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Daniel O'Malley

Publications and source records attributed to Daniel O'Malley.

At least 37 records · Page 2Linked to original sources
arXiv2023

Learning the Factors Controlling Mineralization for Geologic Carbon Sequestration

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.

cs.CE↗
arXiv2023

Reconstruction of Fields from Sparse Sensing: Differentiable Sensor Placement Enhances Generalization

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.

physics.geo-ph↗
arXiv2023

JuliQAOA: Fast, Flexible QAOA Simulation

We introduce JuliQAOA, a simulation package specifically built for the Quantum Alternating Operator Ansatz (QAOA). JuliQAOA does not require a circuit-level description of QAOA problems, or another package to simulate such circuits, instead relying on a more direct linear algebra implementation. This allows for increased QAOA-specific performance improvements, as well as improved flexibility and generality. JuliQAOA is the first QAOA package designed to aid in the study of both constrained and unconstrained combinatorial optimization problems, and can easily include novel cost functions, mixer Hamiltonians, and other variations. JuliQAOA also includes robust and extensible methods for learning optimal angles. Written in the Julia language, JuliQAOA outperforms existing QAOA software packages and scales well to HPC-level resources. JuliQAOA is available at https://github.com/lanl/JuliQAOA.jl.

quant-ph↗
arXiv2023

Learning a General Model of Single Phase Flow in Complex 3D Porous Media

Modeling effective transport properties of 3D porous media, such as permeability, at multiple scales is challenging as a result of the combined complexity of the pore structures and fluid physics - in particular, confinement effects which vary across the nanoscale to the microscale. While numerical simulation is possible, the computational cost is prohibitive for realistic domains, which are large and complex. Although machine learning models have been proposed to circumvent simulation, none so far has simultaneously accounted for heterogeneous 3D structures, fluid confinement effects, and multiple simulation resolutions. By utilizing numerous computer science techniques to improve the scalability of training, we have for the first time developed a general flow model that accounts for the pore-structure and corresponding physical phenomena at scales from Angstrom to the micrometer. Using synthetic computational domains for training, our machine learning model exhibits strong performance (R$^2$=0.9) when tested on extremely diverse real domains at multiple scales.

physics.geo-ph↗
arXiv2023

Computationally Efficient and Error Aware Surrogate Construction for Numerical Solutions of Subsurface Flow Through Porous Media

Limiting the injection rate to restrict the pressure below a threshold at a critical location can be an important goal of simulations that model the subsurface pressure between injection and extraction wells. The pressure is approximated by the solution of Darcy's partial differential equation (PDE) for a given permeability field. The subsurface permeability is modeled as a random field since it is known only up to statistical properties. This induces uncertainty in the computed pressure. Solving the PDE for an ensemble of random permeability simulations enables estimating a probability distribution for the pressure at the critical location. These simulations are computationally expensive, and practitioners often need rapid online guidance for real-time pressure management. An ensemble of numerical PDE solutions is used to construct a Gaussian process regression model that can quickly predict the pressure at the critical location as a function of the extraction rate and permeability realization. Our first novel contribution is to identify a sampling methodology for the random environment and matching kernel technology for which fitting the Gaussian process regression model scales as O(n log n) instead of the typical O(n^3) rate in the number of samples n used to fit the surrogate. The surrogate model allows almost instantaneous predictions for the pressure at the critical location as a function of the extraction rate and permeability realization. Our second contribution is a novel algorithm to calibrate the uncertainty in the surrogate model to the discrepancy between the true pressure solution of Darcy's equation and the numerical solution. Although our method is derived for building a surrogate for the solution of Darcy's equation with a random permeability field, the framework broadly applies to solutions of other PDE with random coefficients.

stat.CO↗
arXiv2023

Progressive reduced order modeling: empowering data-driven modeling with selective knowledge transfer

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.

cs.LG↗
arXiv2023

Addressing Quantum's "Fine Print": State Preparation and Information Extraction for Quantum Algorithms and Geologic Fracture Networks

