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At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Streamlining Ocean Dynamics Modeling with Fourier Neural Operators: A Multiobjective Hyperparameter and Architecture Optimization Approach

Training an effective deep learning model to learn ocean processes involves careful choices of various hyperparameters. We leverage DeepHyper’s advanced search algorithms for multiobjective optimization, streamlining the development of neural networks tailored for ocean modeling. The focus is on optimizing Fourier neural operators (FNOs), a data-driven model capable of simulating complex ocean behaviors. Selecting the correct model and tuning the hyperparameters are challenging tasks, requiring much effort to ensure model accuracy. DeepHyper allows efficient exploration of hyperparameters associated with data preprocessing, FNO architecture-related hyperparameters, and various model training strategies. We aim to obtain an optimal set of hyperparameters leading to the most performant model. Moreover, on top of the commonly used mean squared error for model training, we propose adopting the negative anomaly correlation coefficient as the additional loss term to improve model performance and investigate the potential trade-off between the two terms. The numerical experiments show that the optimal set of hyperparameters enhanced model performance in single timestepping forecasting and greatly exceeded the baseline configuration in the autoregressive rollout for long-horizon forecasting up to 30 days. Utilizing DeepHyper, we demonstrate an approach to enhance the use of FNO in ocean dynamics forecasting, offering a scalable solution with improved precision.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

B-DeepONet: An enhanced Bayesian DeepONet for solving noisy parametric PDEs using accelerated replica exchange SGLD

Here, the Deep Operator Network (DeepONet) is a neural network architecture used to approximate operators, including the solution operator of parametric PDEs. DeepONets have shown remarkable approximation ability. However, the performance of DeepONets deteriorates when the training data is polluted with noise, a scenario that occurs in practice. To handle noisy data, we propose a Bayesian DeepONet based on replica exchange Langevin diffusion (reLD). Replica exchange uses two particles. The first particle trains a DeepONet to exploit the loss landscape and make predictions. The other particle trains a different DeepONet to explore the loss landscape and escape local minima via swapping. Compared to DeepONets trained with state-of-the-art gradient-based algorithms (e.g., Adam), the proposed Bayesian DeepONet greatly improves the training convergence for noisy scenarios and accurately estimates the uncertainty. To further reduce the high computational cost of the reLD training of DeepONets, we propose (1) an accelerated training framework that exploits the DeepONet's architecture to reduce its computational cost up to 25% without compromising performance and (2) a transfer learning strategy that accelerates training DeepONets for PDEs with different parameter values. Finally, we illustrate the effectiveness of the proposed Bayesian DeepONet using four parametric PDE problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Operator learning for predicting multiscale bubble growth dynamics

We report simulating and predicting multiscale problems that couple multiple physics and dynamics across many orders of spatiotemporal scales is a great challenge that has not been investigated systematically by deep neural networks (DNNs). Herein, we develop a framework based on operator regression, the so-called deep operator network (DeepONet), with the long-term objective to simplify multiscale modeling by avoiding the fragile and time-consuming “hand-shaking” interface algorithms for stitching together heterogeneous descriptions of multiscale phenomena. To this end, as a first step, we investigate if a DeepONet can learn the dynamics of different scale regimes, one at the deterministic macroscale and the other at the stochastic microscale regime with inherent thermal fluctuations. Specifically, we test the effectiveness and accuracy of the DeepONet in predicting multirate bubble growth dynamics, which is described by a Rayleigh–Plesset (R–P) equation at the macroscale and modeled as a stochastic nucleation and cavitation process at the microscale by dissipative particle dynamics (DPD). First, we generate data using the R–P equation for multirate bubble growth dynamics caused by randomly time-varying liquid pressures drawn from Gaussian random fields (GRFs). Our results show that properly trained DeepONets can accurately predict the macroscale bubble growth dynamics and can outperform long short-term memory networks. We also demonstrate that the DeepONet can extrapolate accurately outside the input distribution using only very few new measurements. Subsequently, we train the DeepONet with DPD data corresponding to stochastic bubble growth dynamics. Although the DPD data are noisy and we only collect sparse data points on the trajectories, the trained DeepONet model is able to predict accurately the mean bubble dynamics for time-varying GRF pressures. Taken together, our findings demonstrate that DeepONets can be employed to unify the macroscale and microscale models of the multirate bubble growth problem, hence providing new insight into the role of operator regression via DNNs in tackling realistic multiscale problems and in simplifying modeling with heterogeneous descriptions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Long-time integration of parametric evolution equations with physics-informed DeepONets

