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DOE OSTI2020

Recovery of Damaged Information and the Out-of-Time-Ordered Correlators

The evolution with a complex Hamiltonian generally leads to information scrambling. A time-reversed dynamics unwinds this scrambling and thus leads to the original information recovery. In this work, we show that if the scrambled information is, in addition, partially damaged by a local measurement, then such a damage can still be treated by application of the time-reversed protocol. This information recovery is described by the long-time saturation value of a certain out-of-time-ordered correlator of local variables. We also propose a simple test that distinguishes between quantum and reversible classical chaotic information scrambling.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Barren Plateaus Preclude Learning Scramblers

Scrambling processes, which rapidly spread entanglement through many-body quantum systems, are difficult to investigate using standard techniques, but are relevant to quantum chaos and thermalization. In this Letter, we ask if quantum machine learning (QML) could be used to investigate such processes. In this study we prove a no-go theorem for learning an unknown scrambling process with QML, showing that it is highly probable for any variational Ansatz to have a barren plateau landscape, i.e., cost gradients that vanish exponentially in the system size. This implies that the required resources scale exponentially even when strategies to avoid such scaling (e.g., from Ansatz -based barren plateaus or no-free-lunch theorems) are employed. Furthermore, we numerically and analytically extend our results to approximate scramblers. Hence, our work places generic limits on the learnability of unitaries when lacking prior information.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Learning in Modal Space: Solving Time-Dependent Stochastic PDEs Using Physics-Informed Neural Networks

One of the open problems in scientific computing is the long-time integration of nonlinear stochastic partial differential equations (SPDEs), especially with arbitrary initial data. We address this problem by taking advantage of recent advances in scientific machine learning and the spectral dynamically orthogonal (DO) and borthogonal (BO) methods for representing stochastic processes. The recently introduced DO/BO methods reduce the SPDE to solving a system of deterministic PDEs and a system of stochastic ordinary differential equations. Specifically, we propose two new physics-informed neural networks (PINNs) for solving time-dependent SPDEs, namely the neural network (NN)-DO/BO methods. The proposed methods incorporate the DO/BO constraints into the loss function (along with the modal decomposition of the SPDE) with an implicit form instead of generating explicit expressions for the temporal derivatives of the DO/BO modes. Hence, the NN-DO/BO methods can overcome some of the drawbacks of the original DO/BO methods. For example, we do not need the assumption that the covariance matrix of the random coefficients is invertible as in the original DO method, and we can remove the assumption of no eigenvalue crossing as in the original BO method. Moreover, the NN-DO/BO methods can be used to solve time-dependent stochastic inverse problems with the same formulation and same computational complexity as for forward problems. Furthermore, we demonstrate the capability of the proposed methods via several numerical examples, namely: (1) A linear stochastic advection equation with deterministic initial condition: we obtain good results with the proposed methods, while the original DO/BO methods cannot be applied directly in this case. (2) Long-time integration of the stochastic Burgers' equation: we show the good performance of NN-DO/BO methods, especially the effectiveness of the NN-BO approach for such problems with many eigenvalue crossings during the whole time evolution, while the original BO method fails. (3) Nonlinear reaction diffusion equation: we consider both the forward problem and the inverse problems, including very noisy initial point values, to investigate the flexibility of the NN-DO/BO methods in handling inverse and mixed type problems. Taken together, these simulation results demonstrate that the NN-DO/BO methods can be employed to effectively quantify uncertainty propagation in a wide range of physical problems, but future work should address the efficiency issue of PINNs for forward problems.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Explaining Missing Data in Graphs: A Constraint-based Approach

Abstract: This paper introduces a constraint-based approach to clarify missing values in graphs. Our method capitalizes on a set S of graph data constraints. An explanation is a sequence of operational enforcement of S towards the recovery of interested yet missing data (e.g., attribute values, edges). We show that constraint-based approach helps us to understand not only why a value is missing, but also how to recover the missing value. We study S-explanation problem, which is to compute the optimal explanations with guarantees on the informativeness and conciseness. We show the problem is in ?P^2 for established graph data constraints such as graph keys and graph association rules. We develop an efficient bidirectional algorithm to compute optimal explanations, without enforcing S on the entire graph. We also show our algorithm can be easily extended to support graph refinement within limited time, and to explain missing answers. Using real-world graphs, we experimentally verify the effectiveness and efficiency of our algorithms.