Quantum algorithms provide an exponential speedup for solving certain classes of linear systems, including those that model geologic fracture flow. However, this revolutionary gain in efficiency does not come without difficulty. Quantum algorithms require that problems satisfy not only algorithm-specific constraints, but also application-specific ones. Otherwise, the quantum advantage carefully attained through algorithmic ingenuity can be entirely negated. Previous work addressing quantum algorithms for geologic fracture flow has illustrated core algorithmic approaches while incrementally removing assumptions. This work addresses two further requirements for solving geologic fracture flow systems with quantum algorithms: efficient system state preparation and efficient information extraction. Our approach to addressing each is consistent with an overall exponential speed-up.

quant-ph↗
arXiv2023

Machine Learning Based Approach to Predict Ductile Damage Model Parameters for Polycrystalline Metals

Damage models for ductile materials typically need to be parameterized, often with the appropriate parameters changing for a given material depending on the loading conditions. This can make parameterizing these models computationally expensive, since an inverse problem must be solved for each loading condition. Using standard inverse modeling techniques typically requires hundreds or thousands of high-fidelity computer simulations to estimate the optimal parameters. Additionally, the time of a human expert is required to set up the inverse model. Machine learning has recently emerged as an alternative approach to inverse modeling in these settings, where the machine learning model is trained in an offline manner and new parameters can be quickly generated on the fly, after training is complete. This work utilizes such a workflow to enable the rapid parameterization of a ductile damage model called TEPLA with a machine learning inverse model. The machine learning model can efficiently estimate the model parameters much faster, as compared to previously employed methods, such as Bayesian calibration. The results demonstrate good accuracy on a synthetic test dataset and is validated against experimental data.

cond-mat.mtrl-sci↗
arXiv2023

Characterizing the impacts of multi-scale heterogeneity on solute transport in fracture networks

We model flow and transport in three-dimensional fracture networks with varying degrees of fracture-to-fracture aperture/permeability heterogeneity and network density to show how changes in these properties can cause the emergence of anomalous flow and transport behavior. If fracture-to-fracture aperture heterogeneity is increased in sparse networks, velocity fluctuations can inhibit high flow rates and solute transport can be delayed, even in cases where hydraulic aperture is monotonically increased. As the density of the networks is increased, more connected pathways allow for particles to bypass these effects. We discover transition behavior where with relatively few connected pathways in a network from inflow to outflow boundaries, the first arrival times of particles are not heavily affected by fracture-to-fracture aperture heterogeneity, but the scaling behavior of the tails is strongly influenced due to the particles being forced to sample some of the heterogeneity in the velocity field caused by aperture differences. These results reinforce the importance of considering multi-scale effects in fractured systems and can inform flow and transport processes in both natural and engineered fracture systems, especially the latter where high aperture fractures are often stimulated and connect to existing fracture networks with smaller apertures.

physics.geo-ph↗
arXiv2023

Numerical Evidence for Exponential Speed-up of QAOA over Unstructured Search for Approximate Constrained Optimization

Despite much recent work, the true promise and limitations of the Quantum Alternating Operator Ansatz (QAOA) are unclear. A critical question regarding QAOA is to what extent its performance scales with the input size of the problem instance, in particular the necessary growth in the number of QAOA rounds to reach a high approximation ratio. We present numerical evidence for an exponential speed-up of QAOA over Grover-style unstructured search in finding approximate solutions to constrained optimization problems. Our result provides a strong hint that QAOA is able to exploit the structure of an optimization problem and thus overcome the lower bound for unstructured search. To this end, we conduct a comprehensive numerical study on several Hamming-weight constrained optimization problems for which we include combinations of all standardly studied mixer and phase separator Hamiltonians (Ring mixer, Clique mixer, Objective Value phase separator) as well as quantum minimum-finding inspired Hamiltonians (Grover mixer, Threshold-based phase separator). We identify Clique-Objective-QAOA with an exponential speed-up over Grover-Threshold-QAOA and tie the latter's scaling to that of unstructured search, with all other QAOA combinations coming in at a distant third. Our result suggests that maximizing QAOA performance requires a judicious choice of mixer and phase separator, and should trigger further research into other QAOA variations.

