SEARCH · Search NASA
Results for “Operator learning”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
HYDROGEN RECOVERY USING AN AI-ARC-PLASMA LEARNING OPERATIONAL SYSTEM (HALO) FOR OILFIELD WASTE TRANSFORMATION TO VALUE ADDED PRODUCTS
Explore the source record for details and available documents.
Hydrogen-Recovery Using an AI-Arc-Plasma Learning Operational System For Produced Water (HALO)
Explore the source record for details and available documents.
Weighted Composition Operators for Learning Nonlinear Dynamics
Operator theoretic methods in dynamical system have been dominated by the use of Koopman operators and their continuous time counterparts, such as Koopman Generators and Liouville Operators. The advantage gained from their use primarily stems from the ability to extract subspaces and eigenfunctions within a space of observables that are invariant with respect to the Koopman operator over that space. When this occurs, a dynamic mode decomposition of the systems state provides a linear model for the dynamical system. Not all Koopman operators have eigenfunctions that may be exploited in this manner. However, the framework can still be leveraged for approximations using other operators. In this setting, we present a different operator for the study of dynamical systems, the weighted composition operator. These operators are compact for a wide range of dynamics and spaces, and through their interactions with occupation kernels and vector valued kernels, they admit an estimation of the underlying dynamics. Here, this manuscript presents a new algorithm for the data driven study of dynamical systems from data, and also provides two numerical experiments where convergence is achieved as a proof of concept.
Learning-Based Load Control to Support Resilient Networked Microgrid Operations
Microgrids have proven to be an effective option for increasing the resiliency of critical end-use loads during extreme events. Building on past operational experiences, some microgrid operators are examining the potential to network microgrids to further improve resiliency. However, the frequency deviations experienced on isolated microgrids during transient events, such as switching operations, step increases in load, and loss of generation, are significantly larger than those typically seen on bulk transmission systems. The larger frequency deviations can cause a loss of inverter-connected assets, resulting in a loss of power to critical end-use loads. This paper presents a method of mitigating the impact of transient events by engaging end-use loads using Grid-Friendly Appliance TM (GFA) controllers. An online, i.e., real-time, device-level algorithm is presented, which adjusts individual GFA controller frequency set-points based on the operational characteristics of each end-use load, and on the changing grid dynamic characteristics. The presented method improves the dynamic stability of the networked microgrid operations while minimizing the interruptions to end-use loads. The presented work is validated with dynamic simulations using a modified version of the IEEE 123-node test system with three microgrids, using the GridLAB-D TM simulation environment.
Model-parallel Fourier neural operators as learned surrogates for large-scale parametric PDEs
Fourier neural operators (FNOs) are a recently introduced neural network architecture for learning solution operators of partial differential equations (PDEs), which have been shown to perform significantly better than comparable deep learning approaches. Once trained, FNOs can achieve speed-ups of multiple orders of magnitude over conventional numerical PDE solvers. However, due to the high dimensionality of their input data and network weights, FNOs have so far only been applied to two-dimensional or small three-dimensional problems. To remove this limited problem-size barrier, we propose a model-parallel version of FNOs based on domain-decomposition of both the input data and network weights. Here, we demonstrate that our model-parallel FNO is able to predict time-varying PDE solutions of over 2.6 billion variables on Perlmutter using up to 512 A100 GPUs and show an example of training a distributed FNO on the Azure cloud for simulating multiphase CO 2 dynamics in the Earth’s subsurface.
MIONet: Learning Multiple-Input Operators via Tensor Product
As an emerging paradigm in scientific machine learning, neural operators aim to learn operators, via neural networks, that map between infinite-dimensional function spaces. Several neural operators have been recently developed. However, all the existing neural operators are only designed to learn operators defined on a single Banach space; i.e., the input of the operator is a single function. Here, for the first time, we study the operator regression via neural networks for multiple-input operators defined on the product of Banach spaces. We first prove a universal approximation theorem of continuous multiple-input operators. We also provide a detailed theoretical analysis including the approximation error, which provides guidance for the design of the network architecture. Based on our theory and a low-rank approximation, we propose a novel neural operator, MIONet, to learn multiple-input operators. MIONet consists of several branch nets for encoding the input functions and a trunk net for encoding the domain of the output function. Here, we demonstrate that MIONet can learn solution operators involving systems governed by ordinary and partial differential equations. In our computational examples, we also show that we can endow MIONet with prior knowledge of the underlying system, such as linearity and periodicity, to further improve accuracy.
Scaling Field-Theoretic Simulation for Multicomponent Mixtures with Neural Operators
Multicomponent polymer mixtures are ubiquitous in biological self-organization but are notoriously difficult to study computationally. Plagued by both slow single molecule relaxation times and slow equilibration within dense mixtures, molecular dynamics simulations are typically infeasible at the spatial scales required to study the stability of mesophase structure. Polymer field theories offer an attractive alternative, but analytical calculations are only tractable for mean-field theories and nearby perturbations, constraints that become especially problematic for fluctuation-induced effects such as coacervation. Here, we show that a recently developed technique for obtaining numerical solutions to partial differential equations based on operator learning, neural operators, lends itself to a highly scalable training strategy by parallelizing per-species operator maps. We illustrate the efficacy of our approach on six-component mixtures with randomly selected compositions and that it significantly outperforms the state-of-the-art pseudospectral integrators for field-theoretic simulations, especially as polymer lengths become long.
Regression-based projection for learning Mori-Zwanzig operators
Explore the source record for details and available documents.
