Aleksandra Pachalieva, Daniel O'Malley, Dylan Robert Harp et al.
Avoiding over-pressurization in subsurface reservoirs is critical for applications like CO2 sequestration and wastewater injection. Managing the pressures by controlling injection/extraction are challenging because of complex heterogeneity in the subsurface. The heterogeneity typically requires high-fidelity physics-based models to make predictions on CO$_2$ fate. Furthermore, characterizing the heterogeneity accurately is fraught with parametric uncertainty. Accounting for both, heterogeneity and uncertainty, makes this a computationally-intensive problem challenging for current reservoir simulators. To tackle this, we use differentiable programming with a full-physics model and machine learning to determine the fluid extraction rates that prevent over-pressurization at critical reservoir locations. We use DPFEHM framework, which has trustworthy physics based on the standard two-point flux finite volume discretization and is also automatically differentiable like machine learning models. Our physics-informed machine learning framework uses convolutional neural networks to learn an appropriate extraction rate based on the permeability field. We also perform a hyperparameter search to improve the model's accuracy. Training and testing scenarios are executed to evaluate the feasibility of using physics-informed machine learning to manage reservoir pressures. We constructed and tested a sufficiently accurate simulator that is 400000 times faster than the underlying physics-based simulator, allowing for near real-time analysis and robust uncertainty quantification.
Satish Karra, Mohamed Mehana, Nicholas Lubbers et al.
Throughout computational science, there is a growing need to utilize the continual improvements in raw computational horsepower to achieve greater physical fidelity through scale-bridging over brute-force increases in the number of mesh elements. For instance, quantitative predictions of transport in nanoporous media, critical to hydrocarbon extraction from tight shale formations, are impossible without accounting for molecular-level interactions. Similarly, inertial confinement fusion simulations rely on numerical diffusion to simulate molecular effects such as non-local transport and mixing without truly accounting for molecular interactions. With these two disparate applications in mind, we develop a novel capability which uses an active learning approach to optimize the use of local fine-scale simulations for informing coarse-scale hydrodynamics. Our approach addresses three challenges: forecasting continuum coarse-scale trajectory to speculatively execute new fine-scale molecular dynamics calculations, dynamically updating coarse-scale from fine-scale calculations, and quantifying uncertainty in neural network models.
Teeratorn Kadeethum, Daniel O'Malley, Youngsoo Choi et al.
Data-driven modeling can suffer from a constant demand for data, leading to reduced accuracy and impractical for engineering applications due to the high cost and scarcity of information. To address this challenge, we propose a progressive reduced order modeling framework that minimizes data cravings and enhances data-driven modeling's practicality. Our approach selectively transfers knowledge from previously trained models through gates, similar to how humans selectively use valuable knowledge while ignoring unuseful information. By filtering relevant information from previous models, we can create a surrogate model with minimal turnaround time and a smaller training set that can still achieve high accuracy. We have tested our framework in several cases, including transport in porous media, gravity-driven flow, and finite deformation in hyperelastic materials. Our results illustrate that retaining information from previous models and utilizing a valuable portion of that knowledge can significantly improve the accuracy of the current model. We have demonstrated the importance of progressive knowledge transfer and its impact on model accuracy with reduced training samples. For instance, our framework with four parent models outperforms the no-parent counterpart trained on data nine times larger. Our research unlocks data-driven modeling's potential for practical engineering applications by mitigating the data scarcity issue. Our proposed framework is a significant step toward more efficient and cost-effective data-driven modeling, fostering advancements across various fields.
Agnese Marcato, Daniel O'Malley, Hari Viswanathan et al.
Recreating complex, high-dimensional global fields from limited data points is a grand challenge across various scientific and industrial domains. Given the prohibitive costs of specialized sensors and the frequent inaccessibility of certain regions of the domain, achieving full field coverage is typically not feasible. Therefore, the development of algorithms that intelligently improve sensor placement is of significant value. In this study, we introduce a general approach that employs differentiable programming to exploit sensor placement within the training of a neural network model in order to improve field reconstruction. We evaluated our method using two distinct datasets; the results show that our approach improved test scores. Ultimately, our method of differentiable placement strategies has the potential to significantly increase data collection efficiency, enable more thorough area coverage, and reduce redundancy in sensor deployment.
