March 28, 2025 Abstract After decades of evolution, the financial system has increasingly deviated from an idealized framework based on precise theorems. With the development of data science and machine intelligence, researchers are trying to digitalize and automate market prediction. However, existing methodologies struggle to represent the diversity of individuals and are regardless of the domino effects of interactions on market dynamics, leading to the poor performance facing abnormal market conditions where non-quantitative information dominates the market. To alleviate these disadvantages requires the introduction of knowledge about how non-quantitative information, like news and policy, affects market dynamics. This study investigates overcoming these challenges through rehearsing potential market trends based on the financial large language model agents whose behaviors are aligned with their cognition and analyses in markets. We propose a hierarchical knowledge architecture for financial large language model agents, integrating fine-tuned language models and specialized generators optimized for trading scenarios. For financial market, we develop an advanced interactive behavioral simulation system that enables users to configure agents and automate market simulations. In this work, we take commodity futures as an example to research the effectiveness of our methodologies. Our real-world case simulation succeeds in rehearsing abnormal market dynamics under geopolitical events and reaches an average accuracy of 3.4% across various points in time after the event on predicting futures price. Under normal market conditions, with corresponding news, our simulator also exhibits lower mean square error than series deep learning models and large language models in predicting three-day futures price of specific commodities. All experimental results demonstrate our method effectively leverages diverse information to simulate behaviors and their impact on market dynamics through systematic interaction. 1 Main The proliferation of financial derivatives in commodity markets, including forward contracts, futures, and options, has been primarily driven by the necessity for price risk mitigation. While these instruments enable investors to profit through finance, they have transformed commodity trading markets into complex human systems [1, 2, 3]. Due to its zero-sum properties, commodity futures represent a relatively straightforward segment within the financial system.

In various geosciences branches, including mineral exploration, geometallurgical characterization on established mining operations, and remote sensing, the regionalized input variables are spatially well-sampled across the domain of interest, limiting the scope of spatial uncertainty quantification procedures. In turn, response outcomes such as the mineral potential in a given region, mining throughput, metallurgical recovery, or in-situ estimations from remote satellite imagery, are usually modeled from a much-restricted subset of testing samples, collected at certain locations due to accessibility restrictions and the high acquisition costs. Our limited understanding of these functions, in terms of the multi-dimensional complexity of causalities and unnoticed dependencies on inaccessible inputs, may lead to observing changes in such functions based on their geographical location. Pooling together different response functions across the domain is critical to correctly predict outcome responses, the uncertainty associated with these inferred values, and the significance of inputs in such predictions at unexplored areas. This paper introduces the notion of a dual random field (dRF), where the response function itself is considered a regionalized variable. In this way, different established response models across the geographic domain can be considered as observations of a dRF realization, enabling the spatial inference and uncertainty assessment of both response models and their predictions. We explain how dRFs inherit all the properties from classical random fields, allowing the use of standard Gaussian simulation procedures to simulate them. These models are combined to obtain a mineral potential response, providing an example of how to rigorously integrate machine learning approaches with geostatistics.

Brazil's mining major Vale is set to start applying machine learning to identify new drilling targets at its Coleman nickel mine. Coleman Mine, which is the flagship asset of Vale in Ontario, Canada, is part of the company's base metals operations. Vale has selected technology company GoldSpot Discoveries to examine and analyse the vast amount of data acquired by it over decades of mining at Coleman. GoldSpot Discoveries' team of geologists and data scientists will also discover previously unrecognised data trends, which may point to unknown areas of in-depth mineralisation. By using its geoscience and machine science expertise, GoldSpot Discoveries' team will clean, unify and analyse exploration data from Vale's Coleman Mine.

We treat the problem of estimation of orientation parameters whose values are invariant to transformations from a spherical symmetry group. Previous work has shown that any such group-invariant distribution must satisfy a restricted finite mixture representation, which allows the orientation parameter to be estimated using an Expectation Maximization (EM) maximum likelihood (ML) estimation algorithm. In this paper, we introduce two parametric models for this spherical symmetry group estimation problem: 1) the hyperbolic Von Mises Fisher (VMF) mixture distribution and 2) the Watson mixture distribution. We also introduce a new EM-ML algorithm for clustering samples that come from mixtures of group-invariant distributions with different parameters. We apply the models to the problem of mean crystal orientation estimation under the spherically symmetric group associated with the crystal form, e.g., cubic or octahedral or hexahedral. Simulations and experiments establish the advantages of the extended EM-VMF and EM-Watson estimators for data acquired by Electron Backscatter Diffraction (EBSD) microscopy of a polycrystalline Nickel alloy sample.

This paper considers statistical estimation problems where the probability distribution of the observed random variable is invariant with respect to actions of a finite topological group. It is shown that any such distribution must satisfy a restricted finite mixture representation. When specialized to the case of distributions over the sphere that are invariant to the actions of a finite spherical symmetry group $\mathcal G$, a group-invariant extension of the Von Mises Fisher (VMF) distribution is obtained. The $\mathcal G$-invariant VMF is parameterized by location and scale parameters that specify the distribution's mean orientation and its concentration about the mean, respectively. Using the restricted finite mixture representation these parameters can be estimated using an Expectation Maximization (EM) maximum likelihood (ML) estimation algorithm. This is illustrated for the problem of mean crystal orientation estimation under the spherically symmetric group associated with the crystal form, e.g., cubic or octahedral or hexahedral. Simulations and experiments establish the advantages of the extended VMF EM-ML estimator for data acquired by Electron Backscatter Diffraction (EBSD) microscopy of a polycrystalline Nickel alloy sample.