Sub-Surface Mineral Prospectivity Modelling

Full waveform inversion (FWI) estimates subsurface velocity from seismic recordings, but its ill-posedness and nonlinearity make accurate reconstruction strongly dependent on initialization and prior information. Diffusion posterior sampling provides a learned geological prior, yet directly coupling its denoiser to the nonlinear wave solver can yield unreliable physical guidance. We propose Physical-State-Guided Diffusion Sampling (PSG), which couples a persistent physical velocity to the diffusion prior through a Gaussian bridge. The physical state is refined by waveform fitting regularized by the denoised velocity, and in turn guides the reverse diffusion process. This formulation separates the wave-equation and denoiser gradients while preserving conventional FWI initialization and accumulated optimization history. On four OpenFWI families, PSG's terminal denoised estimates outperform classical and diffusion-based baselines under clean and missing-trace acquisitions and maintain strong structural recovery under measurement noise. Repeated stochastic runs preserve the dominant geological structures, with ensemble variability concentrated near geological interfaces and positively associated with local inversion error. A frozen OpenFWI-trained prior further supports inversion of the larger Marmousi, Overthrust, and BP2004 Salt models, recovering complex geological structures without retraining.

The research explores the pioneering integration of Physics-Informed Neural Networks (PINNs) into the domain of Ground-Penetrating Radar (GPR) data prediction. This research presents a detailed development framework for a specialized PINN model, proficient at interpreting and forecasting GPR data, much like how medical imaging models predict tumor behavior. By harnessing the synergy between deep learning algorithms and the physical laws governing subsurface structures or in medical terms, human tissues the model effectively embeds the physics of electromagnetic wave propagation into its architecture. This ensures that predictions not only align with fundamental physical principles but also mirror the precision needed in medical diagnostics for detecting and monitoring tumors. The suggested deep learning structure comprises three components: a CNN, a spatial feature channel attention (SFCA) mechanism, and ConvLSTM, along with temporal feature frame attention (TFFA) modules. The attention mechanism computes channel attention and temporal attention weights using self-adaptation, thereby fine tuning the visual and temporal feature responses to extract the most pertinent and significant visual and temporal features. By integrating physics directly into the neural network, our model has shown enhanced accuracy in forecasting GPR data. This improvement is vital for conducting effective assessments of bridge deck conditions and other evaluations related to civil infrastructure. The use of Physics Informed Neural Networks (PINNs) has demonstrated the potential to transform the field of Non-Destructive Evaluation (NDE) by enhancing the precision of infrastructure deterioration predictions. Moreover, it offers a deeper insight into the fundamental mechanisms of deterioration, viewed through the prism of physics-based models.

Automated detection of subsurface cavities from Ground Penetrating Radar (GPR) is most difficult in soft, high-water-content ground, where conductive, water-saturated soil attenuates the signal and degrades cavity reflections, yet this is also the condition under which cavities most readily form. This paper proposes TriView-YOLO, a multi-view YOLOv12 detector for road cavity screening in such ground. Three co-registered views (longitudinal B-scan, horizontal C-scan, and cross-section B-scan) form a 9-channel input fused by a TripleInputConv layer that replaces the YOLOv12 stem; the rest of the network is unchanged, and bounding boxes are required on the longitudinal view only. Training used 1,600 expert-verified field samples, principally metropolitan road surveys of Bangkok, Thailand, acquired with a vehicle-mounted multichannel three-dimensional GPR mobile mapping system, with surveys over the firmer subgrades of Japan added to training and validation only. The test set comes exclusively from the Bangkok surveys, over soft marine clay with 80-140% water content and a water table at 1-2 m depth, a ground condition for which no dedicated deep learning cavity-detection evaluation has been reported. On this unaugmented, field-only test set, split randomly within surveys, the proposed model attains mAP50 of 0.558 +/- 0.028 over three seeds at 23.6 GFLOPs and 3.1 ms per image. Ablations show that removing the auxiliary views lowers mAP50 and recall, whereas public and synthetic training images, DINOv3 features, larger model scale, and COCO pretraining bring no gain.

