arXiv subjects

Tapan Mukerji

Publications and source records attributed to Tapan Mukerji.

At least 19 recordsLinked to original sources

arXiv2026

Geometry-aware Latent Autoregressive Generative Model for PDEs in Complex Domains

Solving multiphysics partial differential equations (PDEs) remains a major challenge in scientific computing, especially for highly complex $μ$m-scale tortuous geometries critical to energy and chemical engineering. We address this challenge by proposing a Geometry-aware Latent Autoregressive generative Model for PDEs (GeoLAMP) for solving physics within highly irregular and tortuous structures. GeoLAMP introduces a dual-encoder architecture on graph representations to jointly capture global topology and fine-scale geometric features, enabling an effective transition from real-space fields to compact latent representations. In the latent space, we propose a causal self-attention transformer with flow matching to model temporal dynamics, allowing stable and scalable block-wise autoregressive prediction. A flexible decoder reconstructs high-resolution physical fields on arbitrary points. We establish three multiphysics benchmark datasets in complex geometries, covering reactive flow, heat convection, and elasticity. GeoLAMP consistently achieves the most stable autoregression performance on these datasets, maintaining low errors throughout the entire rollout horizon. Our results provide a systematic study of geometry-aware learning for PDEs in $μ$m-scale complex geometries and offer new insights into block-wise time marching of latent autoregressive PDE modeling via a flow matching framework.

cs.LG↗

arXiv2026

A convolutional neural network surrogate for hierarchical homogenization: fast elastic moduli prediction of digital rocks

Digital rock physics (DRP) aims to estimate effective rock properties (e.g., elastic moduli) directly from 3D micro-CT images. However, direct numerical simulations (DNS) on high-resolution large 3D scans are often computationally prohibitive and severely limit the application of DRP. To address this bottleneck, we combine a lightweight 3D convolutional neural network (CNN) with hierarchical homogenization (HHM) and apply it to determine effective elastic moduli. In this scheme, a large rock image is divided into subcubes. The CNN replaces costly DNS by directly predicting subcube elastic moduli, while HHM upscales subcube-level predictions to the full rock. Using a shared convolutional backbone, we systematically compare three training targets: (i) full anisotropic $6\times6$ stiffness tensors, (ii) isotropic bulk and shear moduli $(K, G)$, and (iii) Hashin--Shtrikman (HS)-normalized factors. Across multiple rock types, all three models agree well with DNS results while substantially reducing the computational cost. Moreover, training from scratch on each rock type is fast enough that transfer learning is unnecessary. Across all three targets, the accuracy is comparable. In our comparative study, the HS-normalized factor offers the best overall speed--accuracy trade-off while guaranteeing physical consistency, making it a convenient default. The isotropic $(K, G)$ target is a slightly more accurate alternative.

physics.comp-ph↗

arXiv2026

FMSIM: A Multimodal Flow Matching Framework for Conditional Geomodeling

Subsurface geomodeling plays a critical role in reservoir characterization, uncertainty quantification, and subsurface flow prediction. However, integrating heterogeneous sources of geological information, including conceptual geological descriptions, sparse well observations, and spatial prior constraints, remains a significant challenge for traditional geostatistical and data-driven geomodeling approaches. In this study, we present FMSIM, a multi-modal conditional flow matching framework for subsurface facies model generation. FMSIM utilizes a deep learning formulation to learn a velocity field that transports samples from a simple prior distribution to a complex geological facies distribution. Global geological semantic information is incorporated through a learned semantic representation framework and a learned prior model, while local hard constraints are enforced via an iterative projection strategy during sampling to ensure 100% fidelity to well observations. Additionally, a temporal guidance gating mechanism is introduced to regulate the influence of spatial probability maps, balancing large-scale trend alignment with fine-scale geological variability. Benefiting from the framework design, the model enables efficient and stable training with a simple loss function. The framework's fully convolutional architecture also demonstrates promising generalization to moderately larger grid sizes not seen during training without retraining. Results on a synthetic fluvial channel dataset indicate that FMSIM captures complex non-stationary geological features and produces geologically consistent realizations under multi-modal conditioning. This approach offers a flexible tool for incorporating conceptual geological knowledge, sparse observational data, and spatial priors into probabilistic subsurface geomodeling workflows.