Agnese Marcato, Aleksandra Pachalieva, Ryley G. Hill et al.
Accurately predicting when and how materials fail is critical to designing safe, reliable structures, mechanical systems, and engineered components that operate under stress. Yet, fracture behavior remains difficult to model across the diversity of materials, geometries, and loading conditions in real-world applications. While machine learning (ML) methods show promise, most models are trained on narrow datasets, lack robustness, and struggle to generalize. Meanwhile, physics-based simulators offer high-fidelity predictions but are fragmented across specialized methods and require substantial high-performance computing resources to explore the input space. To address these limitations, we present a data-driven foundation model for fracture prediction, a transformer-based architecture that operates across simulators, a wide range of materials (including plastic-bonded explosives, steel, aluminum, shale, and tungsten), and diverse loading conditions. The model supports both structured and unstructured meshes, combining them with large language model embeddings of textual input decks specifying material properties, boundary conditions, and solver settings. This multimodal input design enables flexible adaptation across simulation scenarios without changes to the model architecture. The trained model can be fine-tuned with minimal data on diverse downstream tasks, including time-to-failure estimation, modeling fracture evolution, and adapting to combined finite-discrete element method simulations. It also generalizes to unseen materials such as titanium and concrete, requiring as few as a single sample, dramatically reducing data needs compared to standard ML. Our results show that fracture prediction can be unified under a single model architecture, offering a scalable, extensible alternative to simulator-specific workflows.
For decades, corporations and governments have relied on scanned documents to record vast amounts of information. However, extracting this information is a slow and tedious process due to the sheer volume and complexity of these records. The rise of Vision Language Models (VLMs) presents a way to efficiently and accurately extract the information out of these documents. The current automated workflow often requires a two-step approach involving the extraction of information using optical character recognition software and subsequent usage of large language models for processing this information. Unfortunately, these methods encounter significant challenges when dealing with noisy scanned documents, often requiring computationally expensive language models to handle high information density effectively. In this study, we propose PatchFinder, an algorithm that builds upon VLMs to improve information extraction. First, we devise a confidence-based score, called Patch Confidence, based on the Maximum Softmax Probability of the VLMs' output to measure the model's confidence in its predictions. Using this metric, PatchFinder determines a suitable patch size, partitions the input document into overlapping patches, and generates confidence-based predictions for the target information. Our experimental results show that PatchFinder, leveraging Phi-3v, a 4.2-billion-parameter VLM, achieves an accuracy of 94% on our dataset of 190 noisy scanned documents, outperforming ChatGPT-4o by 18.5 percentage points.
Aleksandra Pachalieva, Jeffrey D. Hyman, Daniel O'Malley et al.
We perform a set of flow and reactive transport simulations within three-dimensional fracture networks to learn the factors controlling mineral reactions. CO$_2$ mineralization requires CO$_2$-laden water, dissolution of a mineral that then leads to precipitation of a CO$_2$-bearing mineral. Our discrete fracture networks (DFN) are partially filled with quartz that gradually dissolves until it reaches a quasi-steady state. At the end of the simulation, we measure the quartz remaining in each fracture within the domain. We observe that a small backbone of fracture exists, where the quartz is fully dissolved which leads to increased flow and transport. However, depending on the DFN topology and the rate of dissolution, we observe a large variability of these changes, which indicates an interplay between the fracture network structure and the impact of geochemical dissolution. In this work, we developed a machine learning framework to extract the important features that support mineralization in the form of dissolution. In addition, we use structural and topological features of the fracture network to predict the remaining quartz volume in quasi-steady state conditions. As a first step to characterizing carbon mineralization, we study dissolution with this framework. We studied a variety of reaction and fracture parameters and their impact on the dissolution of quartz in fracture networks. We found that the dissolution reaction rate constant of quartz and the distance to the flowing backbone in the fracture network are the two most important features that control the amount of quartz left in the system. For the first time, we use a combination of a finite-volume reservoir model and graph-based approach to study reactive transport in a complex fracture network to determine the key features that control dissolution.