Gravimetry images subsurface density contrasts associated with geological structures, geothermal systems, and intrusive bodies. Recovering a three-dimensional density model from gravity observations is highly ill-posed because of its non-uniqueness, limited data coverage, and the attenuation of the gravity field with depth. Classical inversion methods rely on explicit regularization and parameter tuning, whereas supervised deep-learning approaches require representative gravity--density pairs that are rarely available. This paper proposes an unsupervised depth-aware implicit neural representation for 3D gravity inversion. The density volume is represented by multiple coordinate-based neural networks assigned to overlapping depth slabs and optimized directly from the observed gravity measurements through the sensitivity matrix. Slab-specific Fourier features, physics-based depth gains, and scheduled regularization provide structural priors without requiring labeled density models. Experiments on four synthetic scenarios show that the proposed method provides better overall performance in terms of RMSE, PSNR, and SSIM than the evaluated conventional and neural baselines. It also recovers more compact and spatially coherent density bodies, improves the separation of nearby anomalies, preserves internal structures, and reconstructs their vertical extent better. These results indicate that the proposed depth-aware formulation helps to mitigate the depth ambiguity inherent in gravity inversion. In the field experiment, where no ground-truth density model was available, the method produced compact, separated, and vertically coherent anomalies consistent with the observed gravity pattern.

In this paper, a parametric physics-informed neural network for solving the heterogeneous soil thermal problem with borehole heat exchangers (BHEs) as singular sources is developed. There are three novel features in the present framework; namely, (i) the singularity is naturally removed by using analytical line source models; (ii) using the explicit formulation for gradient thermal conductivity enables physics-informed learning of the parametrization featuring the conductivity; (iii) the learned correction is utilized as an efficient universal corrector via superposition principles. We first introduce the decomposition of the temperature change and transform the approximation of the entire heterogeneous response to the correction compensating the difference between the practical solution and idealized homogeneous approximation. In such a way, the delta function singularity is excluded and the bulk heat transfer is captured for the sake of facilitating the effective training of the neural network. The original problem is then reformulated as a governing correction diffusion or advection-diffusion equation subject to a homogeneous initial condition. The linearly varying thermal conductivity is used to model the soil heterogeneity. We propose a physics-informed neural network to approximate a universal corrector with respect to a single borehole with unit heat extraction rate. As a result, the network is trained by minimizing the physics-informed and data-anchored loss function that is evaluated for sampled conductivity parameters on adaptively selected training points. In addition, we include the location indicator function regarding the source as a feature input of network and find that it helps the network to process the local information. We perform numerical tests to exhibit the effectiveness of the proposed method based on three different analytical models.

Clandestine tunneling beneath oil and gas pipelines enables fuel theft, smuggling, and sabotage, yet conventional monitoring detects damage only after a pipeline has been compromised. Ground-penetrating radar (GPR) can image such tunnels non-invasively, but manual radargram interpretation does not scale to continuous corridor surveillance, and supervised detectors require tunnel examples that are scarce in practice. We present a fully unsupervised detection pipeline trained exclusively on normal subsurface radargrams collected at a purpose-built field site containing three buried tunnels at 1.5-3 m depth. A denoising convolutional autoencoder learns the structure of anomaly-free ground; at inference, tunnels are flagged by reconstruction error. Our central contribution is a depth-restricted top-k anomaly score, which pools the highest reconstruction errors only within the depth band where tunnels can physically occur. This physically motivated rule raises AUC from 0.986 to 0.994 and cuts missed detections from 74 to 17 of 634 tunnel windows, relative to whole-image scoring, without any retraining or labels. We further show that the optimal top-k fraction interacts with the depth restriction - 1% pooling is best on full images, 5% once scoring is depth-restricted - and that spatial voting across overlapping survey windows helps weak per-image detectors but offers no benefit once the scoring rule is strong. The final system attains AUC 0.994, F1 0.975, recall 0.973, and precision 0.976 on 1,600 field test windows spanning 55 survey lines, at a 1.6% false-alarm rate, using no tunnel labels for training, scoring, or threshold calibration.

