arXiv subjects

Tapan Mukerji

Publications and source records attributed to Tapan Mukerji.

32 records · Page 2Linked to original sources

arXiv2023

Prediction of fluid flow in porous media by sparse observations and physics-informed PointNet

We predict steady-state Stokes flow of fluids within porous media at pore scales using sparse point observations and a novel class of physics-informed neural networks, called "physics-informed PointNet" (PIPN). Taking the advantages of PIPN into account, three new features become available compared to physics-informed convolutional neural networks for porous medium applications. First, the input of PIPN is exclusively the pore spaces of porous media (rather than both the pore and grain spaces). This feature diminishes required computer memory. Second, PIPN represents the boundary of pore spaces smoothly and realistically (rather than pixel-wise representations). Third, spatial resolution can vary over the physical domain (rather than equally spaced resolutions). This feature enables users to reach an optimal resolution with a minimum computational cost. The performance of our framework is evaluated by the study of the influence of noisy sensor data, pressure observations, and spatial correlation length.

physics.flu-dyn↗

arXiv2023

Homogenizing elastic properties of large digital rock images by combining CNN with hierarchical homogenization method

Determining effective elastic properties of rocks from their pore-scale digital images is a key goal of digital rock physics (DRP). Direct numerical simulation (DNS) of elastic behavior, however, incurs high computational cost; and surrogate machine learning (ML) model, particularly convolutional neural network (CNN), show promises to accelerate homogenization process. 3D CNN models, however, are unable to handle large images due to memory issues. To address this challenge, we propose a novel method that combines 3D CNN with hierarchical homogenization method (HHM). The surrogate 3D CNN model homogenizes only small subimages, and a DNS is used to homogenize the intermediate image obtained by assembling small subimages. The 3D CNN model is designed to output the homogenized elastic constants within the Hashin-Shtrikman (HS) bounds of the input images. The 3D CNN model is first trained on data comprising equal proportions of five sandstone (quartz mineralogy) images, and, subsequently, fine-tuned for specific rocks using transfer learning. The proposed method is applied to homogenize the rock images of size 300x300x300 and 600x600x600 voxels, and the predicted homogenized elastic moduli are shown to agree with that obtained from the brute-force DNS. The transferability of the trained 3D CNN model (using transfer learning) is further demonstrated by predicting the homogenized elastic moduli of a limestone rock with calcite mineralogy. The surrogate 3D CNN model in combination with the HHM is thus shown to be a promising tool for the homogenization of large 3D digital rock images and other random media

physics.geo-ph↗

arXiv2023

ChatGPT for Programming Numerical Methods

ChatGPT is a large language model recently released by the OpenAI company. In this technical report, we explore for the first time the capability of ChatGPT for programming numerical algorithms. Specifically, we examine the capability of GhatGPT for generating codes for numerical algorithms in different programming languages, for debugging and improving written codes by users, for completing missed parts of numerical codes, rewriting available codes in other programming languages, and for parallelizing serial codes. Additionally, we assess if ChatGPT can recognize if given codes are written by humans or machines. To reach this goal, we consider a variety of mathematical problems such as the Poisson equation, the diffusion equation, the incompressible Navier-Stokes equations, compressible inviscid flow, eigenvalue problems, solving linear systems of equations, storing sparse matrices, etc. Furthermore, we exemplify scientific machine learning such as physics-informed neural networks and convolutional neural networks with applications to computational physics. Through these examples, we investigate the successes, failures, and challenges of ChatGPT. Examples of failures are producing singular matrices, operations on arrays with incompatible sizes, programming interruption for relatively long codes, etc. Our outcomes suggest that ChatGPT can successfully program numerical algorithms in different programming languages, but certain limitations and challenges exist that require further improvement of this machine learning model.

cs.LG↗

arXiv2023

Bayesian Geophysical Basin Modeling with Seismic Kinematics Metrics to Quantify Uncertainty for Pore Pressure Prediction

