipeline’s preference for PDE would persist if the data-generating process were itself a PDE with added observation noise; an additional cross-modality simulation study is required to confirm that the selection procedure does not embed an intrinsic modality bias.

    Authors: The referee correctly notes that the current synthetic experiments only probe recovery when the ground truth is an ABM. While this design directly tests the surprising result that PDEs can be preferred even when the data are generated by an ABM, a symmetric experiment with PDE-generated data (plus realistic observation noise) is needed to confirm the absence of an intrinsic bias favoring PDEs. We will therefore add a cross-modality simulation study in the revised manuscript. We note that this will increase computational cost, but the additional experiments are feasible within the ABC pipeline already implemented. revision: yes

Circularity Check

0 steps flagged

No circularity; pipeline applies external criteria to independently generated data

full rationale

The paper generates artificial datasets from ABMs, then applies ABC for parameter estimation, UQ, and selection via information criteria plus out-of-sample forecasting to compare PDE vs. ABM modalities. No derivation step reduces by construction to its inputs (no self-definitional relations, no fitted parameters renamed as predictions, no load-bearing self-citations, no uniqueness theorems or ansatzes imported from prior author work). The central claim is an empirical outcome of applying the pipeline to external data, not a closed loop. The result is therefore self-contained against the stated benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review provides no details on specific free parameters, axioms, or invented entities; the pipeline relies on standard ABC and information criteria whose details are not specified.

pith-pipeline@v0.9.1-grok · 5744 in / 1259 out tokens · 36831 ms · 2026-06-27T10:53:58.778623+00:00 · methodology

discussion (0)

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