In this article, we present dynamic modeling, gait synthesis, and feedback control design for a modular novel subsurface robot, designed for human-free subsurface exploration and excavation. The subsurface propagator design is based on two major aspects: 1) anchor and propel movement like an earthworm and 2) excavation similar to tunnel boring machines. This design is decoupled into five separate modules: one drill head to excavate and create cavity for propagation, two modules to anchor the robot, and two modules to enable propagation of the body. In order to design a controller for each of the modules, dynamic models using the Euler-Lagrange framework are developed. These mathematical models are used as a baseline to design controlled decoupled operation of the different joint movements. The operation of robotic assembly is constructed via a centralized state machine for gait synthesis with integration of the designed feedback controller. The controllers are tested on the real robot geometry to aid sim-to-real integration: A physics-based Unity simulation using a CAD model of the robot and integration of the trained controller via ROS verifies the performance of the robot. The experimental results demonstrate that the proposed design, controllers and the gait synthesis strategy together are capable of anchoring the robot in place and creating an total advancement of 30,mm into the soil after completing 3 gait cycles.

We propose a self-supervised pretraining framework for learning sub-surface scattering (SSS) light transport representations from minimal input. Our method leverages a stereo projector-camera setup that captures only eight high-frequency phase-shift profilometry (PSP) images per view to pretrain an encoder in a multi-view, multi-object setting. We introduce a tailored augmentation strategy for PSP-based SSS data, and show that it significantly outperforms standard ImageNet-style augmentations for SSL pretraining. The pretrained encoder learns generalizable SSS representations that transfer effectively to downstream tasks, including spatially varying relighting and representation evaluation using a kNN classifier. Combined with a decoder, the model reconstructs dense scattering footprint responses, trained using a dedicated cost function that improves accuracy, particularly for anisotropic footprints. Despite using only eight input images per view, our approach generalizes to unseen objects with complex geometry and material properties, achieving high-fidelity reconstructions while requiring orders of magnitude fewer images than prior methods.

In this paper we present a spectral optical inversion for skin for path tracing-based rendering of subsurface scattering. Skin is a complex multilayered medium, with appearance determined by the mixture of biophysical chromophores. However, current methods rely on medium homogeneization, with optical parameters obtained via albedo inversion from a reflectance texture and hand-tuned scattering distance and anisotropy. This results into significant art-skilled manual labor for authoring, and an inaccurate scattering profile for skin. To solve these problems, we generalize existing albedo inversion techniques, and propose a framework that predicts full-spectral skin scattering parameters from a single RGB diffuse albedo. Our method builds upon a new mixture-of-media representation, that approximates the aggregated multilayered appearance of skin by mixing the aggregated scattering of three uncorrelated media. We train a chained neural decoder that maps RGB diffuse albedo to the optical properties of the mixture of media, including anisotropy, scattering radius and scattering albedo. Then, we show this mixture can be used in a random-walk-based path tracer with minimal modifications, by simply randomly selecting the medium to traverse.

Karst aquifers provide critical freshwater resources but pose significant hazards due to their complex and poorly understood subsurface geometry. Mapping these environments is challenging because sonar data from underwater exploration is sparse and noisy, while navigation estimates suffer from drift limiting standard 3D reconstruction methods. We present a pipeline for reconstructing underwater karst conduits from a sonar profiler. We combine a continuous-time SLAM approach to correct trajectory drift with a novel two-stage deep learning method for surface reconstruction, producing an immersive and navigable 3D mesh for hydrogeological analysis.