Bayesian geophysical basin modeling (BGBM) methodology is an interdisciplinary workflow that incorporates data, geological expertise, and physical processes through Bayesian inference in sedimentary basin models. Its application culminates in subsurface models that integrate the geo-history of a basin, rock physics definitions, well log and drilling data, and seismic information. Monte Carlo basin modeling realizations are performed by sampling from prior probability distributions on facies parameters and basin boundary conditions. After data assimilation, the accepted set of posterior sub-surface models yields uncertainty quantification of subsurface properties. This procedure is especially suitable for pore pressure prediction in a predrill stage. However, the high computational cost of seismic data assimilation decreases the practicality of the workflow. Therefore, we introduce and investigate seismic traveltimes criteria as computationally faster proxies for analyzing the seismic data likelihood when employing BGBM. The proposed surrogate schemes weigh the prior basin model results with the available seismic data with no need to perform expensive seismic depth-migration procedures for each Monte Carlo realization. Furthermore, we apply BGBM in a real field case from the Gulf of Mexico using a 2D section for pore pressure prediction considering different kinematics criteria. BGBM implementation with the novel seismic data assimilation proxies is compared with a computationally expensive benchmark approach. Moreover, we validate and compare the outcomes for predicted pore pressure with mud-weight data from a blind well. The fast proxy of analyzing the depth-positioning of seismic horizons proposed in this work yields similar uncertainty quantification results in pore pressure prediction compared to the benchmark. These fast proxies make the BGBM methodology efficient and practical.

physics.geo-ph↗

arXiv2022

Physics-informed PointNet: A deep learning solver for steady-state incompressible flows and thermal fields on multiple sets of irregular geometries

We present a novel physics-informed deep learning framework for solving steady-state incompressible flow on multiple sets of irregular geometries by incorporating two main elements: using a point-cloud based neural network to capture geometric features of computational domains, and using the mean squared residuals of the governing partial differential equations, boundary conditions, and sparse observations as the loss function of the network to capture the physics. While the solution of the continuity and Navier-Stokes equations is a function of the geometry of the computational domain, current versions of physics-informed neural networks have no mechanism to express this functionally in their outputs, and thus are restricted to obtain the solutions only for one computational domain with each training procedure. Using the proposed framework, three new facilities become available. First, the governing equations are solvable on a set of computational domains containing irregular geometries with high variations with respect to each other but requiring training only once. Second, after training the introduced framework on the set, it is now able to predict the solutions on domains with unseen geometries from seen and unseen categories as well. The former and the latter both lead to savings in computational costs. Finally, all the advantages of the point-cloud based neural network for irregular geometries, already used for supervised learning, are transferred to the proposed physics-informed framework. The effectiveness of our framework is shown through the method of manufactured solutions and thermally-driven flow for forward and inverse problems.

physics.flu-dyn↗

arXiv2022

Direct Estimation of Porosity from Seismic Data using Rock and Wave Physics Informed Neural Networks (RW-PINN)

Petrophysical inversion is an important aspect of reservoir modeling. However due to the lack of a unique and straightforward relationship between seismic traces and rock properties, predicting petrophysical properties directly from seismic data is a complex task. Many studies have attempted to identify the direct end-to-end link using supervised machine learning techniques, but face different challenges such as a lack of large petrophysical training dataset or estimates that may not conform with physics or depositional history of the rocks. We present a rock and wave physics informed neural network (RW-PINN) model that can estimate porosity directly from seismic image traces with no or limited number of wells, with predictions that are consistent with rock physics and geologic knowledge of deposition. As an example, we use the uncemented sand rock physics model and normal-incidence wave physics to guide the learning of RW-PINN to eventually get good estimates of porosities from normal-incidence seismic traces and limited well data. Training RW-PINN with few wells (weakly supervised) helps in tackling the problem of non-uniqueness as different porosity logs can give similar seismic traces. We use weighted normalized root mean square error loss function to train the weakly supervised network and demonstrate the impact of different weights on porosity predictions. The RW-PINN estimated porosities and seismic traces are compared to predictions from a completely supervised model, which gives slightly better porosity estimates but poorly matches the seismic traces, in addition to requiring a large amount of labeled training data. In this paper, we demonstrate the complete workflow for executing petrophysical inversion of seismic data using self-supervised or weakly supervised rock physics informed neural networks.