The "Workshop on Machine learning in heterogeneous porous materials" brought together international scientific communities of applied mathematics, porous media, and material sciences with experts in the areas of heterogeneous materials, machine learning (ML) and applied mathematics to identify how ML can advance materials research. Within the scope of ML and materials research, the goal of the workshop was to discuss the state-of-the-art in each community, promote crosstalk and accelerate multi-disciplinary collaborative research, and identify challenges and opportunities. As the end result, four topic areas were identified: ML in predicting materials properties, and discovery and design of novel materials, ML in porous and fractured media and time-dependent phenomena, Multi-scale modeling in heterogeneous porous materials via ML, and Discovery of materials constitutive laws and new governing equations. This workshop was part of the AmeriMech Symposium series sponsored by the National Academies of Sciences, Engineering and Medicine and the U.S. National Committee on Theoretical and Applied Mechanics.
Teeratorn Kadeethum, Daniel O'Malley, Jan Niklas Fuhg et al.
This work is the first to employ and adapt the image-to-image translation concept based on conditional generative adversarial networks (cGAN) towards learning a forward and an inverse solution operator of partial differential equations (PDEs). Even though the proposed framework could be applied as a surrogate model for the solution of any PDEs, here we focus on steady-state solutions of coupled hydro-mechanical processes in heterogeneous porous media. Strongly heterogeneous material properties, which translate to the heterogeneity of coefficients of the PDEs and discontinuous features in the solutions, require specialized techniques for the forward and inverse solution of these problems. Additionally, parametrization of the spatially heterogeneous coefficients is excessively difficult by using standard reduced order modeling techniques. In this work, we overcome these challenges by employing the image-to-image translation concept to learn the forward and inverse solution operators and utilize a U-Net generator and a patch-based discriminator. Our results show that the proposed data-driven reduced order model has competitive predictive performance capabilities in accuracy and computational efficiency as well as training time requirements compared to state-of-the-art data-driven methods for both forward and inverse problems.
The permeability of complex porous materials can be obtained via direct flow simulation, which provides the most accurate results, but is very computationally expensive. In particular, the simulation convergence time scales poorly as simulation domains become tighter or more heterogeneous. Semi-analytical models that rely on averaged structural properties (i.e. porosity and tortuosity) have been proposed, but these features only summarize the domain, resulting in limited applicability. On the other hand, data-driven machine learning approaches have shown great promise for building more general models by virtue of accounting for the spatial arrangement of the domains solid boundaries. However, prior approaches building on the Convolutional Neural Network (ConvNet) literature concerning 2D image recognition problems do not scale well to the large 3D domains required to obtain a Representative Elementary Volume (REV). As such, most prior work focused on homogeneous samples, where a small REV entails that that the global nature of fluid flow could be mostly neglected, and accordingly, the memory bottleneck of addressing 3D domains with ConvNets was side-stepped. Therefore, important geometries such as fractures and vuggy domains could not be well-modeled. In this work, we address this limitation with a general multiscale deep learning model that is able to learn from porous media simulation data. By using a coupled set of neural networks that view the domain on different scales, we enable the evaluation of large images in approximately one second on a single Graphics Processing Unit. This model architecture opens up the possibility of modeling domain sizes that would not be feasible using traditional direct simulation tools on a desktop computer.