Data Analytics↗

DOE OSTI2025

Predicting runtime and resource utilization of jobs on integrated cloud and HPC systems

Recent advances in virtualization technologies used in cloud computing offer performance that closely approaches bare-metal levels. Combined with specialized instance types and high-speed networking services for cluster computing, cloud platforms have become a compelling option for high-performance computing (HPC). However, most current batch job schedulers in HPC systems are designed for homogeneous clusters and make decisions based on limited information about jobs and system status. Scientists typically submit computational jobs to these schedulers with a requested runtime that is often over- or under-estimated. More accurate runtime predictions can help schedulers make better decisions and reduce job turnaround times. Here, they can also support decisions about migrating jobs to the cloud to avoid long queue wait times in HPC systems.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Matrix Completion Using Alternating Minimization for Distribution System State Estimation

This paper examines the problem of state estimation in power distribution systems under low-observability conditions. The recently proposed constrained matrix completion method which combines the standard matrix completion method and power flow constraints has been shown to be effective in estimating voltage phasors under low-observability conditions using single-snapshot information. However, the method requires solving a semidefinite programming (SDP) problem, which becomes computationally infeasible for large systems and if multiple-snapshot (time-series) information is used. This paper proposes an efficient algorithm to solve the constrained matrix completion problem with time-series data. This algorithm is based on reformulating the matrix completion problem as a bilinear (non-convex) optimization problem, and applying the alternating minimization algorithm to solve this problem. This paper proves the summable convergence of the proposed algorithm, and demonstrates its efficacy and scalability via IEEE 123-bus system and a real utility feeder system. This paper also explores the value of adding more data from the history in terms of computation time and estimation accuracy.

41 EE - Solar Energy Technologies Office (EE-4S)↗

DOE OSTI2020

Matrix Completion Using Alternating Minimization for Distribution System State Estimation: Preprint

41 EE - Solar Energy Technologies Office (EE-4S)↗

DOE OSTI2022

Hybrid data-driven and model-informed online tool wear detection in milling machines

Precision machining tool wear is responsible for low product throughput and quality. Monitoring the tool wear online is vital to prevent degradation in machining quality. However, direct real-time tool wear measurement is not practical. This paper presents residual-based anomaly detection models, combining a hybrid model comprised of a physics-based model and a data-driven model (a decision tree or a neural network) to predict signals of interest (e.g., power or forces) under nominal conditions, followed by Page’s cumulative sum test for detecting tool wear on-line using the computer numerical control machine measurements. The most informative features are ranked using dynamic programming and its approximation variants from real-time measurements and machine settings, such as the width of cut, depth of cut, feed rate and spindle speed, that serve as inputs to the predictive models. The baseline nominal model is incrementally updated with experimental data via a gradient boosted adaptation model to generate the residuals that account for discrepancies between the actual machine data under normal conditions and the baseline nominal model predictions. The hybrid model is validated against 20 Mazak milling machine experimental tests and one Haas run-to-failure experiment. The proposed anomaly detector is applied to synthetic data from simulations of the physics-based model at different operating conditions, measurement noise levels, and tool wear levels, and the methods were able to achieve an overall 92% accuracy in data with 1% noise. The anomaly detection methods based on hybrid model reduced the false alarms of either the data-driven or physical-based models alone, and are found to be capable of good online detection of tool wear.

42 ENGINEERING↗

DOE OSTI2024

Advancements in Multiphysics Microdepletion Analysis of an eVinci TM -like Microreactor Leveraging OpenMC-CRAB Workflow