Ordinary and partial differential equations (ODEs/PDEs) play a paramount role in analyzing and simulating complex dynamic processes across all corners of science and engineering. In recent years machine learning tools are aspiring to introduce new effective ways of simulating such equations, however existing approaches are not able to reliably return stable and accurate predictions across long temporal horizons. We aim to address this challenge by introducing an effective framework for learning evolution operators that map random initial conditions to associated ODE/PDE solutions within a short time interval. Such operators can be parametrized by deep neural networks that are trained in an entirely self-supervised manner without requiring one to generate any paired input-output observations. Global long-time predictions across a range of initial conditions can be then obtained by iteratively evaluating the trained model using each prediction as the initial condition for the next evaluation step. Here, this introduces a new approach to temporal domain decomposition that is shown to be effective in performing accurate long-time simulations for a wide range of parametric ODE and PDE systems, from wave propagation, to reaction-diffusion dynamics and stiff chemical kinetics, introducing a new way of rapidly emulating non-equilibrium processes in science and engineering.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Convolutional neural networks for intra-hour solar forecasting based on sky image sequences

Accurate and timely solar forecasts play an increasingly critical role in power systems. Compared to longer forecasting timescales, very short-term solar forecasting has lagged behind in both research and practice. In this paper, we propose deep convolutional neural networks (CNNs) to provide operational intra-hour (10-minute-ahead to 60-minute-ahead) solar forecasts. We develop two CNN structures inspired by a widely-used CNN architecture. The CNNs are tailored to our solar forecasting regression tasks and rely solely on sky image sequences. Case studies based on six years of data (over 150,000 data points) demonstrate that the best CNN model has forecast skill scores of 20%-39% over the naive persistence of cloudiness benchmark, even at these very short timescales. The CNNs also have consistently superior performance when compared to shallow machine learning models with meteorological predictors, where the improvement averages around 7%. The sensitivity analyses show that the sky image length, resolution, and weather conditions have impacts on the deep learning model accuracy. In our intra-hour problem with specific setups, two sky images with a 10-minute 128 x 128 resolution yield the most accurate forecasts. Current limitations, future work, and deployment challenges and solutions are also discussed.

14 SOLAR ENERGY↗
DOE OSTI2023

Applications of physics informed neural operators

Abstract We present a critical analysis of physics-informed neural operators (PINOs) to solve partial differential equations (PDEs) that are ubiquitous in the study and modeling of physics phenomena using carefully curated datasets. Further, we provide a benchmarking suite which can be used to evaluate PINOs in solving such problems. We first demonstrate that our methods reproduce the accuracy and performance of other neural operators published elsewhere in the literature to learn the 1D wave equation and the 1D Burgers equation. Thereafter, we apply our PINOs to learn new types of equations, including the 2D Burgers equation in the scalar, inviscid and vector types. Finally, we show that our approach is also applicable to learn the physics of the 2D linear and nonlinear shallow water equations, which involve three coupled PDEs. We release our artificial intelligence surrogates and scientific software to produce initial data and boundary conditions to study a broad range of physically motivated scenarios. We provide the source code , an interactive website to visualize the predictions of our PINOs, and a tutorial for their use at the Data and Learning Hub for Science .