quant-ph↗
arXiv2023

The Quantum Alternating Operator Ansatz for Satisfiability Problems

We comparatively study, through large-scale numerical simulation, the performance across a large set of Quantum Alternating Operator Ansatz (QAOA) implementations for finding approximate and optimum solutions to unconstrained combinatorial optimization problems. Our survey includes over 100 different mixing unitaries, and we combine each mixer with both the standard phase separator unitary representing the objective function and a thresholded version. Our numerical tests for randomly chosen instances of the unconstrained optimization problems Max 2-SAT and Max 3-SAT reveal that the traditional transverse-field mixer with the standard phase separator performs best for problem sizes of 8 through 14 variables, while the recently introduced Grover mixer with thresholding wins at problems of size 6. This result (i) corrects earlier work suggesting that the Grover mixer is a superior mixer based only on results from problems of size 6, thus illustrating the need to push numerical simulation to larger problem sizes to more accurately predict performance; and (ii) it suggests that more complicated mixers and phase separators may not improve QAOA performance.

quant-ph↗
arXiv2023

Quantum Computing and Preconditioners for Hydrological Linear Systems

Modeling hydrological fracture networks is a hallmark challenge in computational earth sciences. Accurately predicting critical features of fracture systems, e.g. percolation, can require solving large linear systems far beyond current or future high performance capabilities. Quantum computers can theoretically bypass the memory and speed constraints faced by classical approaches, however several technical issues must first be addressed. Chief amongst these difficulties is that such systems are often ill-conditioned, i.e. small changes in the system can produce large changes in the solution, which can slow down the performance of linear solving algorithms. We test several existing quantum techniques to improve the condition number, but find they are insufficient. We then introduce the inverse Laplacian preconditioner, which improves the scaling of the condition number of the system from $O(N)$ to $O(\sqrt{N})$ and admits a quantum implementation. These results are a critical first step in developing a quantum solver for fracture systems, both advancing the state of hydrological modeling and providing a novel real-world application for quantum linear systems algorithms.

physics.comp-ph↗
arXiv2022

Quantum Algorithms for Geologic Fracture Networks

Solving large systems of equations is a challenge for modeling natural phenomena, such as simulating subsurface flow. To avoid systems that are intractable on current computers, it is often necessary to neglect information at small scales, an approach known as coarse-graining. For many practical applications, such as flow in porous, homogenous materials, coarse-graining offers a sufficiently-accurate approximation of the solution. Unfortunately, fractured systems cannot be accurately coarse-grained, as critical network topology exists at the smallest scales, including topology that can push the network across a percolation threshold. Therefore, new techniques are necessary to accurately model important fracture systems. Quantum algorithms for solving linear systems offer a theoretically-exponential improvement over their classical counterparts, and in this work we introduce two quantum algorithms for fractured flow. The first algorithm, designed for future quantum computers which operate without error, has enormous potential, but we demonstrate that current hardware is too noisy for adequate performance. The second algorithm, designed to be noise resilient, already performs well for problems of small to medium size (order 10 to 1000 nodes), which we demonstrate experimentally and explain theoretically. We expect further improvements by leveraging quantum error mitigation and preconditioning.

quant-ph↗
arXiv2022

Physics-embedded inverse analysis with automatic differentiation for the earth's subsurface

