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At least 1,027 records · Page 57
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Detection of DoS Attacks Using ARFIMA Modeling of GOOSE Communication in IEC 61850 Substations

Integration of Information and Communication Technology (ICT) in modern smart grids (SGs) offers many advantages including the use of renewables and an effective way to protect, control and monitor the energy transmission and distribution. To reach an optimal operation of future energy systems, availability, integrity and confidentiality of data should be guaranteed. Research on the cyber-physical security of electrical substations based on IEC 61850 is still at an early stage. In the present work, we first model the network traffic data in electrical substations, then, we present a statistical Anomaly Detection (AD) method to detect Denial of Service (DoS) attacks against the Generic Object Oriented Substation Event (GOOSE) network communication. According to interpretations on the self-similarity and the Long-Range Dependency (LRD) of the data, an Auto-Regressive Fractionally Integrated Moving Average (ARFIMA) model was shown to describe well the GOOSE communication in the substation process network. Based on this ARFIMA-model and in view of cyber-physical security, an effective model-based AD method is developed and analyzed. Two variants of the statistical AD considering statistical hypothesis testing based on the Generalized Likelihood Ratio Test (GLRT) and the cumulative sum (CUSUM) are presented to detect flooding attacks that might affect the availability of the data. Our work presents a novel AD method, with two different variants, tailored to the specific features of the GOOSE traffic in IEC 61850 substations. The statistical AD is capable of detecting anomalies at unknown change times under the realistic assumption of unknown model parameters. The performance of both variants of the AD method is validated and assessed using data collected from a simulation case study. We perform several Monte-Carlo simulations under different noise variances. The detection delay is provided for each detector and it represents the number of discrete time samples after which an anomaly is detected. In fact, our statistical AD method with both variants (CUSUM and GLRT) has around half the false positive rate and a smaller detection delay when compared with two of the closest works found in the literature. Our AD approach based on the GLRT detector has the smallest false positive rate among all considered approaches. Whereas, our AD approach based on the CUSUM test has the lowest false negative rate thus the best detection rate. Depending on the requirements as well as the costs of false alarms or missed anomalies, both variants of our statistical detection method can be used and are further analyzed using composite detection metrics.

IEC 61850 electrical substations↗
DOE OSTI2020

Rendezvous algorithms for large-scale modeling and simulation

Rendezvous algorithms encode a communication pattern that is useful when processors sending data do not know who the receiving processors should be, or vice versa. The idea is to define an intermediate decomposition where datums from different sending processors can ”rendezvous” to perform a computation, in a manner that both the senders and eventual receivers of the results can identify the appropriate rendezvous processor. Though they were originally designed for interpolating between overlaid grids with independent parallel decompositions (Plimpton et al., 2004), we have recently found rendezvous algorithms useful for a variety of operations in particle- or grid-based simulation codes when running large problems on large numbers of processors. In particular, we show they can perform well when a load-balanced intermediate decomposition is randomized and not spatial, requiring all-to-all communication to move data between processors. In this case rendezvous algorithms leverage the large bisection communication bandwidths which parallel machines provide. We describe how rendezvous algorithms work in a scientific computing context and give specific examples for molecular dynamics and Direct Simulation Monte Carlo codes which result in dramatic performance improvements versus simpler algorithms which do not scale as well. We explain how a generic rendezvous algorithm can be implemented, and also point out similarities with the MapReduce paradigm popularized by Google and Hadoop.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Frame invariant neural network closures for Kraichnan turbulence