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Mixed Precision Fermi-Operator Expansion on Tensor Cores from a Machine Learning Perspective

Here we present a second-order recursive Fermi-operator expansion scheme using mixed precision floating point operations to perform electronic structure calculations using tensor core units. A performance of over 100 teraFLOPs is achieved for half-precision floating point operations on Nvidia’s A100 tensor core units. The second-order recursive Fermi-operator scheme is formulated in terms of a generalized, differentiable deep neural network structure, which solves the quantum mechanical electronic structure problem. We demonstrate how this network can be accelerated by optimizing the weight and bias values to substantially reduce the number of layers required for convergence. We also show how this machine learning approach can be used to optimize the coefficients of the recursive Fermi-operator expansion to accurately represent the fractional occupation numbers of the electronic states at finite temperatures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Polarized target nuclear magnetic resonance measurements with deep neural networks

Continuous-wave Nuclear Magnetic Resonance (CW-NMR) operated in constant-current mode has served as a foundational technique for polarization measurement in solid-state dynamically polarized targets within nuclear and high-energy physics experiments for several decades, and it remains an essential tool. Conventional Q-meter-based phase-sensitive detection is critical for precise real-time determination of target polarization during scattering runs. However, the accuracy and reliability of these measurements are frequently compromised by elevated noise levels, baseline drift, and systematic uncertainties arising from signal isolation and fitting, ultimately degrading the overall experimental figure of merit. In this work, we report the first successful application of neural network architectures to continuous-wave NMR polarization metrology. By leveraging advanced machine learning techniques for signal extraction and denoising, we achieve a substantial reduction of fitting uncertainties under a variety of realistic simulated and experimental conditions. These improvements translate directly into more robust real-time (online) polarization monitoring and higher precision in subsequent offline analysis. By reducing analysis-induced uncertainty, the resulting methodology can improve the effective figure of merit for scattering experiments employing dynamically polarized targets and provides a new toolset for NMR-based polarimetry in high-energy and nuclear physics.

Metrology↗
DOE OSTI2024

Learning the boundary-to-domain mapping using Lifting Product Fourier Neural Operators for partial differential equations

Neural operators such as the Fourier Neural Operator (FNO) have been shown to provide resolution-independent deep learning models that can learn mappings between function spaces. For example, an initial condition can be mapped to the solution of a partial differential equation (PDE) at a future time-step using a neural operator. Despite the popularity of neural operators, their use to predict solution functions over a domain given only data over the boundary (such as a spatially varying Dirichlet boundary condition) remains unexplored. In this paper, we refer to such problems as boundary-to-domain problems; they have a wide range of applications in areas such as fluid mechanics, solid mechanics, heat transfer etc. We present a novel FNO-based architecture, named Lifting Product FNO (or LP-FNO) which can map arbitrary boundary functions defined on the lower-dimensional boundary to a solution in the entire domain. Specifically, two FNOs defined on the lower-dimensional boundary are lifted into the higher dimensional domain using our proposed lifting product layer. We demonstrate the efficacy and resolution independence of the proposed LP-FNO for the 2D Poisson equation.

Kashi, Aditya↗
DOE OSTI2022

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.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Probing Electron Beam Induced Transformations on a Single-Defect Level via Automated Scanning Transmission Electron Microscopy

A robust approach for real-time analysis of the scanning transmission electron microscopy (STEM) data streams, based on ensemble learning and iterative training (ELIT) of deep convolutional neural networks, is implemented on an operational microscope, enabling the exploration of the dynamics of specific atomic configurations under electron beam irradiation via an automated experiment in STEM. Combined with beam control, this approach allows studying beam effects on selected atomic groups and chemical bonds in a fully automated mode. Here, in this study, we demonstrate atomically precise engineering of single vacancy lines in transition metal dichalcogenides and the creation and identification of topological defects in graphene. The ELIT-based approach facilitates direct on-the-fly analysis of the STEM data and engenders real-time feedback schemes for probing electron beam chemistry, atomic manipulation, and atom by atom assembly.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Physics-informed latent neural operator for real-time predictions of time-dependent parametric PDEs