physics.geo-ph↗

arXiv2026

DiffSIM: Unconditional and conditional facies simulation based on denoising diffusion generative models

Constructing subsurface facies models that are geologically plausible and constrained by well facies is essential for analyzing sedimentary evolution, reservoir characterization, and flow simulation. Recent deep generative model-based geomodelling methods have demonstrated promising capabilities for both unconditional and conditional settings. We investigate denoising diffusion models as a generative framework for producing realistic and diverse facies realizations in both settings. Diffusion models generate samples through a fixed forward noising process and a learned reverse denoising process. For unconditional geomodelling, we use denoising diffusion probabilistic models (DDPMs) to learn geological patterns from training facies models, and adopt denoising diffusion implicit models (DDIMs) to accelerate sampling by reducing inference steps from 1500 to 50 (30x fewer steps). We assess the geological plausibility using data distribution, class proportions, variograms, and geometric features. To enable conditional generation, we encode well facies and their spatial locations as conditional indicators and apply a mask-based denoising strategy that generates facies only in between-well regions, guaranteeing hard conditioning without introducing additional loss weights. We evaluate both unconditional and conditional generation on three scenarios: two two-dimensional cases (meandering channels and point bars) and one three-dimensional point-bar case. Across these scenarios, unconditional generation reproduces geological realism, and conditional generation honors well data while producing geologically consistent between-well realizations, demonstrating practical utility for facies geomodelling applications.

physics.geo-ph↗

arXiv2025

Seismic inversion using hybrid quantum neural networks

Seismic inversion-including post-stack, pre-stack, and full waveform inversion is compute and memory-intensive. Recently, several approaches, including physics-informed machine learning, have been developed to address some of these limitations. Motivated by the potential of quantum computing, we report on our attempt to map one such classical physics-informed algorithm to a quantum framework. The primary goal is to investigate the technical challenges of this mapping, given that quantum algorithms rely on computing principles fundamentally different from those in classical computing. Quantum computers operate using qubits, which exploit superposition and entanglement, offering the potential to solve classically intractable problems. While current quantum hardware is limited, hybrid quantum-classical algorithms-particularly in quantum machine learning (QML)-demonstrate potential for near-term applications and can be readily simulated. We apply QML to subsurface imaging through the development of a hybrid quantum physics-informed neural network (HQ-PINN) for post-stack and pre-stack seismic inversion. The HQ-PINN architecture adopts an encoder-decoder structure: a hybrid quantum neural network encoder estimates P- and S-impedances from seismic data, while the decoder reconstructs seismic responses using geophysical relationships. Training is guided by minimizing the misfit between the input and reconstructed seismic traces. We systematically assess the impact of quantum layer design, differentiation strategies, and simulator backends on inversion performance. We demonstrate the efficacy of our approach through the inversion of both synthetic and the Sleipner field datasets. The HQ-PINN framework consistently yields accurate results, showcasing quantum computing's promise for geosciences and paving the way for future quantum-enhanced geophysical workflows.

quant-ph↗

arXiv2025

Vision Mamba for Permeability Prediction of Porous Media

Vision Mamba has recently received attention as an alternative to Vision Transformers (ViTs) for image classification. The network size of Vision Mamba scales linearly with input image resolution, whereas ViTs scale quadratically, a feature that improves computational and memory efficiency. Moreover, Vision Mamba requires a significantly smaller number of trainable parameters than traditional convolutional neural networks (CNNs), and thus, they can be more memory efficient. Because of these features, we introduce, for the first time, a neural network that uses Vision Mamba as its backbone for predicting the permeability of three-dimensional porous media. We compare the performance of Vision Mamba with ViT and CNN models across multiple aspects of permeability prediction and perform an ablation study to assess the effects of its components on accuracy. We demonstrate in practice the aforementioned advantages of Vision Mamba over ViTs and CNNs in the permeability prediction of three-dimensional porous media. We make the source code publicly available to facilitate reproducibility and to enable other researchers to build on and extend this work. We believe the proposed framework has the potential to be integrated into large vision models in which Vision Mamba is used instead of ViTs.