Numerical simulations of geophysical and atmospheric flows have to rely on parameterizations of subgrid scale processes due to their limited spatial resolution. Despite substantial progress in developing parameterization (or closure) models for subgrid scale (SGS) processes using physical insights and mathematical approximations, they remain imperfect and can lead to inaccurate predictions. In recent years, machine learning has been successful in extracting complex patterns from high-resolution spatio-temporal data, leading to improved parameterization models, and ultimately better coarse grid prediction. However, the inability to satisfy known physics and poor generalization hinders the application of these models for real-world problems. In this work, we put forth a frame invariant closure approach to improve the accuracy and generalizability of deep learning-based subgrid scale closure models by embedding physical symmetries directly into the structure of the neural network. Specifically, we utilized specialized layers within the convolutional neural network in such a way that desired constraints are theoretically guaranteed without the need for any regularization terms. We demonstrate our framework for a two-dimensional decaying turbulence test case mostly characterized by the forward enstrophy cascade. We show that our frame invariant SGS model (i) accurately predicts the subgrid scale source term, (ii) respects the physical symmetries such as translation, Galilean, and rotation invariance, and (iii) is numerically stable when implemented in coarse-grid simulation with generalization to different initial conditions and Reynolds number. This work opens up a possibility of connecting physics-based theories and data-driven modeling paradigms, and thus represents a promising step towards the development of physically consistent data-driven turbulence closure models.

42 ENGINEERING↗
DOE OSTI2020

Cyber Security Analysis for Nuclear Reactor Control Systems (Final Technical Report)

This project investigated the cyber-security impacts of moving from an all analog, point-to-point, instrumentation and control (I&C) system to a digital I&C system based on Modbus and a shared communication medium. A formalism called a hybrid attack graph was expanded to support the nuclear research reactor system. The hybrid attack graph allows one to check a system for vulnerabilities, in this case cyber-security vulnerabilities, and to document the attack vectors (scenarios) causing those vulnerabilities. In parallel, a simulation of the system was developed to model both the physical reactor parameters and operations, as well as the network interconnects and communications. This simulation platform was modeled on the nuclear research reactor located at Washington State University. The simulation platform provided a sandbox to evaluate and quantify the impact of identified and proposed vulnerabilities in the system and to determine the effectiveness of countermeasures at stopping these attacks. The simulation and hybrid attack graph tools were integrated to provide a streamlined process of generating attack scenarios, playing those scenarios out in the simulation, and then analyzing the results to correlate system state to states in the hybrid attack graph. This process was used to (1) quantify the impact of attack scenarios and (2) to determine if the system moved through the hybrid attack graph as anticipated. The hybrid attack graph tool was extended and customized to produce a tool to automatically identify critical assets (CAs) and critical digital assets (CDAs) as defined by NRC Regulatory Guide 5.71. This tool was verified using the nuclear research reactor at Washington State University. Finally, a series of educational modules covering the findings of the different aspects of this research have been created.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Aeroelastic Modelling of Large Wind Turbines: Towards a Unified OpenFAST-SEAHOWL Approach

In recent years, the scale of wind turbines has significantly increased to maximize energy capture for a given site (particularly offshore), presenting new challenges in terms of structural design and dynamics. As towers grow taller and blades grow longer, flexion and torsion of the latter have a non-negligible impact on the behavior and performance of the turbine in terms of overall loads, power production, and control. When representing large-scale wind turbines numerically to capture these important effects, particular attention must therefore be given to the level of fidelity for representing each structural component, as well as the coupling scheme used between them to keep simulations accurate, stable, and efficient. To address this issue, we combine here the two following tools: (1) OpenFAST, the reference whole-turbine simulation tool from NREL with standalone modules covering each physics and the choice between loose coupling and a new tight coupling scheme for structural dynamics, and (2) SEAHOWL, the whole-turbine simulation tool from TotalEnergies with monolithic coupling of structural dynamics through Project Chrono and partitioned coupling for multiphysics interactions.

17 WIND ENERGY↗
DOE OSTI2024

The Effect of the Prior and the Experimental Design on the Inference of the Precision Matrix in Gaussian Chain Graph Models

Here, we investigate whether (and how) experimental design could aid in the estimation of the precision matrix in a Gaussian chain graph model, especially the interplay between the design, the effect of the experiment and prior knowledge about the effect. Estimation of the precision matrix is a fundamental task to infer biological graphical structures like microbial networks. We compare the marginal posterior precision of the precision matrix under four priors: flat, conjugate Normal-Wishart, Normal-MGIG and a general independent. Under the flat and conjugate priors, the Laplace-approximated posterior precision is not a function of the design matrix rendering useless any efforts to find an optimal experimental design to infer the precision matrix. In contrast, the Normal-MGIG and general independent priors do allow for the search of optimal experimental designs, yet there is a sharp upper bound on the information that can be extracted from a given experiment. We confirm our theoretical findings via a simulation study comparing (i) the KL divergence between prior and posterior and (ii) the Stein’s loss difference of MAPs between random and no experiment. Our findings provide practical advice for domain scientists conducting experiments to better infer the precision matrix as a representation of a biological network.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Towards sharp error analysis of extended Lagrangian molecular dynamics

