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DOE OSTI2024

RandONets: Shallow networks with random projections for learning linear and nonlinear operators

Deep neural networks have been extensively used for the solution of both the forward and the inverse problem for dynamical systems. However, their implementation necessitates optimizing a high-dimensional space of parameters and hyperparameters. This fact, along with the requirement of substantial computational resources, pose a barrier to achieving high numerical accuracy, but also interpretability. Here, to address the above challenges, we present Random Projection-based Operator Networks (RandONets): shallow networks with random projections and tailor-made numerical analysis methods that learn accurately and fast linear and nonlinear operators. Building on previous works, we prove that RandOnets are universal approximators of linear and nonlinear operators. Due to their simplicity, RandONets provide a one-step transformation of the input space, facilitating interpretability. For the evaluation of their performance, we focus on operators of PDEs. We show, that RandONets outperform by several orders of magnitude, both in terms of numerical approximation accuracy and computational cost, the “vanilla” DeepONets. Hence, we believe that our method will trigger further developments in the field of scientific machine learning, for the development of new ‘’light”schemes that will provide high accuracy while reducing dramatically the computational cost. A MATLAB toolbox for RandONets, including demos, is available on GitHub at https://github.com/GianlucaFabiani/RandONets.

Interpretable machine learning↗

DOE OSTI2018

Robust and non-fragile finite time H{sub ∞} synchronization control for complex networks with uncertain inner coupling

This paper addresses robust finite time H{sub ∞} synchronization problem for non-fragile complex networks with uncertain inner coupling. In order to achieve synchronization, a non-fragile controller subjected to randomly occurring perturbations will be considered. By constructing a suitable Lyapunov–Krasovskii functional and utilizing reciprocally convex approach, the criteria for the networks are established in terms of linear matrix inequalities (LMIs). Theoretical analysis and numerical simulations about robust finite time H{sub ∞} synchronization for uncertain inner coupling complex networks are presented.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2011

Performance Enhancement of the RatCAP Awake Rate Brain PET System

The first full prototype of the RatCAP PET system, designed to image the brain of a rat while conscious, has been completed. Initial results demonstrated excellent spatial resolution, 1.8 mm FWHM with filtered backprojection and <1.5 mm FWHM with a Monte Carlo based MLEM method. However, noise equivalent countrate studies indicated the need for better timing to mitigate the effect of randoms. Thus, the front-end ASIC has been redesigned to minimize time walk, an accurate coincidence time alignment method has been implemented, and a variance reduction technique for the randoms is being developed. To maximize the quantitative capabilities required for neuroscience, corrections are being implemented and validated for positron range and photon noncollinearity, scatter (including outside the field of view), attenuation, randoms, and detector efficiency (deadtime is negligible). In addition, a more robust and compact PCI-based optical data acquisition system has been built to replace the original VME-based system while retaining the linux-based data processing and image reconstruction codes. Finally, a number of new animal imaging experiments have been carried out to demonstrate the performance of the RatCAP in real imaging situations, including an F-18 fluoride bone scan, a C-11 raclopride scan, and a dynamic C-11 methamphetamine scan.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2015

Long-term Results of the UCSF-LBNL Randomized Trial: Charged Particle With Helium Ion Versus Iodine-125 Plaque Therapy for Choroidal and Ciliary Body Melanoma

Purpose: Relevant clinical data are needed given the increasing national interest in charged particle radiation therapy (CPT) programs. Here we report long-term outcomes from the only randomized, stratified trial comparing CPT with iodine-125 plaque therapy for choroidal and ciliary body melanoma. Methods and Materials: From 1985 to 1991, 184 patients met eligibility criteria and were randomized to receive particle (86 patients) or plaque therapy (98 patients). Patients were stratified by tumor diameter, thickness, distance to disc/fovea, anterior extension, and visual acuity. Tumors close to the optic disc were included. Local tumor control, as well as eye preservation, metastases due to melanoma, and survival were evaluated. Results: Median follow-up times for particle and plaque arm patients were 14.6 years and 12.3 years, respectively (P=.22), and for those alive at last follow-up, 18.5 and 16.5 years, respectively (P=.81). Local control (LC) for particle versus plaque treatment was 100% versus 84% at 5 years, and 98% versus 79% at 12 years, respectively (log rank: P=.0006). If patients with tumors close to the disc (<2 mm) were excluded, CPT still resulted in significantly improved LC: 100% versus 90% at 5 years and 98% versus 86% at 12 years, respectively (log rank: P=.048). Enucleation rate was lower after CPT: 11% versus 22% at 5 years and 17% versus 37% at 12 years, respectively (log rank: P=.01). Using Cox regression model, likelihood ratio test, treatment was the most important predictor of LC (P=.0002) and eye preservation (P=.01). CPT was a significant predictor of prolonged disease-free survival (log rank: P=.001). Conclusions: Particle therapy resulted in significantly improved local control, eye preservation, and disease-free survival as confirmed by long-term outcomes from the only randomized study available to date comparing radiation modalities in choroidal and ciliary body melanoma.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