cs.CV↗

arXiv2025

Deep learning forecasts the spatiotemporal evolution of fluid-induced microearthquakes

Microearthquakes (MEQs) generated by subsurface fluid injection record the evolving stress state and permeability of reservoirs. Forecasting their full spatiotemporal evolution is therefore critical for applications such as enhanced geothermal systems (EGS), CO$_2$ sequestration and other geo-engineering applications. We present a transformer-based deep learning model that ingests hydraulic stimulation history and prior MEQ observations to forecast four key quantities: cumulative MEQ count, cumulative logarithmic seismic moment, and the 50th- and 95th-percentile extents ($P_{50}, P_{95}$) of the MEQ cloud. Applied to the EGS Collab Experiment 1 dataset, the model achieves $R^2 >0.98$ for the 1-second forecast horizon and $R^2 >0.88$ for the 15-second forecast horizon across all targets, and supplies uncertainty estimates through a learned standard deviation term. These accurate, uncertainty-quantified forecasts enable real-time inference of fracture propagation and permeability evolution, demonstrating the strong potential of deep-learning approaches to improve seismic-risk assessment and guide mitigation strategies in future fluid-injection operations.

physics.geo-ph↗

arXiv2025

Physics-informed KAN PointNet: Deep learning for simultaneous solutions to inverse problems in incompressible flow on numerous irregular geometries

Kolmogorov-Arnold Networks (KANs) have gained attention as an alternative to traditional multilayer perceptrons (MLPs) for deep learning applications in computational physics, particularly for solving inverse problems with sparse data, as exemplified by the physics-informed Kolmogorov-Arnold network (PIKAN). However, the capability of KANs to simultaneously solve inverse problems over multiple irregular geometries within a single training run remains unexplored. To address this gap, we introduce the physics-informed Kolmogorov-Arnold PointNet (PI-KAN-PointNet), in which shared KANs are integrated into the PointNet architecture to capture the geometric features of computational domains. The loss function comprises the squared residuals of the governing equations, computed via automatic differentiation, along with sparse observations and partially known boundary conditions. We construct shared KANs using Jacobi polynomials and investigate their performance by considering Jacobi polynomials of different degrees and types in terms of both computational cost and prediction accuracy. As a benchmark test case, we consider natural convection in a square enclosure with a cylinder, where the cylinder's shape varies across a dataset of 135 geometries. PI-KAN-PointNet offers two main advantages. First, it overcomes the limitation of current PIKANs, which are restricted to solving only a single computational domain per training run, thereby reducing computational costs. Second, when comparing the performance of PI-KAN-PointNet with that of the physics-informed PointNet using MLPs, we observe that, with approximately the same number of trainable parameters and comparable computational cost in terms of the number of epochs, training time per epoch, and memory usage, PI-KAN-PointNet yields more accurate predictions, particularly for values on unknown boundary conditions involving nonsmooth geometries.

cs.LG↗

arXiv2025

Pix2Geomodel: A Next-Generation Reservoir Geomodeling with Property-to-Property Translation

Accurate geological modeling is critical for reservoir characterization, yet traditional methods struggle with complex subsurface heterogeneity, and they have problems with conditioning to observed data. This study introduces Pix2Geomodel, a novel conditional generative adversarial network (cGAN) framework based on Pix2Pix, designed to predict reservoir properties (facies, porosity, permeability, and water saturation) from the Rotliegend reservoir of the Groningen gas field. Utilizing a 7.6 million-cell dataset from the Nederlandse Aardolie Maatschappij, accessed via EPOS-NL, the methodology included data preprocessing, augmentation to generate 2,350 images per property, and training with a U-Net generator and PatchGAN discriminator over 19,000 steps. Evaluation metrics include pixel accuracy (PA), mean intersection over union (mIoU), frequency weighted intersection over union (FWIoU), and visualizations assessed performance in masked property prediction and property-to-property translation tasks. Results demonstrated high accuracy for facies (PA 0.88, FWIoU 0.85) and water saturation (PA 0.96, FWIoU 0.95), with moderate success for porosity (PA 0.70, FWIoU 0.55) and permeability (PA 0.74, FWIoU 0.60), and robust translation performance (e.g., facies-to-facies PA 0.98, FWIoU 0.97). The framework captured spatial variability and geological realism, as validated by variogram analysis, and calculated the training loss curves for the generator and discriminator for each property. Compared to traditional methods, Pix2Geomodel offers enhanced fidelity in direct property mapping. Limitations include challenges with microstructural variability and 2D constraints, suggesting future integration of multi-modal data and 3D modeling (Pix2Geomodel v2.0). This study advances the application of generative AI in geoscience, supporting improved reservoir management and open science initiatives.