The extended Lagrangian molecular dynamics (XLMD) method provides a useful framework for reducing the computational cost of a class of molecular dynamics simulations with constrained latent variables. The XLMD method relaxes the constraints by introducing a fictitious mass ε for the latent variables and solving a set of singularly perturbed ordinary differential equations. While favorable numerical performance of XLMD has been demonstrated in several different contexts in the past decade, mathematical analysis of the method remains scarce. Here, we propose the first error analysis of the XLMD method in the context of a classical polarizable force field model. While the dynamics with respect to the atomic degrees of freedom are general and nonlinear, the key mathematical simplification of the polarizable force field model is that the constraints on the latent variables are given by a linear system of equations. We prove that when the initial value of the latent variables is compatible in a sense that we define, XLMD converges as the fictitious mass ε is made small with $\mathscr{O}$(ε) error for the atomic degrees of freedom and with $\mathscr{O}$($\sqrt{ε}$) error for the latent variables, when the dimension of the latent variable d' is 1. Furthermore, when the initial value of the latent variables is improved to be optimally compatible in a certain sense, we prove that the convergence rate can be improved to $\mathscr{O}$(ε) for the latent variables as well. Numerical results verify that both estimates are sharp not only for d'=1, but also for arbitrary d'. In the setting of general d', we do obtain convergence, but with the non-sharp rate of $\mathscr{O}$($\sqrt{ε}$) for both the atomic and latent variables.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2025

Advancing Multi-Hazard Risk and Safety Considerations for Aging Nuclear Facilities (Revision 1)

This project will demonstrate a multi-hazard time-dependent probabilistic risk assessment (PRA) approach for nuclear facilities considering aging-related deterioration of structures. A generic pressurized water reactor (PWR) reactor subjected to seismic mainshock-aftershock sequences considering the aging of the containment structure will be used as a case study to demonstrate the multi-hazard PRA approach. Using advanced modeling and simulation, seismic mainshock-aftershock fragility functions will be simulated for the containment structure considering aging effects. A multi-hazard PRA model for a generic PWR reactor will be built to quantify the multi-hazard core damage frequency (CDF) and large early release frequency (LERF) with explicit time-dependent modeling of event sequences. To date, the cascading impacts of multi-hazards are not adequately accounted for in the PRA models for nuclear facilities. In addition, for both initial and periodic evaluation of facilities to withstand natural phenomena hazards (NPH), deterioration of the SSCs due to aging and other effects is not adequately considered. By advancing multi-hazard considerations accounting for aging effects, this project will contribute to improved understanding of the safety of aging nuclear facilities. Project outcomes such as the multi-hazard CDF and LERF will also allow facility owners to optimize upgrade and retrofit protocols. This project is divided into two components: (1) advanced modeling and simulations; and (2) multi-hazard PRA. For the first component, Idaho National Laboratory’s (INL) Multi-hazard Analysis for STOchastic time-DOmaiN phenomena (MASTODON) and BlackBear codes will be used to simulate the seismic response and damage of a containment structure under cascading mainshock-aftershock sequences with aging effects. Uncertainties related to the seismic inputs, material parameters, and environmental factors such as temperature and humidity will be identified and propagated to the fragility functions. These fragility functions, which consider aging effects, will be time dependent. The second component will take the fragility information from the first component to build a multi-hazard time-dependent PRA model starting from a generic PWR model to evaluate the multi-hazard CDF and LERF and characterize the associated consequences. For this component, OpenPRA Web Application and SAPHIRE code will be used. Events such as the Fukushima Daiichi accident have highlighted the importance of considering the cascading impacts of multi-hazards for PRA. Moreover, many of the reactors in the current nuclear fleet in the United States (US) are already operating well beyond their initially planned design life, and applications for further extensions to operating licenses are being considered. Therefore, considering multi-hazard effects and aging deterioration in the NPH risk assessment process will contribute to the safety of both existing and future nuclear facilities. Outcomes of this project will thus directly benefit the standards DOE-STD-1020-16 and DOE-HDBK-1224-18.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