Nuclear microreactors (MRs) are a class of nuclear reactor technology, characterized by reduced dimensions, modular design, and reduced power output in contrast to conventional Light Water Reactors (LWRs). MRs are proposed for supplying electricity and eventual process heat to remote locations, such as military installations and disaster-affected areas. Current research work sponsored by the US Department of Energy Microreactor Program (MRP) is devoted to the development of novel modeling and simulation tools to better support MR vendors and regulatory bodies. Notably, the NRC is projected to utilize the CRAB multiphysics software driver for executing both design and beyond-design-basis accident analyses. Furthermore, the NRC has been utilizing the MELCOR code to calculate mechanistic source terms during accidents. Since MELCOR relies on isotopic inventory and reactor temperature/power profiles under accident conditions, which theoretically can be derived from CRAB, the goal is to establish a comprehensive CRAB-MELCOR computational framework. Past work was focused on testing and demonstrating CRAB's capability to generate results that can be used to inform mechanistic source term calculations in MELCOR. In particular, a computational workflow leveraging OpenMC-generated microscopic cross sections and CRAB was first applied to perform multiphysics microscopic depletion calculation followed by an accident scenario for a stylized microreactor problem. In fiscal year 2024, the research work has been focused on applying the OpenMC-CRAB workflow, which was first tested in fiscal year 2023, to a realistic 3D heat-pipe cooled MR problem representative of the eVinci TM design. The latter computational problem was developed with inputs from WEC to conserve selected neutronic and thermal characteristics of the eVinci TM design without releasing proprietary data. The results of this simulation, encompassing isotopic inventory, power density distribution, and kinetic parameters, will inform both MELCOR and the WEC-developed FATE code for mechanistic source terms calculations. The results from the two codes will then be compared for code verification purposes. This report contains the design characteristics of the realist heat pipe cooled microreactor developed as a use-case for the verification exercise, and the current results for the multiphysics microscopic depletion performed with the OpenMC-CRAB workflow. The results include eigenvalue as a function of time, power distribution at EOL, in addition to nuclides inventory's time evolution and spatial distribution. Finally, we report improvements to the workflow efficiency achieved through a collaboration with the NEAMS programs. Through this collaborative effort, we were able to strongly decrease the computational time for the multiphysics microdepletion calculation (i.e., from 17.4 hours to 5.7 hours on 280 processors) in addition to simplifying the interface to generate isotopics spatial distribution utilizable by FATE and MELCOR. Future work, including the improvement of the current microscopic cross-sections' library and the simulation of an accident scenario at EOL, is also discussed.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2023

Rapid Computational Identification of Therapeutic Targets for Pathogens

Biological threats continue to persist and evolve as an important challenge to national security. There are multiple ways in which novel viral pathogens could emerge to pose a serious threat to human health. This project developed a pathogen target identification tool that can rapidly respond to a novel or emerging viral biological threat. A set of computational tools were developed that provide detailed information on the newly sequenced genes, their protein products and the drug target sites for the proteins that are best suited for biological countermeasure development. Three key innovations were developed in the project. 1) Development of a new extensive database of protein pocket structures with structure-based search algorithms to rapidly link novel protein targets with the complete collection of previously experimentally solved protein structures. 2) A novel clustering pipeline was introduced to group matching structures and associated small-molecule binding ligands into a consensus protein pocket with the associated small-molecule chemotypes predicted to fit in the pocket site. The matching experimentally solved structures were used to inform the value of different target sites. 3) Where there are viral protein targets with pockets structurally matched to similar human proteins, a biological knowledge graph, which links molecular interactions with human disease, was used to further assess the potential negative impact of a viral protein target with similarities to human proteins that could have important off target side effects. In total, the project produced a new resource for rapid and detailed assessment of promising targets for countermeasures, reflecting the ongoing wet lab, clinical, and computational data being collected. These capabilities will improve the ability to respond to a biological threat in multiple domains.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2023

Understanding the hydrological response of a headwater-dominated catchment by analysis of distributed surface–subsurface interactions