physics.geo-ph↗

arXiv2022

Computation of effective elastic moduli of rocks using hierarchical homogenization

This work focuses on computing the homogenized elastic properties of rocks from 3D micro-computed-tomography (micro-CT) scanned images. The accurate computation of homogenized properties of rocks, archetypal random media, requires both resolution of intricate underlying microstructure and large field of view, resulting in huge micro-CT images. Homogenization entails solving the local elasticity problem computationally which can be prohibitively expensive for a huge image. To mitigate this problem, we use a renormalization method inspired scheme, the hierarchical homogenization method, where a large image is partitioned into smaller subimages. The individual subimages are separately homogenized using periodic boundary conditions, and then assembled into a much smaller intermediate image. The intermediate image is again homogenized, subject to the periodic boundary condition, to find the final homogenized elastic constant of the original image. An FFT-based elasticity solver is used to solve the associated periodic elasticity problem. The error in the homogenized elastic constant is empirically shown to follow a power law scaling with exponent -1 with respect to the subimage size across all five microstructures of rocks. We further show that the inclusion of surrounding materials during the homogenization of the small subimages reduces error in the final homogenized elastic moduli while still respecting the power law with the exponent of -1. This power law scaling is then exploited to determine a better approximation of the large heterogeneous microstructures based on Richardson extrapolation

physics.geo-ph↗

arXiv2021

Point-Cloud Deep Learning of Porous Media for Permeability Prediction

We propose a novel deep learning framework for predicting permeability of porous media from their digital images. Unlike convolutional neural networks, instead of feeding the whole image volume as inputs to the network, we model the boundary between solid matrix and pore spaces as point clouds and feed them as inputs to a neural network based on the PointNet architecture. This approach overcomes the challenge of memory restriction of graphics processing units and its consequences on the choice of batch size, and convergence. Compared to convolutional neural networks, the proposed deep learning methodology provides freedom to select larger batch sizes, due to reducing significantly the size of network inputs. Specifically, we use the classification branch of PointNet and adjust it for a regression task. As a test case, two and three dimensional synthetic digital rock images are considered. We investigate the effect of different components of our neural network on its performance. We compare our deep learning strategy with a convolutional neural network from various perspectives, specifically for maximum possible batch size. We inspect the generalizability of our network by predicting the permeability of real-world rock samples as well as synthetic digital rocks that are statistically different from the samples used during training. The network predicts the permeability of digital rocks a few thousand times faster than a Lattice Boltzmann solver with a high level of prediction accuracy.

eess.IV↗

arXiv2021

Consistency and prior falsification of training data in seismic deep learning: Application to offshore deltaic reservoir characterization

Deep learning applications of seismic reservoir characterization often require generation of synthetic data to augment available sparse labeled data. An approach for generating synthetic training data consists of specifying probability distributions modeling prior geologic uncertainty on reservoir properties and forward modeling the seismic data. A prior falsification approach is critical to establish the consistency of the synthetic training data distribution with real seismic data. With the help of a real case study of facies classification with convolutional neural networks (CNNs) from an offshore deltaic reservoir, we highlight several practical nuances associated with training deep learning models on synthetic seismic data. We highlight the issue of overfitting of CNNs to the synthetic training data distribution and propose regularization strategies to address it. We demonstrate the efficacy of our proposed strategies by training the CNN on synthetic data and making robust predictions with real 3D partial stack seismic data.

physics.geo-ph↗

arXiv2020

Bayesian Optimized Monte Carlo Planning

Online solvers for partially observable Markov decision processes have difficulty scaling to problems with large action spaces. Monte Carlo tree search with progressive widening attempts to improve scaling by sampling from the action space to construct a policy search tree. The performance of progressive widening search is dependent upon the action sampling policy, often requiring problem-specific samplers. In this work, we present a general method for efficient action sampling based on Bayesian optimization. The proposed method uses a Gaussian process to model a belief over the action-value function and selects the action that will maximize the expected improvement in the optimal action value. We implement the proposed approach in a new online tree search algorithm called Bayesian Optimized Monte Carlo Planning (BOMCP). Several experiments show that BOMCP is better able to scale to large action space POMDPs than existing state-of-the-art tree search solvers.

