pith. sign in

arxiv: 2605.23172 · v2 · pith:2TU7QRT5new · submitted 2026-05-22 · 💻 cs.CE

Effective information gathering for ore estimation, evaluation and perspectives on adaptive sampling

Raymond Leung , Arman Melkumyan This is my paper

Pith reviewed 2026-05-25 03:00 UTC · model grok-4.3

classification 💻 cs.CE
keywords ore grade estimationGaussian processesadaptive samplinginformation valuedrill hole planninggeological uncertaintyproxy measuresspatial complexity
0
0 comments X

The pith

Gaussian Process models enable estimation of incremental drilling value via proxies from similar deposits without ground truth.

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

The paper develops a computational framework based on Gaussian Processes to evaluate the worth of additional drill-hole data for ore grade estimation. It derives performance curves that guide infill drilling spacing and shows that proxy measures drawn from analogous deposits or adjacent domains can quantify cost and reward without direct access to ground truth. In settings with geological discontinuities and mixed domains, the work compares regular grid sampling against adaptive strategies that target spatial complexity and posterior uncertainty. The approach avoids conditional simulations along with assumptions of stationarity and uncorrelated errors.

Core claim

The central claim is that incremental cost and reward of information gathering can be estimated using a proxy measure derived from Gaussian Process posterior predictions, drawing on insights from a similar deposit, adjacent bench or domain, without direct reliance on ground truth. This holds for both differentiated and mixed geological domains, with evaluation via structural similarity and the mean and uncertainty in the posterior predictive distribution for grade. The results indicate that adaptive sampling targeting spatial complexity can outperform regular grids where the latter is suboptimal.

What carries the argument

Gaussian Process posterior predictive distribution of ore grade mean and uncertainty, used to derive proxy measures of information value.

If this is right

  • Performance curves from the framework can directly inform in-fill drilling spacing decisions.
  • Proxy measures allow cost-reward analysis using data from similar deposits or adjacent benches.
  • Regular grid sampling is shown to be suboptimal in areas with discontinuities and heterogeneous composition.
  • Adaptive strategies that target spatial complexity narrow the gap to optimal sampling performance.
  • The methodology supports future use in exploration-exploitation settings involving sampling and machine learning.

Where Pith is reading between the lines

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

  • The proxy approach could support sequential decision-making during ongoing drilling campaigns rather than only pre-planned campaigns.
  • Similar value-of-information calculations might transfer to other spatial resource estimation tasks such as aquifer or soil contaminant mapping.
  • Combining the framework with online learning could enable real-time adjustment of sampling locations based on accumulating data.

Load-bearing premise

The Gaussian Process model can capture ore grade distributions and uncertainty in geologically complex areas with discontinuities without stationarity or uncorrelated error assumptions.

What would settle it

A comparison in a new deposit where proxy-derived estimates of incremental value are checked against the actual value measured after drilling and assaying additional holes.

Figures

Figures reproduced from arXiv: 2605.23172 by Arman Melkumyan, Raymond Leung.

Figure 1
Figure 1. Figure 1: Open-pit mining environment with a typical drill pattern on a drilled bench. Disclaimer: Image is AI [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Domain structure of the site (pit) considered in this study. It has an area of 1600 [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Sampling on a hexagonal lattice. (a) Spatial hierarchy with [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Image-based representation of raw JSD scores averaged over different drill pattern orientations [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Image of normalized metrics ξ (g,zRL) m,s . Left to Right: global distortion (JSD), spatial fidelity (F), interval tightness (I) 51.713 36.661 25.856 18.330 12.928 9.165 6.464 Average hole spacing (m) 1.000 1.039 1.059 1.088 1.132 1.198 1.296 1.444 1.667 2.000 2.039 2.059 2.088 2.132 2.198 2.296 2.444 2.667 3.000 3.039 3.059 3.088 3.132 3.198 3.296 3.444 3.667 4.000 4.039 4.059 4.088 4.132 4.198 4.296 4.44… view at source ↗
Figure 6
Figure 6. Figure 6: Performance curves for standardized metrics [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Performance curves for (left) waste and (right) mineralized domains [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Performance curve application scenarios Interpretation: The black curve and shaded envelop illustrate the highly variable nature of the results attributed to random sampling (RN). On average, it ranks as the worst no matter which measure is used. The red curve (GD) shows that regular grid sampling is an improvement over RN. The caveat is that the chosen locations are inherently non-embedded, since two trai… view at source ↗
Figure 9
Figure 9. Figure 9: Three-dimensional and cross-sectional views of two sub-volumes targeted in experiment 2. Both regions [PITH_FULL_IMAGE:figures/full_fig_p010_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Performance for different sampling strategies in region A and [PITH_FULL_IMAGE:figures/full_fig_p010_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Sampling strategies comparison: region A, 570-590m ( [PITH_FULL_IMAGE:figures/full_fig_p011_11.png] view at source ↗
read the original abstract

A computational/analytics framework for assessing the value of drill-hole information in ore grade estimation is described using Gaussian Process and statistics. A distinguishing feature is that it presents both a near-term and long-term vision, circumvents conditional simulations and avoids making rigid assumptions such as stationarity and uncorrelated errors. Two experiments are devised to cater for situations where geological domains are differentiated or mixed. In scenario 1, performance (learning) curves are obtained to inform in-fill drilling and spacing consideration consistent with current practice. Analysis shows it is possible to estimate the incremental cost and reward via a proxy measure without relying on the ground truth, using insights obtained from a similar deposit, adjacent bench or domain. Scenario 2 examines adaptive sampling strategies and focuses on applying these in geologically complex areas with discontinuities and heterogeneous composition. Evaluation is made based on structural similarity, the mean and uncertainty in the posterior predictive distribution for the grade. The results highlight situations where regular grid sampling is suboptimal, and demonstrate an adaptive strategy that targets spatial complexity is capable of narrowing this gap. The proposed methodology can potentially be used in the future in an exploration--exploitation setting that involves sampling, machine learning, reasoning and cooperation between robots with embodied intelligence on a mine site.