Deep operator network (DeepONet) has shown significant promise as surrogate models for systems governed by partial differential equations (PDEs), enabling accurate mappings between infinite-dimensional function spaces. However, when applied to systems with high-dimensional input-output mappings arising from large numbers of spatial and temporal collocation points, these models often require heavily overparameterized networks, leading to long training times. Latent DeepONet addresses some of these challenges by introducing a two-step approach: first learning a reduced latent space using a separate model, followed by operator learning within this latent space. While efficient, this method is inherently data-driven and lacks mechanisms for incorporating physical laws, limiting its robustness and generalizability in data-scarce settings. Here, in this work, we propose PI-Latent-NO, a physics-informed latent neural operator framework that integrates governing physics directly into the learning process. Our architecture features two coupled DeepONets trained end-to-end: a Latent-DeepONet that learns a low-dimensional representation of the solution, and a Reconstruction-DeepONet that maps this latent representation back to the physical space. By embedding PDE constraints into the training via automatic differentiation, our method eliminates the need for labeled training data and ensures physics-consistent predictions. The proposed framework is both memory and compute-efficient, exhibiting near-constant scaling with problem size and demonstrating significant speedups over traditional physics-informed operator models. We validate our approach on a range of parametric PDEs, showcasing its accuracy, scalability, and suitability for real-time prediction in complex physical systems.

Latent representations↗
DOE OSTI2024

Distributed-Memory Sparse Deep Neural Network Inference Using Global Arrays

Partitioned Global Address Space (PGAS) models exhibit tremendous promise in developing efficient and productive distributed-memory parallel applications. They have been used extensively in scientific computations due to conveniently offering a ``shared-memory''-like model and convenient interfaces that separate communication with synchronization. Traditionally, PGAS communication models have been applied to dense/contiguously distributed data, but most modern applications depict varied levels of sparsity. Existing PGAS models require certain adaptations to support distributed sparse computations, since associated computations often require matrix arithmetic, in addition to data movement. The Global Arrays toolkit from Pacific Northwest National Laboratory (PNNL) is one of the earliest PGAS models to combine one-sided data communication and distributed matrix operations and is still used in the popular NWChem quantum chemistry suite. Recently, we have expanded the Global Arrays toolkit to support common sparse operations, like sparse matrix-dense matrix multiplies (SpMM), sparse matrix-sparse matrix multiplication (SpGEMM) and Sampled Dense-Dense Matrix Multiplication (SDDMM). As it turns out, these operations are the bedrock of sparse Deep Learning (DL); sparse deep neural networks and Graph Neural Networks (GNNs) have gained increasing attention recently in achieving speedups on training and inference with reduced memory footprints. Unlike scientific applications in High Performance Computing (HPC), modern (distributed-memory capable) DL toolkits often rely on non-standardized and closed-source vendor software optimizations, creating challenges in software-hardware co-design at scale. Our goal is to support a variety of distributed-memory sparse matrix operations and helper functions in the newly created Sparse Global Arrays (SGA), such that it is possible to build portable and productive Machine Learning scenarios for algorithm/software and hardware codesign purposes. Contemporary data-parallel schemes for training/inference are undergoing a major overhaul since model replication limits scalability and causes resource inefficiencies. As such, we have adopted tensor parallelism in decomposing the model and inputs, to mitigate memory issues. Current implementation is built on top of MPI and uses CPUs to maximize the portability across the platforms.

Distributed computing, machine learning↗
DOE OSTI2024

Accelerated CO2 Storage Optimization Using Multi-Resolution Fourier Neural Operator at the Illinois Basin Decatur Project (IBDP)

This paper presents a deep learning-based approach for optimizing CO2 injection in carbon capture and storage (CCS) operations. We developed a multi-resolution machine learning model to significantly reduce data generation costs. Utilizing this proxy model, we implemented a multi-objective genetic algorithm to optimize well control during the CO2 injection process. The proposed approach was applied to the Illinois Basin Decatur Project (IBDP), successfully optimizing the CO2 injection schedule based on three key objectives: maximizing the amount of CO2 stored, maximizing sweep efficiency, and minimizing pressure increase. The use of the proxy model accelerated the optimization workflow by two orders of magnitude, while the cost of data generation for the proxy model was reduced by 90% by utilizing a coarse-scale model.

