Scientific Foundation

BRZ Quantum Mining grounds its technology in rigorous principles of probabilistic modelling, decision theory and sequential planning under uncertainty. Our approach is based on the understanding that subsurface resource exploration and development are not static problems, but dynamic processes requiring progressive decisions based on partial and continuously updated information.

Using Bayesian frameworks, partially observable Markov decision processes (POMDPs), and advanced closed-loop planning methods, BRZ integrates geological modelling, data inversion and predictive simulation into a single coherent framework. This architecture enables the evaluation of the value of information for each new measurement and the optimization of entire sequences of data acquisition, systematically and economically reducing uncertainty.

The following sections present the conceptual foundations, methodological formulation and illustrative cases that demonstrate the robustness of this approach, including applications in synthetic two-dimensional settings and generalizations to real-world mineral and energy exploration scenarios.

Sequential Decision-Making Under Uncertainty

Geoscientific models are based on geoscientific data; therefore, building better models — in the sense of achieving more accurate predictions — often requires acquiring additional data.

In decision theory, questions regarding which additional data are expected to best improve predictions and decisions fall within the domain of value of information and optimal Bayesian experimental design. However, these approaches typically optimize only a single data acquisition campaign at a time.

In many real-world scenarios — particularly in Earth resource exploration — it is necessary to plan long sequences of data acquisition campaigns. Geoscientific data collection can be costly and time-consuming, requiring effective campaign planning to allocate resources optimally. Each measurement in a data acquisition sequence has the potential to inform where best to take subsequent measurements; however, directly optimizing a closed-loop sequence of measurements requires solving an intractable combinatorial problem.

In this work, we formulate sequential geoscientific data acquisition as a partially observable Markov decision process (POMDP). We then present methodologies to solve the sequential problem using Monte Carlo planning methods.

We demonstrate the effectiveness of the proposed approach in a simple synthetic 2D exploration problem. Results show that the sequential approach significantly outperforms conventional methods in reducing uncertainty. Although discussed in the context of mineral exploration, this approach is likely applicable to other geoscientific modelling challenges.

Theoretical and Geostatistical Foundations

Mineral Exploration as a Sequential Decision Problem

Mineral exploration requires making sequential decisions about what type of data to acquire, where to collect it and at what resolution, with the objective of identifying economically viable deposits. In other words, it is a problem of sequential decision-making under uncertainty.

These problems have been studied across geosciences, but often within non-sequential frameworks. Spatial experimental design optimization is well established. McBratney (1981) described methods for optimal sampling design based on Matheron’s theory of regionalized variables (1971), modelling spatial dependence using semivariograms. In the 1990s, extensive debate emerged in soil science regarding the adaptation of geostatistics and its role in optimal survey design.

Geostatistics has also been applied to environmental monitoring. However, geostatistical methods are often non-Bayesian, which can be a limitation when spatial structures (such as variograms) are themselves uncertain. Researchers such as Diggle and Lophaven (2006) developed Bayesian approaches for optimal spatial design.

Drilling Optimization

Drilling and Resource Delineation

Optimal drillhole placement in mineral exploration and mining has received significant attention. Some methodologies aim to minimize uncertainty in spatial properties using geostatistical algorithms. Others rely on decision theory and value of information concepts to quantify the economic value of acquired data.

Here, we emphasize the sequential nature of the problem and demonstrate that sequential data acquisition is superior to non-sequential approaches — a concept discussed since the 1970s.

Closed-Loop Planning

Sequential Planning Methods

The core challenge lies in the exponential growth of possible sequences. For example, planning 10 campaigns across 100 potential locations results in more than 17 billion possible sequences. Many problems require more than 10 acquisition steps to identify economically viable deposits.

Sequential planning methods determine each action after observing the outcome of the previous one. This can be done in:

Open-loop mode: optimizes each action based on immediate return, without considering future impact
Closed-loop mode: optimizes actions to maximize the expected return of the entire sequence

Closed-loop methods generally outperform open-loop approaches but require significantly greater computational effort.

Recent approaches include Bayesian optimization, receding horizon control and particle swarm optimization. While viable, these methods are suboptimal.

Closed-loop approaches, by contrast, leverage reinforcement learning, dynamic programming and Monte Carlo planning, identifying optimal sequences through interaction with simulated environments. These methods have achieved state-of-the-art performance in domains such as autonomous driving (Brechtel et al., 2014) and robotic control (Grigorescu et al., 2020).

Few works have applied these approaches to resource exploration. Torrado et al. (2017) proposed a Monte Carlo planning method for sequential reservoir development. This work represents one of the first general approaches to optimal closed-loop decision-making applied to sequential geoscientific data acquisition.

Illustrative Case

Sequential Data Acquisition in Resource Exploration

We illustrate the framework using an analogue case containing key elements of real exploration planning. The methodology is designed to be modular, allowing components such as inverse modelling, geological modelling and forward data simulation to be replaced without affecting the sequential acquisition framework.

We focus on the exploration of subsurface ore bodies. The problem definition includes:

A representation of the current state of knowledge about the physical world
A description of existing or planned data acquisition
Rewards and costs associated with the exploration process

Subsurface knowledge and uncertainty are typically represented as probability distributions over system parameters. Grid-based models describing geological, geophysical and geochemical properties may be too high-dimensional for direct decision-making.

A realization (in geostatistical terms) represents a plausible configuration of the physical world. A set of realizations provides a practical way to represent subsurface uncertainty, where variability across realizations reflects uncertainty.

Ore bodies can be difficult to identify due to multiple factors. In geophysical surveys, many geological features can mimic ore signatures. Additionally, ore bodies are rarely ideal anomalies within homogeneous environments, as tectonic, metamorphic and sedimentary processes may have altered their structure.

We construct an analogue scenario to capture these complexities. While illustrated in 1D, the methodology extends to 2D and 3D.

Mineralization is represented as a unimodal function, though multiple peaks may exist
Background geological variation is modelled as a structured Gaussian process
The sum of mineralization and background variation produces the measurable signal

When a threshold is exceeded, the resulting region defines the economic target (“ore body”), characterized here by volume.

Measurements provide indirect information about economic parameters. While they do not directly observe these values, they reduce uncertainty, typically quantified using Bayesian methods.

Instead of traditional conditional geostatistical simulation, we solve Bayesian inverse problems to jointly infer mineralization and background fields. Measurements are assumed to have negligible noise but limited spatial coverage.

2D Case Study

We test the methodology in a two-dimensional analogue. Mineralization is parameterized by a width parameter σ, assumed to follow a uniform distribution. Geological variation is modelled as a Gaussian process.

The central question becomes:

What is the optimal sequence of data acquisition to inform the decision to mine or not, based on whether the deposit exceeds a minimum economic threshold?

Conclusions and Outlook

We presented a Bayesian framework for sequential decision-making in geoscientific modelling through data acquisition planning, applied to mineral exploration. The problem is formulated as a POMDP and solved using hierarchical Bayesian belief models with particle filtering, Gaussian process regression and Monte Carlo tree search (POMCPOW).

Results show that closed-loop sequential approaches significantly outperform conventional grid-based methods. Recommended measurements improved accuracy and reduced uncertainty much faster, leading to shorter and more efficient campaigns.

The methodology is general and applicable across multiple domains of resource exploration. The specific belief models and solvers used are not mandatory, allowing flexibility in implementation.