Geosteering requires navigating a well trajectory through an unknown geological configuration, while sequentially updating decisions based on indirect measurements acquired during drilling. This work presents an uncertainty-aware geosteering framework that tightly integrates particle filtering for probabilistic subsurface interpretation with value-based reinforcement learning for sequential decision-making. Geological uncertainty ahead of the drill bit is represented explicitly through a particle filter (PF), enabling belief-informed control rather than deterministic trajectory correction. The framework couples PF belief updates with belief-informed decision policies and evaluates three decision-making options that operate under identical uncertainty representations: an interpretable Approximate Dynamic Programming (ADP) scheme, a Deep Q-learning baseline, and a Dual Deep Reinforcement Learning (Dual DRL) architecture trained with a target Q-network scheme for stability, using a dueling (value/advantage) decomposition for Q-value parameterization. Beyond final placement performance, we assess policy behavior using stability-oriented metrics that quantify steering smoothness over time, providing additional operational insight into how decision policies respond as uncertainty evolves. The framework is integrated with an API for validation within an industrial geosteering simulator under realistic measurement noise and drilling constraints. Using identical geological realizations, operational limits, and reward definitions across methods, the experiments provide a controlled and high-fidelity evaluation of how alternative decision policies behave throughout the drilling process, rather than evaluating performance solely from the final well trajectory.

Salt-dome delineation is a critical, high-impact task in subsurface geological interpretation, driving decisions in hydrocarbon exploration, reservoir modeling, and drilling safety. While convolutional encoder-decoder architectures have delivered significant improvements in automated salt segmentation, their widespread application is severely limited by data sovereignty concerns, dataset bias, and the scarcity of labeled seismic volumes. This paper introduces FedSaltNet, a Federated Learning (FL) framework explicitly engineered for robust, generalizable, and privacy preserving salt-dome segmentation. We couple a lightweight Small U-Net backbone, chosen for its efficiency and regularization properties with a novel Foreground-Weighted (FG-WEIGHTED) aggregation strategy designed to tackle domain-specific class imbalance. Through an extensive comparative study emulating non-IID conditions across four diverse seismic datasets (TGS, SEAM, F3, GBS), we demonstrate two critical findings: The FG-WEIGHTED algorithm effectively mitigates data heterogeneity, yielding a 4.0% relative improvement in Intersection over Union (IoU) over the best conventional FL method. The simple U-Net architecture proved essential, outperforming the higher capacity ResNet-18 U-Net variant by 166% in average IoU, underscoring the necessity of architectural simplicity in data-constrained federated environments. FedSaltNet provides a validated, high-performance solution that establishes the viability of federated deep learning for collaborative, next-generation subsurface interpretation.

Data assimilation (DA) in subsurface flow entails calibrating model parameters to match observed data, typically at wells, while preserving geological realism. Latent diffusion models (LDMs) provide efficient mappings from high-dimensional geological model space to a low-dimensional latent variable, reducing the dimensionality of the inverse problem while maintaining plausibility in posterior geomodels. However, the high nonlinearity in the LDM mapping may degrade the performance of Kalman-gain-based ensemble updates. We present a systematic comparison of DA algorithms applied to large-scale 3D channelized geomodels with hierarchical geological uncertainty. We compare model-space and latent-space DA using the ensemble smoother with multiple data assimilation (ESMDA), and demonstrate a key trade-off: model-space updates achieve significant uncertainty reduction but produce geologically unrealistic posterior models, while latent-space updates preserve realism but exhibit limited uncertainty reduction. Motivated by this, we explore rigorous Markov chain Monte Carlo (MCMC) and Sequential Monte Carlo (SMC) algorithms in the 3D-LDM latent space. To accommodate their high computational demands, we develop a fast surrogate flow model that approximates well-rate responses. MCMC and SMC are evaluated against ESMDA across three synthetic test cases, with DA performed in the LDM latent space. All models maintain geological realism due to the LDM parameterization. MCMC and SMC are consistent with one another and achieve lower data mismatch and more uncertainty reduction than latent-space ESMDA. Our overall results demonstrate that ensemble Kalman methods may provide overestimated posterior uncertainty with highly nonlinear parameterizations, while rigorous Monte Carlo sampling, enabled by fast surrogate models, can provide a more reliable alternative.