accelerated CO2 storage optimization↗
DOE OSTI2023

Deep Learning Accelerated History Matching and Forecasting in Geologic CO 2 Sequestration [Slides]

We have successfully developed a predictive workflow for the Geologic CO 2 Sequestration using a deep learning model based on the Fourier Neural Operator. The workflow has high accuracy for predicting pressure & saturation during the injection and post-injection periods and has decent accuracy for predicting water and CO 2 production rates during injection period. It is necessary to train exclusive DNN models for pressure prediction in long term GCS, but for saturation prediction, we can use a single model to predict it.

58 GEOSCIENCES↗
DOE OSTI2021

A seamless multiscale operator neural network for inferring bubble dynamics

Modelling multiscale systems from nanoscale to macroscale requires the use of atomistic and continuum methods and, correspondingly, different computer codes. Here, we develop a seamless method based on DeepONet, which is a composite deep neural network (a branch and a trunk network) for regressing operators. In particular, we consider bubble growth dynamics, and we model tiny bubbles of initial size from 100 nm to 10 $\mathrm {\mu }\textrm {m}$ , modelled by the Rayleigh–Plesset equation in the continuum regime above 1 $\mathrm {\mu }\textrm {m}$ and the dissipative particle dynamics method for bubbles below 1 $\mathrm {\mu }\textrm {m}$ in the atomistic regime. After an offline training based on data from both regimes, DeepONet can make accurate predictions of bubble growth on-the-fly (within a fraction of a second) across four orders of magnitude difference in spatial scales and two orders of magnitude in temporal scales. The framework of DeepONet is general and can be used for unifying physical models of different scales in diverse multiscale applications.

Mechanics↗
DOE OSTI2022

Enhanced Oblique Decision Tree Enabled Policy Extraction for Deep Reinforcement Learning in Power System Emergency Control

Deep reinforcement learning (DRL) algorithms have successfully solved many challenging problems in various power system control scenarios. However, their decision-making process is usually regarded as black-boxes. Furthermore, how DRL models interact with human intelligence remains an open problem. Thus, this paper proposes a policy extraction framework to extract a complex DRL model into an explainable policy. This framework includes three parts: 1) DRL training and data generation. We train an agent for a specific control task and generate data, which contains the control policy of the agent. 2) Policy extraction. We propose an information gain rate based weighted oblique decision tree (IGR-WODT) for DRL policy extraction. 3) Policy evaluation. We define three metrics to evaluate the performance of the proposed approach. A case study for the under-voltage load shedding problem shows that the IGR-WODT presents a performance enhancement compared with DRL, weighted oblique decision tree, and univariate decision tree. The proposed policy extraction method could provide an intuitive explanation of the neural network decision-making process to the dispatchers when making final decisions on power grid operation. Also, the resulted rule-based controller could replace the deep neural network-based controller in many field edge devices with limited computing resources, providing comparable performance.

deep reinforcement learning↗
DOE OSTI2024

On the Training and Generalization of Deep Operator Networks

Here, we present a novel training method for deep operator networks (DeepONets), one of the most popular neural network models for operators. DeepONets are constructed by two subnetworks, namely the branch and trunk networks. Typically, the two subnetworks are trained simultaneously, which amounts to solving a complex optimization problem in a high dimensional space. In addition, the nonconvex and nonlinear nature makes training very challenging. To tackle such a challenge, we propose a two-step training method that trains the trunk network first and then sequentially trains the branch network. The core mechanism is motivated by the divide-and-conquer paradigm and is the decomposition of the entire complex training task into two subtasks with reduced complexity. Therein the Gram–Schmidt orthonormalization process is introduced which significantly improves stability and generalization ability. On the theoretical side, we establish a generalization error estimate in terms of the number of training data, the width of DeepONets, and the number of input and output sensors. Numerical examples are presented to demonstrate the effectiveness of the two-step training method, including Darcy flow in heterogeneous porous media.

deep operator networks↗