cs.AI↗

arXiv2020

Improved POMDP Tree Search Planning with Prioritized Action Branching

Online solvers for partially observable Markov decision processes have difficulty scaling to problems with large action spaces. This paper proposes a method called PA-POMCPOW to sample a subset of the action space that provides varying mixtures of exploitation and exploration for inclusion in a search tree. The proposed method first evaluates the action space according to a score function that is a linear combination of expected reward and expected information gain. The actions with the highest score are then added to the search tree during tree expansion. Experiments show that PA-POMCPOW is able to outperform existing state-of-the-art solvers on problems with large discrete action spaces.

cs.LG↗

arXiv2020

Real-Time Well Log Prediction From Drilling Data Using Deep Learning

The objective is to study the feasibility of predicting subsurface rock properties in wells from real-time drilling data. Geophysical logs, namely, density, porosity and sonic logs are of paramount importance for subsurface resource estimation and exploitation. These wireline petro-physical measurements are selectively deployed as they are expensive to acquire; meanwhile, drilling information is recorded in every drilled well. Hence a predictive tool for wireline log prediction from drilling data can help management make decisions about data acquisition, especially for delineation and production wells. This problem is non-linear with strong ineractions between drilling parameters; hence the potential for deep learning to address this problem is explored. We present a workflow for data augmentation and feature engineering using Distance-based Global Sensitivity Analysis. We propose an Inception-based Convolutional Neural Network combined with a Temporal Convolutional Network as the deep learning model. The model is designed to learn both low and high frequency content of the data. 12 wells from the Equinor dataset for the Volve field in the North Sea are used for learning. The model predictions not only capture trends but are also physically consistent across density, porosity, and sonic logs. On the test data, the mean square error reaches a low value of 0.04 but the correlation coefficient plateaus around 0.6. The model is able however to differentiate between different types of rocks such as cemented sandstone, unconsolidated sands, and shale.

physics.geo-ph↗

arXiv2019

Approximate Bayesian inference of seismic velocity and pore pressure uncertainty with basin modeling, rock physics and imaging constraints

We present a methodology for quantifying seismic velocity and pore pressure uncertainty that incorporates information regarding the geological history of a basin, rock physics, well log, drilling and seismic data. In particular, our approach relies on linking velocity models to the basin modeling outputs of porosity, mineral volume fractions and pore pressure through rock physics models. We account for geological uncertainty by defining prior probability distributions on uncertain parameters and performing Monte Carlo basin simulations. We perform probabilistic calibration of the basin model outputs by defining data likelihood distributions to represent well data uncertainty. Rock physics modeling transforms the basin modeling outputs to give us multiple velocity realizations used to perform multiple depth migrations. We present an approximate Bayesian inference framework which uses migration velocity analysis in conjunction with well data for updating velocity and basin modeling uncertainty. We apply our methodology in 2D to a real field case from Gulf of Mexico and demonstrate that our methodology allows building a geologic and physical model space for velocity and pore pressure prediction with reduced uncertainty.

physics.geo-ph↗

arXiv2019

Seismic Bayesian evidential learning: Estimation and uncertainty quantification of sub-resolution reservoir properties

We present a framework that enables estimation of low-dimensional sub-resolution reservoir properties directly from seismic data, without requiring the solution of a high dimensional seismic inverse problem. Our workflow is based on the Bayesian evidential learning approach and exploits learning the direct relation between seismic data and reservoir properties to efficiently estimate reservoir properties. The theoretical framework we develop allows incorporation of non-linear statistical models for seismic estimation problems. Uncertainty quantification is performed with Approximate Bayesian Computation. With the help of a synthetic example of estimation of reservoir net-to-gross and average fluid saturations in sub-resolution thin-sand reservoir, several nuances are foregrounded regarding the applicability of unsupervised and supervised learning methods for seismic estimation problems. Finally, we demonstrate the efficacy of our approach by estimating posterior uncertainty of reservoir net-to-gross in sub-resolution thin-sand reservoir from an offshore delta dataset using 3D pre-stack seismic data.

physics.geo-ph↗