Inverse analysis has been utilized to understand unknown underground geological properties by matching the observational data with simulators. To overcome the underconstrained nature of inverse problems and achieve good performance, an approach is presented with embedded physics and a technique known as automatic differentiation. We use a physics-embedded generative model, which takes statistically simple parameters as input and outputs subsurface properties (e.g., permeability or P-wave velocity), that embeds physical knowledge of the subsurface properties into inverse analysis and improves its performance. We tested the application of this approach on four geologic problems: two heterogeneous hydraulic conductivity fields, a hydraulic fracture network, and a seismic inversion for P-wave velocity. This physics-embedded inverse analysis approach consistently characterizes these geological problems accurately. Furthermore, the excellent performance in matching the observational data demonstrates the reliability of the proposed method. Moreover, the application of automatic differentiation makes this an easy and fast approach to inverse analysis when dealing with complicated geological structures.

physics.comp-ph↗
arXiv2022

Quantum Algorithm Implementations for Beginners

As quantum computers become available to the general public, the need has arisen to train a cohort of quantum programmers, many of whom have been developing classical computer programs for most of their careers. While currently available quantum computers have less than 100 qubits, quantum computing hardware is widely expected to grow in terms of qubit count, quality, and connectivity. This review aims to explain the principles of quantum programming, which are quite different from classical programming, with straightforward algebra that makes understanding of the underlying fascinating quantum mechanical principles optional. We give an introduction to quantum computing algorithms and their implementation on real quantum hardware. We survey 20 different quantum algorithms, attempting to describe each in a succinct and self-contained fashion. We show how these algorithms can be implemented on IBM's quantum computer, and in each case, we discuss the results of the implementation with respect to differences between the simulator and the actual hardware runs. This article introduces computer scientists, physicists, and engineers to quantum algorithms and provides a blueprint for their implementations.

cs.ET↗
arXiv2022

Physics-informed machine learning with differentiable programming for heterogeneous underground reservoir pressure management

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.

physics.comp-ph↗
arXiv2022

Fair Sampling Error Analysis on NISQ Devices

We study the status of fair sampling on Noisy Intermediate Scale Quantum (NISQ) devices, in particular the IBM Q family of backends. Using the recently introduced Grover Mixer-QAOA algorithm for discrete optimization, we generate fair sampling circuits to solve six problems of varying difficulty, each with several optimal solutions, which we then run on twenty backends across the IBM Q system. For a given circuit evaluated on a specific set of qubits, we evaluate: how frequently the qubits return an optimal solution to the problem, the fairness with which the qubits sample from all optimal solutions, and the reported hardware error rate of the qubits. To quantify fairness, we define a novel metric based on Pearson's $χ^2$ test. We find that fairness is relatively high for circuits with small and large error rates, but drops for circuits with medium error rates. This indicates that structured errors dominate in this regime, while unstructured errors, which are random and thus inherently fair, dominate in noisier qubits and longer circuits. Our results show that fairness can be a powerful tool for understanding the intricate web of errors affecting current NISQ hardware.

quant-ph↗
arXiv2022

Quantum Annealing Algorithms for Boolean Tensor Networks

Quantum annealers manufactured by D-Wave Systems, Inc., are computational devices capable of finding high-quality solutions of NP-hard problems. In this contribution, we explore the potential and effectiveness of such quantum annealers for computing Boolean tensor networks. Tensors offer a natural way to model high-dimensional data commonplace in many scientific fields, and representing a binary tensor as a Boolean tensor network is the task of expressing a tensor containing categorical (i.e., {0, 1}) values as a product of low dimensional binary tensors. A Boolean tensor network is computed by Boolean tensor decomposition, and it is usually not exact. The aim of such decomposition is to minimize the given distance measure between the high-dimensional input tensor and the product of lower-dimensional (usually three-dimensional) tensors and matrices representing the tensor network. In this paper, we introduce and analyze three general algorithms for Boolean tensor networks: Tucker, Tensor Train, and Hierarchical Tucker networks. The computation of a Boolean tensor network is reduced to a sequence of Boolean matrix factorizations, which we show can be expressed as a quadratic unconstrained binary optimization problem suitable for solving on a quantum annealer. By using a novel method we introduce called \textit{parallel quantum annealing}, we demonstrate that tensor with up to millions of elements can be decomposed efficiently using a DWave 2000Q quantum annealer.

quant-ph↗