Forecasting high-dimensional spatio-temporal systems from sparse measurements

This paper introduces a new neural network architecture designed to forecast high-dimensional spatio-temporal data using only sparse measurements. The architecture uses a two-stage end-to-end framework that combines neural ordinary differential equations (NODEs) with vision transformers. Initially, our approach models the underlying dynamics of complex systems within a low-dimensional space; and then it reconstructs the corresponding high-dimensional spatial fields. Many traditional methods involve decoding high-dimensional spatial fields before modeling the dynamics, while some other methods use an encoder to transition from high-dimensional observations to a latent space for dynamic modeling. In contrast, our approach directly uses sparse measurements to model the dynamics, bypassing the need for an encoder. This direct approach simplifies the modeling process, reduces computational complexity, and enhances the efficiency and scalability of the method for large datasets. We demonstrate the effectiveness of our framework through applications to various spatio-temporal systems, including fluid flows and global weather patterns. Although sparse measurements have limitations, our experiments reveal that they are sufficient to forecast system dynamics accurately over long time horizons. Our results also indicate that the performance of our proposed method remains robust across different sensor placement strategies, with further improvements as the number of sensors increases. This robustness underscores the flexibility of our architecture, particularly in real-world scenarios where sensor data is often sparse and unevenly distributed.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Adaptive Computing for Scale-Up Problems

Adaptive Computing is an application-agnostic outer loop framework to strategically deploy simulations and experiments to guide decision making for scale-up analysis. Resources are allocated over successive batches, which makes the allocation adaptive to some objective such as optimization or model training. The framework enables the characterization and management of uncertainties associated with predictive models of complex systems when scale-up questions lead to significant model extrapolation. A key advancement of this framework is its integration of multi-fidelity surrogate modeling, uncertainty management, and automated orchestration of various computing and experimentation resources into a single integrated software package. This enables efficient multi-fidelity modeling across multiple computing resources by incorporating real-world constraints such as relative queue times and throughput on individual machines into the multi-fidelity sampling decision. We discuss applications of this framework to problems in the renewable energy space, including biofuels production, material synthesis, perovskite crystal growth, and building electrical loads.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2021

SGD-Net: Efficient Model-Based Deep Learning with Theoretical Guarantees

Deep unfolding networks have recently gained popularity for solving imaging inverse problems. However, the computational and memory complexity of data-consistency layers within traditional deep unfolding networks scales with the number of measurements, limiting their applicability to large-scale imaging inverse problems. We propose SGD-Net as a new methodology for improving the efficiency of deep unfolding through stochastic approximations of the data-consistency layers. Our theoretical analysis shows that SGD-Net can be trained to approximate batch deep unfolding networks to an arbitrary precision. Our simulations on intensity diffraction tomography and sparse-view computed tomography show that SGD-Net can match the performance of the traditional batch network at a fraction of training and testing complexity.Deep unfolding networks have recently gained popularity for solving imaging inverse problems. However, the computational and memory complexity of data-consistency layers within traditional deep unfolding networks scales with the number of measurements, limiting their applicability to large-scale imaging inverse problems. We propose SGD-Net as a new methodology for improving the efficiency of deep unfolding through stochastic approximations of the data-consistency layers. Our theoretical analysis shows that SGD-Net can be trained to approximate batch deep unfolding networks to an arbitrary precision. Our simulations on intensity diffraction tomography and sparse-view computed tomography show that SGD-Net can match the performance of the traditional batch network at a fraction of training and testing complexity.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Dynamic, symmetry-preserving, and hardware-adaptable circuits for quantum computing many-body states and correlators of the Anderson impurity model