physics.geo-ph↗

arXiv2025

Image registration of 2D optical thin sections in a 3D porous medium: Application to a Berea sandstone digital rock image

This study proposes a systematic image registration approach to align 2D optical thin-section images within a 3D digital rock volume. Using template image matching with differential evolution optimization, we identify the most similar 2D plane in 3D. The method is validated on a synthetic porous medium, achieving exact registration, and applied to Berea sandstone, where it achieves a structural similarity index (SSIM) of 0.990. With the registered images, we explore upscaling properties based on paired multimodal images, focusing on pore characteristics and effective elastic moduli. The thin-section image reveals 50 % more porosity and submicron pores than the registered CT plane. In addition, bulk and shear moduli from thin sections are 25 % and 30 % lower, respectively, than those derived from CT images. Beyond numerical comparisons, thin sections provide additional geological insights, including cementation, mineral phases, and weathering effects, which are not clear in CT images. This study demonstrates the potential of multimodal image registration to improve computed rock properties in digital rock physics by integrating complementary imaging modalities.

physics.geo-ph↗

arXiv2025

Pre-stack and post-stack seismic inversion using quantum computing

Quantum computing harnesses the principles of quantum mechanics to solve problems that are intractable for classical computers. Quantum annealing, a specialized approach within quantum computing, is particularly effective for optimization tasks, as it leverages quantum tunneling to escape local minima and efficiently explore complex energy landscapes. In geosciences, many problems are framed as high-dimensional optimization problems, including seismic inversion, which aims to estimate subsurface impedances from seismic data for accurate geological interpretation and resource exploration. This study presents a novel application of quantum computing for seismic inversion, marking the first instance of inverting seismic data to estimate both P-wave and S-wave impedances using a quantum annealer. Building upon our prior work, which demonstrated the estimation of acoustic impedances from post-stack data using a two-step framework, we propose an enhanced workflow capable of inverting both post-stack and pre-stack seismic data in a single step. This advancement significantly reduces the number of qubits per model parameter (from 20 to 5) while improving computational speed (from 20 seconds to 6.3 seconds). The seismic inversion is implemented using the D-Wave Leap hybrid solver, achieving impedance estimation within 4-9 seconds, with the quantum processing unit (QPU) contributing just 0.043-0.085 seconds. Comparative analysis with simulated annealing reveals that quantum annealing produces impedance models closely matching true values in a single epoch, whereas simulated annealing requires 10 epochs for improved accuracy. These findings underscore the transformative potential of quantum computing for real-time, high-precision seismic inversion, marking a crucial step toward fully quantum-driven geophysical solutions.

quant-ph↗

arXiv2024

Well log data generation and imputation using sequence-based generative adversarial networks