Predicting the spatial configuration of gas molecules in nanopores of shale formations is crucial for fluid flow forecasting and hydrocarbon reserves estimation. The key challenge in these tight formations is that the majority of the pore sizes are less than 50 nm. At this scale, the fluid properties are affected by nanoconfinement effects due to the increased fluid-solid interactions. For instance, gas adsorption to the pore walls could account for up to 85% of the total hydrocarbon volume in a tight reservoir. Although there are analytical solutions that describe this phenomenon for simple geometries, they are not suitable for describing realistic pores, where surface roughness and geometric anisotropy play important roles. To describe these, molecular dynamics (MD) simulations are used since they consider fluid-solid and fluid-fluid interactions at the molecular level. However, MD simulations are computationally expensive, and are not able to simulate scales larger than a few connected nanopores. We present a method for building and training physics-based deep learning surrogate models to carry out fast and accurate predictions of molecular configurations of gas inside nanopores. Since training deep learning models requires extensive databases that are computationally expensive to create, we employ active learning (AL). AL reduces the overhead of creating comprehensive sets of high-fidelity data by determining where the model uncertainty is greatest, and running simulations on the fly to minimize it. The proposed workflow enables nanoconfinement effects to be rigorously considered at the mesoscale where complex connected sets of nanopores control key applications such as hydrocarbon recovery and CO2 sequestration.
We propose a machine learning approach to address a key challenge in materials science: predicting how fractures propagate in brittle materials under stress, and how these materials ultimately fail. Our methods use deep learning and train on simulation data from high-fidelity models, emulating the results of these models while avoiding the overwhelming computational demands associated with running a statistically significant sample of simulations. We employ a graph convolutional network that recognizes features of the fracturing material and a recurrent neural network that models the evolution of these features, along with a novel form of data augmentation that compensates for the modest size of our training data. We simultaneously generate predictions for qualitatively distinct material properties. Results on fracture damage and length are within 3% of their simulated values, and results on time to material failure, which is notoriously difficult to predict even with high-fidelity models, are within approximately 15% of simulated values. Once trained, our neural networks generate predictions within seconds, rather than the hours needed to run a single simulation.
In brittle fracture applications, failure paths, regions where the failure occurs and damage statistics, are some of the key quantities of interest (QoI). High-fidelity models for brittle failure that accurately predict these QoI exist but are highly computationally intensive, making them infeasible to incorporate in upscaling and uncertainty quantification frameworks. The goal of this paper is to provide a fast heuristic to reasonably estimate quantities such as failure path and damage in the process of brittle failure. Towards this goal, we first present a method to predict failure paths under tensile loading conditions and low-strain rates. The method uses a $k$-nearest neighbors algorithm built on fracture process zone theory, and identifies the set of all possible pre-existing cracks that are likely to join early to form a large crack. The method then identifies zone of failure and failure paths using weighted graphs algorithms. We compare these failure paths to those computed with a high-fidelity model called the Hybrid Optimization Software Simulation Suite (HOSS). A probabilistic evolution model for average damage in a system is also developed that is trained using 150 HOSS simulations and tested on 40 simulations. A non-parametric approach based on confidence intervals is used to determine the damage evolution over time along the dominant failure path. For upscaling, damage is the key QoI needed as an input by the continuum models. This needs to be informed accurately by the surrogate models for calculating effective modulii at continuum-scale. We show that for the proposed average damage evolution model, the prediction accuracy on the test data is more than 90\%. In terms of the computational time, the proposed models are $\approx \mathcal{O}(10^6)$ times faster compared to high-fidelity HOSS.
In this paper, five different approaches for reduced-order modeling of brittle fracture in geomaterials, specifically concrete, are presented and compared. Four of the five methods rely on machine learning (ML) algorithms to approximate important aspects of the brittle fracture problem. In addition to the ML algorithms, each method incorporates different physics-based assumptions in order to reduce the computational complexity while maintaining the physics as much as possible. This work specifically focuses on using the ML approaches to model a 2D concrete sample under low strain rate pure tensile loading conditions with 20 preexisting cracks present. A high-fidelity finite element-discrete element model is used to both produce a training dataset of 150 simulations and an additional 35 simulations for validation. Results from the ML approaches are directly compared against the results from the high-fidelity model. Strengths and weaknesses of each approach are discussed and the most important conclusion is that a combination of physics-informed and data-driven features are necessary for emulating the physics of crack propagation, interaction and coalescence. All of the models presented here have runtimes that are orders of magnitude faster than the original high-fidelity model and pave the path for developing accurate reduced order models that could be used to inform larger length-scale models with important sub-scale physics that often cannot be accounted for due to computational cost.