We present a method to acquire and estimate the sub-surface scattering properties of light transport at a highly detailed level by learning the pixel footprint response at each point on the object surface. The reconstruction leverages 3D scanning techniques as input to a U-Net CNN. A stereo projector-camera setup using phase-shifted profilometry (PSP) patterns efficiently captures the data for a variety of scattering objects. Reconstructing dense pixel footprints allows for relighting with arbitrary high-resolution projector patterns. The final output is a relit color image. Qualitative and quantitative comparison against illuminated real-world captured images demonstrate that the predicted footprints are almost identical to the actual responses. The same model is trained for multiple views across multiple objects such that the learned representations can be used to generalize to unseen sub-surface scattering materials as well.

Mineral prospectivity modelling (MPM) underpins exploration economics, yet most operational pipelines reduce to data-driven classifiers trained on shallow surface proxies. Such models are blind to the subsurface physics that actually localises ore: heat advection, fluid flow, and lithology-dependent precipitation. We present Korzhinskii-Net, a 2-D radial physics-informed neural network (PINN) that couples Darcy flow, advective-diffusive heat transport, and a softplus-saturated reaction rate into a single differentiable forward model, weakly supervised by surface and remote-sensing proxies. The network is named after Dmitri S. Korzhinskii (1899-1985), whose theory of infiltration metasomatism provides the physical scaffold. We evaluate Korzhinskii-Net on six ore provinces spanning three commodity classes - Udokan (sandstone-hosted Cu), Sukhoi Log, Olimpiada, and Berezovskoye (orogenic Au), Vorontsovskoye (Carlin-type Au), and Dalnegorsk (skarn polymetallic) - under a fair, leakage-controlled 5-fold cross-validation protocol with hard ring-shaped negatives and baseline proxy features disabled. Korzhinskii-Net attains a mean PR-AUC of 0.708 versus 0.235 for the strongest classical baseline (support vector machine), and a mean fractional rank of 0.036 versus 0.475. The improvement is consistent across all six provinces and three commodity systems, suggesting that physics-informed differentiable simulators, even when constrained only by global open-data proxies, can recover localisation patterns that pure feature-based learners systematically miss. We release the full pipeline and evaluation harness as open source.

Full waveform inversion (FWI) is the gold standard for subsurface imaging, with applications from carbon sequestration to energy and mineral exploration to earthquake hazard assessment. Machine learning approaches to FWI need field-scale, geologically diverse, and physically realistic training data, but existing resources such as Marmousi, SEAM, and OpenFWI fall short on spatial extent, temporal extent, geological diversity, and physical realism. We address these limitations with SubsurfaceGen, a GPU-accelerated generator for 3D velocity models and seismic data. Along with SubsurfaceGen, we release a paired dataset of 4,276 2D velocity slices, 5 s wavefields, and 8 s shot gathers drawn from 42 realistic, field-scale 3D velocity models, each spanning 10 km x 10 km laterally and 6.19 km deep at 10 m resolution. The dataset spans six geological settings -- four built with SubsurfaceGen and two drawn from prior sources -- relevant for carbon sequestration and hydrocarbon exploration. We use this dataset to evaluate neural operators on wavefield prediction and encoder-decoders on end-to-end velocity inversion, holding out one geological setting for out-of-distribution testing. These experiments surface failure modes at field-scale and demonstrate how SubsurfaceGen and the associated dataset can impact ML-based FWI.