Well log analysis is crucial for hydrocarbon exploration, providing detailed insights into subsurface geological formations. However, gaps and inaccuracies in well log data, often due to equipment limitations, operational challenges, and harsh subsurface conditions, can introduce significant uncertainties in reservoir evaluation. Addressing these challenges requires effective methods for both synthetic data generation and precise imputation of missing data, ensuring data completeness and reliability. This study introduces a novel framework utilizing sequence-based generative adversarial networks (GANs) specifically designed for well log data generation and imputation. The framework integrates two distinct sequence-based GAN models: Time Series GAN (TSGAN) for generating synthetic well log data and Sequence GAN (SeqGAN) for imputing missing data. Both models were tested on a dataset from the North Sea, Netherlands region, focusing on different sections of 5, 10, and 50 data points. Experimental results demonstrate that this approach achieves superior accuracy in filling data gaps compared to other deep learning models for spatial series analysis. The method yielded R^2 values of 0.921, 0.899, and 0.594, with corresponding mean absolute percentage error (MAPE) values of 8.320, 0.005, and 151.154, and mean absolute error (MAE) values of 0.012, 0.005, and 0.032, respectively. These results set a new benchmark for data integrity and utility in geosciences, particularly in well log data analysis.

physics.geo-ph↗

arXiv2024

Enhanced anomaly detection in well log data through the application of ensemble GANs

Although generative adversarial networks (GANs) have shown significant success in modeling data distributions for image datasets, their application to structured or tabular data, such as well logs, remains relatively underexplored. This study extends the ensemble GANs (EGANs) framework to capture the distribution of well log data and detect anomalies that fall outside of these distributions. The proposed approach compares the performance of traditional methods, such as Gaussian mixture models (GMMs), with EGANs in detecting anomalies outside the expected data distributions. For the gamma ray (GR) dataset, EGANs achieved a precision of 0.62 and F1 score of 0.76, outperforming GMM's precision of 0.38 and F1 score of 0.54. Similarly, for travel time (DT), EGANs achieved a precision of 0.70 and F1 score of 0.79, surpassing GMM 0.56 and 0.71. In the neutron porosity (NPHI) dataset, EGANs recorded a precision of 0.53 and F1 score of 0.68, outshining GMM 0.47 and 0.61. For the bulk density (RHOB) dataset, EGANs achieved a precision of 0.52 and an F1 score of 0.67, slightly outperforming GMM, which yielded a precision of 0.50 and an F1 score of 0.65. This work's novelty lies in applying EGANs for well log data analysis, showcasing their ability to learn data patterns and identify anomalies that deviate from them. This approach offers more reliable anomaly detection compared to traditional methods like GMM. The findings highlight the potential of EGANs in enhancing anomaly detection for well log data, delivering significant implications for optimizing drilling strategies and reservoir management through more accurate, data-driven insights into subsurface characterization.

physics.geo-ph↗

arXiv2024

Accelerating Multiphase Flow Simulations with Denoising Diffusion Model Driven Initializations

This study introduces a hybrid fluid simulation approach that integrates generative diffusion models with physics-based simulations, aiming at reducing the computational costs of flow simulations while still honoring all the physical properties of interest. These simulations enhance our understanding of applications such as assessing hydrogen and CO$_2$ storage efficiency in underground reservoirs. Nevertheless, they are computationally expensive and the presence of nonunique solutions can require multiple simulations within a single geometry. To overcome the computational cost hurdle, we propose a hybrid method that couples generative diffusion models and physics-based modeling. We introduce a system to condition the diffusion model with a geometry of interest, allowing to produce variable fluid saturations in the same geometry. While training the model, we simultaneously generate initial conditions and perform physics-based simulations using these conditions. This integrated approach enables us to receive real-time feedback on a single compute node equipped with both CPUs and GPUs. By efficiently managing these processes within one compute node, we can continuously evaluate performance and stop training when the desired criteria are met. To test our model, we generate realizations in a real Berea sandstone fracture which shows that our technique is up to 4.4 times faster than commonly used flow simulation initializations.

physics.geo-ph↗

arXiv2024

A novel Fourier neural operator framework for classification of multi-sized images: Application to three dimensional digital porous media