We present a hardware-reconfigurable ansatz on N q -qubits for the variational preparation of many-body states of the Anderson impurity model (AIM) with N imp + N bath = N q /2 sites, which conserves total charge and spin z component within each variational search subspace. The many-body ground state of the AIM is determined as the minimum over all minima of O(N$^2_ q$) distinct charge-spin sectors. Hamiltonian expectation values are shown to require ω(N q ) < N meas. $\leqslant$ O(N imp N bath ) symmetry-preserving, parallelizable measurement circuits, each amenable to postselection. To obtain the one-particle impurity Green’s function we show how initial Krylov vectors can be computed via midcircuit measurement and how Lanczos iterations can be computed using the symmetry-preserving ansatz. For a single-impurity Anderson model with a number of bath sites increasing from one to seven, we show using numerical emulation that the ease of variational ground-state preparation is suggestive of linear scaling in circuit depth and subquartic scaling in optimizer complexity. We therefore expect that, combined with time-dependent methods for Green’s function computation, our ansatz provides a useful tool to account for electronic correlations on early fault-tolerant processors. Finally, with a view towards computing real materials properties of interest like magnetic susceptibilities and electron-hole propagators, we provide a straightforward method to compute many-body, time-dependent correlation functions using a combination of time evolution, midcircuit measurement-conditioned operations, and the Hadamard test.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Updated parameters of the LArQL model

The need for a microscopic description of scintillation light generation in liquid argon becomes increasingly desirable with the upcoming operation of large scale LArTPCs in the next decade. While a detailed mathematical account of the process is still to be achieved, a phenomenological model for simultaneously treating ionization and scintillation, LArQL, has been successfully employed to describe the range of electric fields from 0 to 0.75 kV/cm and dE/dx from 2 to 40 MeV/cm providing the anti-correlation between the free ionization charge and scintillation light. A reanalysis of the original model parameter values has been performed within a global fit procedure and is presented.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Sampling Low-Dimensional Markovian Dynamics for Preasymptotically Recovering Reduced Models from Data with Operator Inference

This work introduces a method for learning low-dimensional models from data of high-dimensional black-box dynamical systems. The novelty is that the learned models are exactly the reduced models that are traditionally constructed with classical projection-based model reduction techniques. Thus, the proposed approach learns models that are guaranteed to have the well-studied properties of reduced models known from model reduction, without requiring full knowledge of the governing equations and without requiring the operators of the high-dimensional systems. The key ingredient is a new data sampling scheme to obtain re-projected trajectories of high-dimensional systems that correspond to Markovian dynamics in low-dimensional subspaces. The exact recovery of reduced models from these re-projected trajectories is guaranteed pre-asymptotically under certain conditions for finite amounts of data and for a large class of systems with polynomial nonlinear terms. Numerical results demonstrate that the low-dimensional models learned with the proposed approach match reduced models from traditional model reduction up to numerical errors in practice. In conclusion, the numerical results further indicate that low-dimensional models fitted to re-projected trajectories are predictive even in situations where models fitted to trajectories without re-projection are inaccurate and unstable.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Two-Step Hyperparameter Optimization Method: Accelerating Hyperparameter Search by Using a Fraction of a Training Dataset

Abstract Hyperparameter optimization (HPO) is an important step in machine learning (ML) model development, but common practices are archaic—primarily relying on manual or grid searches. This is partly because adopting advanced HPO algorithms introduces added complexity to the workflow, leading to longer computation times. This poses a notable challenge to ML applications, as suboptimal hyperparameter selections curtail the potential of ML model performance, ultimately obstructing the full exploitation of ML techniques. In this article, we present a two-step HPO method as a strategic solution to curbing computational demands and wait times, gleaned from practical experiences in applied ML parameterization work. The initial phase involves a preliminary evaluation of hyperparameters on a small subset of the training dataset, followed by a reevaluation of the top-performing candidate models postretraining with the entire training dataset. This two-step HPO method is universally applicable across HPO search algorithms, and we argue it has attractive efficiency gains. As a case study, we present our recent application of the two-step HPO method to the development of neural network emulators for aerosol activation. Although our primary use case is a data-rich limit with many millions of samples, we also find that using up to 0.0025% of the data—a few thousand samples—in the initial step is sufficient to find optimal hyperparameter configurations from much more extensive sampling, achieving up to 135× speedup. The benefits of this method materialize through an assessment of hyperparameters and model performance, revealing the minimal model complexity required to achieve the best performance. The assortment of top-performing models harvested from the HPO process allows us to choose a high-performing model with a low inference cost for efficient use in global climate models (GCMs).