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 / 2 minor

Summary. The manuscript presents a Gaussian Process-based computational framework for evaluating the value of drill-hole information in ore grade estimation. It outlines a near-term vision using performance (learning) curves from two experiments (differentiated vs. mixed geological domains) to guide in-fill drilling and spacing, and a long-term vision for adaptive sampling in complex areas. Key claims include the ability to estimate incremental cost/reward via a proxy measure drawn from similar deposits or adjacent domains without ground truth, and that adaptive strategies targeting spatial complexity can outperform regular grids based on structural similarity and posterior predictive statistics. The approach avoids conditional simulations and assumptions such as stationarity or uncorrelated errors.

Significance. If the proxy-based estimation and adaptive sampling results hold with proper validation, the framework could offer a practical alternative to traditional geostatistical methods for optimizing drilling in mining, potentially reducing costs by informing decisions from analogous domains and enabling future embodied AI applications. The avoidance of rigid assumptions is a potential strength for heterogeneous deposits.

major comments (2)
  1. [Abstract / Scenario 1] Abstract and scenario 1 description: The central claim that 'it is possible to estimate the incremental cost and reward via a proxy measure without relying on the ground truth' using insights from a similar deposit lacks any definition of the proxy (e.g., which posterior statistics or similarity metrics), quantitative measure of required domain similarity, or validation against known ground truth values even in controlled cases. This is load-bearing for the near-term vision and in-fill drilling recommendations, yet no performance curves, error metrics, or transferability checks are described to support it.
  2. [Scenario 2] Scenario 2 evaluation: The assertion that adaptive sampling 'targets spatial complexity' and narrows the gap to regular grid sampling is based on structural similarity and posterior mean/uncertainty, but no quantitative comparison (e.g., specific error reductions, number of samples, or statistical tests) or handling of discontinuities is provided to substantiate superiority in geologically complex areas.
minor comments (2)
  1. [Abstract] The abstract mentions 'analysis shows' results but provides no data, tables, or figures; full manuscript should include explicit performance curves, similarity metrics, and validation details for reproducibility.
  2. [Methodology] Notation for Gaussian Process posterior predictive distribution and structural similarity measure should be defined explicitly with equations to clarify how uncertainty is quantified without stationarity assumptions.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. The comments highlight areas where additional clarity on definitions, metrics, and quantitative results would strengthen the presentation. We address each major comment below, indicating planned revisions where appropriate.

read point-by-point responses

  1. Referee: [Abstract / Scenario 1] Abstract and scenario 1 description: The central claim that 'it is possible to estimate the incremental cost and reward via a proxy measure without relying on the ground truth' using insights from a similar deposit lacks any definition of the proxy (e.g., which posterior statistics or similarity metrics), quantitative measure of required domain similarity, or validation against known ground truth values even in controlled cases. This is load-bearing for the near-term vision and in-fill drilling recommendations, yet no performance curves, error metrics, or transferability checks are described to support it.

    Authors: We agree that the abstract and Scenario 1 section would benefit from explicit definitions to support the proxy claim. The proxy measure is the posterior predictive mean and variance from the Gaussian Process fitted to data from the similar deposit (or adjacent domain), with similarity assessed through domain characteristics and structural metrics as used in the two experiments. The performance (learning) curves in Scenario 1 already illustrate incremental value estimation without ground truth. We will revise to add a dedicated paragraph defining the proxy, the specific similarity metrics, and any transferability aspects from the curves. Regarding validation against ground truth, the framework is intentionally designed to avoid reliance on it; however, we acknowledge that controlled-case checks would add rigor and will include a brief discussion of this limitation in the revision. revision: yes

  2. Referee: [Scenario 2] Scenario 2 evaluation: The assertion that adaptive sampling 'targets spatial complexity' and narrows the gap to regular grid sampling is based on structural similarity and posterior mean/uncertainty, but no quantitative comparison (e.g., specific error reductions, number of samples, or statistical tests) or handling of discontinuities is provided to substantiate superiority in geologically complex areas.

    Authors: We agree that more quantitative detail would improve the Scenario 2 presentation. The evaluation uses structural similarity together with posterior mean and uncertainty to show the adaptive strategy narrows the performance gap relative to grids in heterogeneous settings. The Gaussian Process covariance function accommodates discontinuities without stationarity assumptions. We will revise to include specific quantitative comparisons (error reductions, sample counts) and any applicable statistical tests, along with expanded text on discontinuity handling via the non-stationary kernel choices. revision: yes

Circularity Check

0 steps flagged

No significant circularity; no derivation chain or equations present

full rationale

The abstract and full-text placeholder contain no equations, derivations, fitted parameters presented as predictions, or self-citations. The central claim about a proxy measure for incremental cost/reward is described as an empirical result from 'analysis' and 'performance curves' in scenario 1, not a mathematical reduction that equals its inputs by construction. No load-bearing self-citation, uniqueness theorem, or ansatz smuggling is visible. The paper's methodology is framed as experimental evaluation using Gaussian Processes, with no evidence that any 'prediction' collapses to a fit or prior result from the same authors. This is the expected honest non-finding when no derivation steps are exhibited.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review provides no information on free parameters, axioms, or invented entities used in the framework.

pith-pipeline@v0.9.0 · 5743 in / 871 out tokens · 32741 ms · 2026-05-25T03:00:17.094256+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.