Autonomous ground vehicles operating in shallow water or flood-prone terrains require dynamic models that account for hydrodynamic forces. However, the simulation and planning tools currently available either lack the physical fidelity or are too computationally expensive to run in real time. This work presents a per-surface neural network surrogate that bridges this gap by predicting geometry-resolved hydrodynamic forces at real-time rates, trained entirely on high-fidelity CFD data from two geometrically distinct vehicles. A vehicle specific Signed Distance Field (SDF) provides per-surface submergence inputs, allowing the model to resolve how loading varies with vehicle geometry, depth, and flow direction. On held-out CFD data, the surrogate achieves a longitudinal-force symmetric MAPE (sMAPE) of 13% and a vertical-force sMAPE of 3-12%, with inference running under 0.9,ms per sample. To evaluate the model under real-world conditions, water wading trials of a full-scale vehicle at different submersion depths are used. Motion capture derived kinematics serve as the surrogate inputs, and the resulting predictions are tested to reproduce known physical relationships between force, speed, and depth. The predicted drag follows quadratic speed scaling ($R^2 \geq 0.97$) and the buoyancy intercepts scale linearly with depth ($R^2 = 0.973$). Neither relationship is encoded in the model training loss, both emerge from the per-surface architecture summing individually predicted surface forces. The resulting framework provides a pathway for embedding physically grounded hydrodynamics into the simulation and planning loops that autonomous ground vehicles depend on in amphibious environments.

Distributed Acoustic Sensing (DAS) has emerged as a transformative technology for near-surface site characterization. When a vertical source is activated along the fiber, DAS measures only the in-line (radial) component of Rayleigh-wave motion. Dispersion data extracted from radial-component waveforms may differ from those obtained from vertical-component measurements, particularly under complex stratigraphic conditions. Hence, a component-consistent forward problem is desired when inverting radial-component DAS dispersion data to retrieve accurate shear wave velocity (Vs) profiles. This study presents a radial-component predominant-mode (RCPM) inversion framework designed for DAS-based surface-wave analysis that explicitly accounts for source-receiver directivity and modal sensitivity of the Rayleigh-wave radial component. The proposed approach matches measured dominant radial dispersion trends with the theoretical mode exhibiting the maximum modal participation. As a result, the RCPM framework eliminates the need for explicit modal indexing, provides a component-consistent interpretation of radial-component dispersion data, and substantially reduces reliance on subjective analyst-driven modal interpretations. The RCPM approach is systematically evaluated using three synthetic ground models and two field DAS datasets. The synthetic results demonstrate that modal energy distribution differs significantly between vertical and radial components in the presence of strong velocity contrasts and velocity reversals, and that conventional inversion approaches may misinterpret modal behavior, resulting in less accurate Vs profiles. In contrast, the RCPM method consistently captures the correct modal response and yields reliable Vs profiles. Application to two field DAS datasets further demonstrates good agreement between the inverted Vs profiles and independent invasive borehole measurements.

Continental-scale knowledge of subsurface temperature is limited by the cost and sparsity of borehole measurements, but such information is essential for geothermal resource assessment and for understanding heat transport in the shallow crust. The thermal field reflects the interaction between lithology, crustal structure, radiogenic heat production, and advective fluid flow, sometimes producing sharp anomalies that are smoothed by conventional interpolation or difficult to capture with physical models. Here we introduce In-Context Earth, a transformer-based model that uses sparse local borehole observations as geological context to predict continuous temperature-at-depth fields with calibrated uncertainty. In the contiguous United States, the model achieves a mean absolute error of 4.7 °C, outperforming the physics-informed Stanford Thermal Model, a model based on AlphaEarth embeddings, the multimodal Transparent Earth model, and universal kriging, while resolving sharper thermal gradients in geothermal provinces. Its uncertainty estimates are well calibrated, with a Kolmogorov-Smirnov statistic of 2.5%. Without finetuning, the model adapts to Alberta, Australia, and the United Kingdom (UK) using only 20 local observations at inference time, maintaining high accuracy in geologically distinct test regions with a mean absolute error of 2.2 °C in Alberta, 6.2 °C in Australia, and 5.4 °C in the UK. Interpretability analyses show that the model learns internal representations of subsurface properties it never observes during training, including seismic velocities, geochemistry, and crustal structure, and uses these representations in physically consistent ways. More broadly, this work shows that in-context learning can use sparse borehole observations for continental-scale subsurface characterization, without requiring dense measurements or region-specific retraining.