Abstract We computationally explore the relationship between surface–subsurface exchange and hydrological response in a headwater-dominated high elevation, mountainous catchment in East River Watershed, Colorado, USA. In order to isolate the effect of surface–subsurface exchange on the hydrological response, we compare three model variations that differ only in soil permeability. Traditional methods of hydrograph analysis that have been developed for headwater catchments may fail to properly characterize catchments, where catchment response is tightly coupled to headwater inflow. Analyzing the spatially distributed hydrological response of such catchments gives additional information on the catchment functioning. Thus, we compute hydrographs, hydrological indices, and spatio-temporal distributions of hydrological variables. The indices and distributions are then linked to the hydrograph at the outlet of the catchment. Our results show that changes in the surface–subsurface exchange fluxes trigger different flow regimes, connectivity dynamics, and runoff generation mechanisms inside the catchment, and hence, affect the distributed hydrological response. Further, changes in surface–subsurface exchange rates lead to a nonlinear change in the degree of connectivity—quantified through the number of disconnected clusters of ponding water—in the catchment. Although the runoff formation in the catchment changes significantly, these changes do not significantly alter the aggregated streamflow hydrograph. This hints at a crucial gap in our ability to infer catchment function from aggregated signatures. We show that while these changes in distributed hydrological response may not always be observable through aggregated hydrological signatures, they can be quantified through the use of indices of connectivity.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Dispersion-enhanced sequential batch sampling for adaptive contour estimation

In computer simulation and optimal design, sequential batch sampling offers an appealing way to iteratively stipulate optimal sampling points based upon existing selections and efficiently construct surrogate modeling. Nonetheless, the issue of near duplicates poses tremendous quandary for sequential learning. It refers to the situation that selected critical points cluster together in each sampling batch, which are individually but not collectively informative towards the optimal design. Near duplicates severely diminish the computational efficiency as they barely contribute extra information towards update of the surrogate. To address this issue, we impose a dispersion criterion on concurrent selection of sampling points, which essentially forces a sparse distribution of critical points in each batch, and demonstrate the effectiveness of this approach in adaptive contour estimation. Specifically, we adopt Gaussian process surrogate to emulate the simulator, acquire variance reduction of the critical region from new sampling points as a dispersion criterion, and combine it with the modified expected improvement (EI) function for critical batch selection. The critical region here is the proximity of the contour of interest. This proposed approach is vindicated in numerical examples of a two-dimensional four-branch function, a four-dimensional function with a disjoint contour of interest and a time-delay dynamic system.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

AI-Enhanced Co-Design for Next-Generation Microelectronics: Innovating Innovation (Workshop Report)

The Artificial Intelligence Enhanced Co-Design for Next Generation Microelectronics virtual workshop was held April 4-5, 2023, and attended by subject matter experts from universities, industry, and national laboratories. This was the third in a series of workshops to motivate the research community to identify and address major challenges facing microelectronics research and production. The 2023 workshop focused on a set of topics from materials to computing algorithms, and included discussions on relevant federal legislation and such as the Creating Helpful Incentives to Produce Semiconductors and Science Act (CHIPS Act) which was signed into law in the summer of 2022. Talks at the workshop included edge computing in radiation environments, new materials for neuromorphic computing, advanced packaging for microelectronics, and new AI techniques. We also received project updates from several of the Department of Energy (DOE) microelectronics co-design projects funded in the fall of 2021, and from three of the Energy Frontier Research Centers (EFRCs) that had been funded in the fall of 2022. The workshop also conducted a set of breakout discussions around the five principal research directions (PRDs) from the 2018 Department of Energy workshop report: 1) define innovative material, device, and architecture requirements driven by applications, algorithms, and software; 2) revolutionize memory and data storage; 3) re-imagine information flow unconstrained by interconnects; 4) redefine computing by leveraging unexploited physical phenomena; 5) reinvent the electricity grid through new materials, devices, and architectures. We tasked each breakout group to consider one primary PRD (and other PRDs as relevant topics arose during discussions) and to address questions such as whether the research community has embraced co-design as a methodology and whether new developments at any level of innovation from materials to programming models requires the research community to reevaluate the PRDs developed back in 2018.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

B-PINNs: Bayesian Physics-informal Neural Networks for Forward and Inverse PDE Problems with Noisy Data