Fourier neural operators (FNOs) are invariant with respect to the size of input images, and thus images with any size can be fed into FNO-based frameworks without any modification of network architectures, in contrast to traditional convolutional neural networks (CNNs). Leveraging the advantage of FNOs, we propose a novel deep-learning framework for classifying images with varying sizes. Particularly, we simultaneously train the proposed network on multi-sized images. As a practical application, we consider the problem of predicting the label (e.g., permeability) of three-dimensional digital porous media. To construct the framework, an intuitive approach is to connect FNO layers to a classifier using adaptive max pooling. First, we show that this approach is only effective for porous media with fixed sizes, whereas it fails for porous media of varying sizes. To overcome this limitation, we introduce our approach: instead of using adaptive max pooling, we use static max pooling with the size of channel width of FNO layers. Since the channel width of the FNO layers is independent of input image size, the introduced framework can handle multi-sized images during training. We show the effectiveness of the introduced framework and compare its performance with the intuitive approach through the example of the classification of three-dimensional digital porous media of varying sizes.

cs.CV↗

arXiv2024

Prediction of Effective Elastic Moduli of Rocks using Graph Neural Networks

This study presents a Graph Neural Networks (GNNs)-based approach for predicting the effective elastic moduli of rocks from their digital CT-scan images. We use the Mapper algorithm to transform 3D digital rock images into graph datasets, encapsulating essential geometrical information. These graphs, after training, prove effective in predicting elastic moduli. Our GNN model shows robust predictive capabilities across various graph sizes derived from various subcube dimensions. Not only does it perform well on the test dataset, but it also maintains high prediction accuracy for unseen rocks and unexplored subcube sizes. Comparative analysis with Convolutional Neural Networks (CNNs) reveals the superior performance of GNNs in predicting unseen rock properties. Moreover, the graph representation of microstructures significantly reduces GPU memory requirements (compared to the grid representation for CNNs), enabling greater flexibility in the batch size selection. This work demonstrates the potential of GNN models in enhancing the prediction accuracy of rock properties and boosting the efficiency of digital rock analysis.

cs.LG↗

arXiv2023

Generating Multiphase Fluid Configurations in Fractures using Diffusion Models

Pore-scale simulations accurately describe transport properties of fluids in the subsurface. These simulations enhance our understanding of applications such as assessing hydrogen storage efficiency and forecasting CO$_2$ sequestration processes in underground reservoirs. Nevertheless, they are computationally expensive due to their mesoscopic nature. In addition, their stationary solutions are not guaranteed to be unique, so multiple runs with different initial conditions must be performed to ensure sufficient sample coverage. These factors complicate the task of obtaining representative and reliable forecasts. To overcome the high computational cost hurdle, we propose a hybrid method that couples generative diffusion models and physics-based modeling. Upon training a generative model, we synthesize samples that serve as the initial conditions for physics-based simulations. We measure the relaxation time (to stationary solutions) of the simulations, which serves as a validation metric and early-stopping criterion. Our numerical experiments revealed that the hybrid method exhibits a speed-up of up to 8.2 times compared to commonly used initialization methods. This finding offers compelling initial support that the proposed diffusion model-based hybrid scheme has potentials to significantly decrease the time required for convergence of numerical simulations without compromising the physical robustness.

physics.geo-ph↗

arXiv2023

Physics-informed PointNet: On how many irregular geometries can it solve an inverse problem simultaneously? Application to linear elasticity

Regular physics-informed neural networks (PINNs) predict the solution of partial differential equations using sparse labeled data but only over a single domain. On the other hand, fully supervised learning models are first trained usually over a few thousand domains with known solutions (i.e., labeled data) and then predict the solution over a few hundred unseen domains. Physics-informed PointNet (PIPN) is primarily designed to fill this gap between PINNs (as weakly supervised learning models) and fully supervised learning models. In this article, we demonstrate that PIPN predicts the solution of desired partial differential equations over a few hundred domains simultaneously, while it only uses sparse labeled data. This framework benefits fast geometric designs in the industry when only sparse labeled data are available. Particularly, we show that PIPN predicts the solution of a plane stress problem over more than 500 domains with different geometries, simultaneously. Moreover, we pioneer implementing the concept of remarkable batch size (i.e., the number of geometries fed into PIPN at each sub-epoch) into PIPN. Specifically, we try batch sizes of 7, 14, 19, 38, 76, and 133. Additionally, the effect of the PIPN size, symmetric function in the PIPN architecture, and static and dynamic weights for the component of the sparse labeled data in the loss function are investigated.

cs.LG↗