Radar sounders are electromagnetic instruments that can probe deep into the subsurface of Earth and other planetary bodies by processing the echo of transmitted radar waves. Conventional approaches for analyzing such data rely on approximate assumptions and often produce point estimates that ignore parameter correlations as well as galactic and measurement noise. We propose a simulation-based inference approach to terrain parameter inversion from radar sounder data, where synthetic observations from a GPU-based simulator are used to train a neural network-based density estimator for neural posterior estimation (NPE). By explicitly conditioning on reference surface assumptions, the proposed framework allows systematic evaluation of posterior robustness to reference surface variability. We demonstrate that our NPE model is well calibrated on simulated data and transferable to real Mars radar profiles, where we analyze terrain parameters using literature-informed reference values.

This study presents an unsupervised machine learning workflow for electrofacies analysis in the offshore Keta Basin, Ghana, where core data are scarce. Six standard wireline logs from Well~C were analysed over a depth interval comprising approximately $11{,}195$ samples. K-means clustering was applied in multivariate log space, with the clustering structure evaluated using inertia and silhouette diagnostics. Four clusters were identified, supported by an average silhouette coefficient of approximately $0.50$, indicating moderate but meaningful separation. The resulting electrofacies exhibit systematic, depth-continuous patterns associated with variations in clay content, porosity, and rock framework properties, forming a geological continuum from shale-dominated to cleaner sandstone-dominated units. The results demonstrate that log-only, unsupervised clustering supported by quantitative metrics provides a robust and reproducible framework for subsurface characterisation. The proposed workflow offers a practical tool for early-stage formation evaluation in frontier offshore basins and a foundation for future integrated studies.

Subsurface ore detection is of paramount importance given the rising depletion of shallow mineral resources in recent years. It is crucial to explore approaches that go beyond the limitations of traditional geological exploration methods. Due to readily available surface readings, joint magnetic and gravitational inversion is a promising new method - given magnetic and gravitational data on a surface, jointly reconstructing the underlying densities that generate them. However, this is ill-posed and has non-unique solutions. Deterministic methods often require handcrafted priors and converge to a single solution and do not capture the distribution, which is often of interest. We introduce a novel framework that reframes 3D gravity and magnetic joint inversion as a rectified flow on the Noddyverse dataset, the largest physics-based dataset for inversion. We introduce a Ginzburg-Landau (GL) regularizer, a generalized version of the Ising model that aids in ore identification, enabling physics-aware training. We also propose a guidance methodology based on GL theory that can be used as a plug-and-play module with existing unconditional denoisers. Lastly, we also train and release a VAE for the 3D densities, which facilitates downstream work in the field.

Obtaining truly representative pore-scale images that match bulk formation properties remains a fundamental challenge in subsurface characterization, as natural spatial heterogeneity causes extracted sub-images to deviate significantly from core-measured values. This challenge is compounded by data scarcity, where physical samples are only available at sparse well locations. This study presents a multi-conditional Generative Adversarial Network (cGAN) framework that generates representative pore-scale images with precisely controlled properties. The framework was trained on thin section samples from four depths (1879.50-1943.50 m) of a carbonate formation, simultaneously conditioning on porosity and depth within a single model. It processes RGB thin section images that preserve critical mineralogical information (anhydrite-dolomite differentiation, grain boundaries, porosity distinctions) lost in conventional grayscale representations, capturing characteristics from grainstone fabrics to crystalline textures with anhydrite inclusions. The model achieved strong porosity control (R^2 = 0.95) across all formations with mean absolute errors of 0.0099-0.0197. Morphological validation confirmed preservation of average pore radius, specific surface area, and tortuosity within acceptable tolerances. Two-point correlation (S2) analysis confirmed that generated images preserve the spatial continuity and characteristic length scales of natural pore networks, with results consistent across the imaging resolutions tested (1.8-3.0 micron/pixel). Validated against core sample properties, generated images showed higher property fidelity with dual-constraint errors of 1.9-12.4% compared to 37.5-713.6% for randomly extracted real sub-images. This capability provides practical tools for subsurface characterization, particularly valuable for carbon storage, geothermal energy, and groundwater management.