One-shot learning for solution operators of partial differential equations
Learning and solving governing equations of a physical system, represented by partial differential equations (PDEs), from data is a central challenge in many areas of science and engineering. Traditional numerical methods can be computationally expensive for complex systems and require complete governing equations. Existing data-driven machine learning methods require large datasets to learn a surrogate solution operator, which could be impractical. Here, we propose a solution operator learning method that requires only one PDE solution, i.e., one-shot learning, along with suitable initial and boundary conditions. Leveraging the locality of derivatives, we define a local solution operator in small local domains, train it using a neural network, and use it to predict solutions of new input functions via mesh-based fixed-point iteration or meshfree neural-network based approaches. We test our method on various PDEs, complex geometries, and a practical spatial infection spread application, demonstrating its effectiveness and generalization capabilities.
Application of Artificial Intelligence/Machine Learning to Operations Research
This report examines the transformative impact of Artificial Intelligence (AI) and Machine Learning (ML) on operations research, private industry, and government sectors, highlighting their applications in automating processes, enhancing decision-making, and optimizing complex systems. AI/ML technologies have revolutionized industries through predictive maintenance, supply chain optimization, and autonomous systems, while also advancing public safety and defense operations. However, challenges such as data integrity, model transparency, and the need for human oversight persist, particularly in high-consequence environments. The report emphasizes the critical role of explainable AI (XAI) and human-computer interaction models like Human-in-the-Loop (HITL) and Human-on-the-Loop (HOTL) in fostering trust and accountability. Balancing automation with ethical responsibility and transparency is essential for the continued successful integration of AI/ML into operational and strategic decision-making frameworks.
GOOML: Geothermal Operational Optimization with Machine Learning
Geothermal Operational Optimization with Machine Learning (GOOML) is a project focused on maximizing increased availability and capacity from existing industrial-scale geothermal generation assets. The GOOML project will develop a suite of machine learning-based algorithms that analyze historical production datasets and provide predictive setpoints for geothermal field operations. Historical datasets from New Zealand and the US will provide the input to develop digital geothermal system twins which allow prediction of market conditions, maintenance operations and steamfield optimization. The algorithms will identify key parameters within fields and suggest setpoints for components of the system to maintain optimal generation. Set-points can be instructed to follow mass flow restrictions, generation maximization and optimal field/reservoir balance and give field operators a guide by which generation can be optimized. The datasets that will be used to develop GOOML are sourced from operating geothermal fields in New Zealand and the United States with varying degrees of complexity. This will ensure that most geothermal systems can utilize the GOOML tool to assist in optimizing operations. GOOML aims to achieve a step-change in geothermal operations by developing state-of-the-art machine learning algorithms, comprehensive data analytics, and a first-of-its-kind automated, intelligent geothermal system model.
Improved Architectures and Training Algorithms for Deep Operator Networks
Operator learning techniques have recently emerged as a powerful tool for learning maps between infinite-dimensional Banach spaces. Trained under appropriate constraints, they can also be effective in learning the solution operator of partial differential equations (PDEs) in an entirely self-supervised manner. In this work we analyze the training dynamics of deep operator networks (DeepONets) through the lens of Neural Tangent Kernel theory, and reveal a bias that favors the approximation of functions with larger magnitudes. To correct this bias we propose to adaptively re-weight the importance of each training example, and demonstrate how this procedure can effectively balance the magnitude of back-propagated gradients during training via gradient descent. We also propose a novel network architecture that is more resilient to vanishing gradient pathologies. Taken together, our developments provide new insights into the training of DeepONets and consistently improve their predictive accuracy by a factor of 10-50x, demonstrated in the challenging setting of learning PDE solution operators in the absence of paired input-output observations.
Nonintrusive projection-based reduced order modeling using stable learned differential operators
Nonintrusive projection-based reduced order models (ROMs) are essential for dynamics prediction in multi-query applications where underlying governing equations are known but the access to the source of the underlying full order model (FOM) is unavailable; that is, FOM is a glass-box. This article proposes a learn-then-project approach for nonintrusive model reduction. In the first step of this approach, high-dimensional stable sparse learned differential operators (S-LDOs) are determined using the generated data. In the second step, the ordinary differential equations, comprising these S-LDOs, are used with suitable dimensionality reduction and low-dimensional subspace projection methods to provide equations for the evolution of reduced states. This approach allows easy integration into the existing intrusive ROM framework to enable nonintrusive model reduction while allowing the use of Petrov–Galerkin projections. The applicability of the proposed approach is demonstrated for Galerkin and LSPG projection-based ROMs through four numerical experiments: 1-D scalar advection, 1-D Burgers, 2-D scalar advection and 1-D scalar advection–diffusion–reaction equations. In conclusion, the results indicate that the proposed nonintrusive ROM strategy provides accurate and stable dynamics prediction.
Learning nonlinear operators in latent spaces for real-time predictions of complex dynamics in physical systems
Abstract Predicting complex dynamics in physical applications governed by partial differential equations in real-time is nearly impossible with traditional numerical simulations due to high computational cost. Neural operators offer a solution by approximating mappings between infinite-dimensional Banach spaces, yet their performance degrades with system size and complexity. We propose an approach for learning neural operators in latent spaces, facilitating real-time predictions for highly nonlinear and multiscale systems on high-dimensional domains. Our method utilizes the deep operator network architecture on a low-dimensional latent space to efficiently approximate underlying operators. Demonstrations on material fracture, fluid flow prediction, and climate modeling highlight superior prediction accuracy and computational efficiency compared to existing methods. Notably, our approach enables approximating large-scale atmospheric flows with millions of degrees, enhancing weather and climate forecasts. Here we show that the proposed approach enables real-time predictions that can facilitate decision-making for a wide range of applications in science and engineering.