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

PastoralScape: An Environment-Driven Model of Vaccination Decision Making Within Pastoralist Groups in East Africa

Economic and cultural resilience among pastoralists in East Africa is threatened by the interconnected forces of climate change, contagious diseases spread and evolving national and international trade. A key factor in the resilience of livestock that communities depend on is human decision making regarding vaccination against prevalent diseases such as Rift Valley fever and Contagious Bovine Pleuropneumonia. This paper describes an agent-based model that couples models of disease propagation, animal health, human decision making, and external GIS data sources capturing measures of foraging condition. We describe the design of the sub-models, their coupling, and demonstrate the sensitivity of the model to parameters that relate to controllable factors such as government and NGO information sources that can influence human decision making patterns. This model is intended to form the basis upon which richer economic and human factor models can be built.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Generating Mixed Patterns of Residential Segregation: An Evolutionary Approach

The Schelling model of residential segregation has demonstrated that even the slightest preference for neighbors of the same race can be amplified into community-wide segregation. However, these models are unable to simulate mixed, coexisting patterns of segregation and integration, which have been seen to exist in cities. Using evolutionary model discovery we demonstrate how including social factors beyond racial bias when modeling relocation behavior enables the emergence of strongly mixed patterns. Our results indicate that the emergence of mixed patterns is better explained by multiple factors influencing the decision to relocate; the most important being the interaction of nonlinear, rapidly diminishing racial bias with a recent, historical tendency to move. Additionally, preference for less isolated neighborhoods or preference for neighborhoods with longer residing neighbors may produce weaker mixed patterns. Finally, this work highlights the importance of exploring the influence of multiple hypothesized factors of decision making, and their interactions, within agent rules, when studying emergent outcomes generated by agent-based models of complex social systems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Supporting hierarchical soil biogeochemical modeling: version 2 of the Biogeochemical Transport and Reaction model (BeTR-v2)

Abstract. Reliable soil biogeochemical modeling is a prerequisite for credible projections of climate change and associated ecosystem feedbacks. This recognition has called for frameworks that can support flexible and efficient development and application of new or alternative soil biogeochemical modules in Earth system models (ESMs). The the Biogeochemical Transport and Reaction model version 1 (BeTR-v1) code (i.e., CLM4-BeTR) is one such framework designed to accelerate the development and integration of new soil biogeochemistry formulations into ESMs and to analyze structural uncertainty in ESM simulations. With a generic reactive transport capability, BeTR-v1 can represent multiphase (e.g., gaseous, aqueous, and solid), multi-tracer (e.g., nitrate and organic carbon), and multi-organism (e.g., plants, bacteria, and fungi) dynamics. Here, we describe the new version, Biogeochemical Transport and Reaction model version 2 (BeTR-v2), which adopts more robust numerical solvers for multiphase diffusion and advection and coupling between biogeochemical reactions and improves code modularization over BeTR-v1. BeTR-v2 better supports different mathematical formulations in a hierarchical manner by allowing the resultant model be run for a single topsoil layer or a vertically resolved soil column, and it allows the model to be fully coupled with the land component of the Energy Exascale Earth System Model (E3SM). We demonstrate the capability of BeTR-v2 with benchmark cases and example soil biogeochemical (BGC) implementations. By taking advantage of BeTR-v2's generic structure integrated in E3SM, we then found that calibration could not resolve biases introduced by different numerical coupling strategies of plant–soil biogeochemistry. These results highlight the importance of numerically robust implementation of soil biogeochemistry and coupling with hydrology, thermal dynamics, and plants – capabilities that the open-source BeTR-v2 provides. We contend that Earth system models should strive to minimize this uncertainty by applying better numerical solvers.

58 GEOSCIENCES↗