We propose a Bayesian physics-informed neural network (B-PINN) to solve both forward and inverse nonlinear problems described by partial differential equations (PDEs) and noisy data. In this Bayesian framework, the Bayesian neural network (BNN) combined with a PINN for PDEs serves as the prior while the Hamiltonian Monte Carlo (HMC) or the variational inference (VI) could serve as an estimator of the posterior. B-PINNs make use of both physical laws and scattered noisy measurements to provide predictions and quantify the aleatoric uncertainty arising from the noisy data in the Bayesian framework. Compared with PINNs, in addition to uncertainty quantification, B-PINNs obtain more accurate predictions in scenarios with large noise due to their capability of avoiding overfitting. We conduct a systematic comparison between the two different approaches for the B-PINNs posterior estimation (i.e., HMC or VI), along with dropout used for quantifying uncertainty in deep neural networks. Our experiments show that HMC is more suitable than VI with mean field Gaussian approximation for the B-PINNs posterior estimation, while dropout employed in PINNs can hardly provide accurate predictions with reasonable uncertainty. Finally, we replace the BNN in the prior with a truncated Karhunen-Loève (KL) expansion combined with HMC or a deep normalizing flow (DNF) model as posterior estimators. The KL is as accurate as BNN and much faster but this framework cannot be easily extended to high-dimensional problems unlike the BNN based framework.

Non linear PDEs, Noisy data, Bysian physics inform↗

DOE OSTI2023

Machine learning–assisted prediction of heat fluxes through thermally anisotropic building envelopes

Thermally anisotropic building envelope (TABE) is a novel active building envelope that can save energy use to maintain thermal comfort in buildings by redirecting heat and coolness from building envelopes to thermal loops. Finite element models (FEMs) can be used to compute the heat fluxes through TABEs, but the high computational cost of finite element simulations has prevented parametric studies and design optimizations. This paper proposes a domain knowledge–informed, finite element–based machine learning framework to reduce the computation cost for the energy management of buildings installed with TABE that uses a ground thermal loop. First, the training heat flux data set was generated by FEM simulations with different thermal loop schedules. Then, both shallow learning models (i.e., multivariate linear regression and eXtreme Gradient Boost, or XGBoost) and a deep learning model (i.e., deep neural network, or DNN) were trained to predict the heat fluxes. Domain knowledge was used for data preprocessing and feature selection. Finally, the suitability of the selected machine learning model was tested under different thermal loop schedules. Herein, the case study results showed that: (1) XGBoost can be as accurate as DNN (coefficient of determination equal to 0.81) with much less training time; (2) the annual energy cost savings for different thermal loop schedules obtained by the XGBoost-predicted and FEM-calculated heat fluxes are consistent, having a difference of only 4%; and (3) XGBoost can reduce the computation time for the annual energy analysis of the case study building with a given thermal loop schedule from around 12 h by using FEM to less than 1 min.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2021

Analytic continuation of noisy data using Adams Bashforth residual neural network

We propose a data-driven learning framework for the analytic continuation problem in numerical quantum many-body physics. Designing an accurate and efficient framework for the analytic continuation of imaginary time using computational data is a grand challenge that has hindered meaningful links with experimental data. The standard Maximum Entropy (MaxEnt)-based method is limited by the quality of the computational data and the availability of prior information. Also, the MaxEnt is not able to solve the inversion problem under high level of noise in the data. Here we introduce a novel learning model for the analytic continuation problem using a Adams-Bashforth residual neural network (AB-ResNet). Additionally, the advantage of this deep learning network is that it is model independent and, therefore, does not require prior information concerning the quantity of interest given by the spectral function. More importantly, the ResNet-based model achieves higher accuracy than MaxEnt for data with higher level of noise. Finally, numerical examples show that the developed AB-ResNet is able to recover the spectral function with accuracy comparable to MaxEnt where the noise level is relatively small.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Measure This, Not That: Pareto Optimal Trade-Offs between Model-Based Information Content and Measurements Cost

The slides present a novel convex optimization formulation to compute the best set of measurements for multi-response dynamical systems with asynchronous time steps that maximize the Fisher information content subject to budget constraints. The trace (A-optimality) or determinant (D-optimality) of the Fisher Information Matrix (FIM) quantifies the information content. The framework supports arbitrary (positive semi-definite) variance and covariances between every pair of responses and their time steps.

Wang, Jialu↗

DOE OSTI2023

Quantum algorithms for geologic fracture networks

Abstract 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 10–1000 nodes), which we demonstrate experimentally and explain theoretically. We expect further improvements by leveraging quantum error mitigation and preconditioning.

58 GEOSCIENCES↗