DOE OSTI2015

Noninvasive differential diagnosis of dental periapical lesions in cone-beam CT scans

Purpose: This paper proposes a novel application of computer-aided diagnosis (CAD) to an everyday clinical dental challenge: the noninvasive differential diagnosis of periapical lesions between periapical cysts and granulomas. A histological biopsy is the most reliable method currently available for this differential diagnosis; however, this invasive procedure prevents the lesions from healing noninvasively despite a report that they may heal without surgical treatment. A CAD using cone-beam computed tomography (CBCT) offers an alternative noninvasive diagnostic tool which helps to avoid potentially unnecessary surgery and to investigate the unknown healing process and rate for the lesions. Methods: The proposed semiautomatic solution combines graph-based random walks segmentation with machine learning-based boosted classifiers and offers a robust clinical tool with minimal user interaction. As part of this CAD framework, the authors provide two novel technical contributions: (1) probabilistic extension of the random walks segmentation with likelihood ratio test and (2) LDA-AdaBoost: a new integration of weighted linear discriminant analysis to AdaBoost. Results: A dataset of 28 CBCT scans is used to validate the approach and compare it with other popular segmentation and classification methods. The results show the effectiveness of the proposed method with 94.1% correct classification rate and an improvement of the performance by comparison with the Simon’s state-of-the-art method by 17.6%. The authors also compare classification performances with two independent ground-truth sets from the histopathology and CBCT diagnoses provided by endodontic experts. Conclusions: Experimental results of the authors show that the proposed CAD system behaves in clearer agreement with the CBCT ground-truth than with histopathology, supporting the Simon’s conjecture that CBCT diagnosis can be as accurate as histopathology for differentiating the periapical lesions.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2025

Static Subspace Approximation for Random Phase Approximation Correlation Energies: Applications to Materials for Catalysis and Electrochemistry

Modeling complex materials using high-fidelity, ab initio methods at low cost is a fundamental goal for quantum chemical software packages. The GW approximation and random phase approximation (RPA) provide a unified description of both electronic structure and total energies using the same physics in a many-body perturbative approach that can be more accurate than generalized-gradient density functional theory (DFT) methods. However, GW/RPA implementations have historically been limited to either specific materials classes or application toward small chemical systems. Here, the static subspace approximation allows for reduced cost full-frequency GW/RPA calculations and has previously been benchmarked thoroughly for GW calculations. Here, we describe our approach to including partial occupations of electronic orbitals in full-frequency GW and RPA calculations for the study of electrocatalysts. We benchmarked RPA total energy calculations using the subspace approximation across a diverse test suite of materials for a variety of computational parameters. The benchmarking quantifies the impact of different extrapolation procedures for representing the static polarizability at infinite screened cutoff, and shows that using screened cutoffs above 20-25 Ryd result in diminishing accuracy returns for predicting RPA total energies. Additionally, for moderately sized electrocatalytic models, 2-3 times fewer computational resources are used to compute RPA total energies by representing the static polarizability with 20-30% of the static subspace basis, with an error of approximately 0.01 eV or better in RPA adsorption energy calculations. Finally, we show that for these electrochemical models RPA can shift DFT adsorption energy shifts by up to 0.5 eV and that GW can frequently shift DFT eigenvalues of surface and adsorbate states by approximately 0.5-1 eV.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2017

Bayesian and variational Bayesian approaches for flows in heterogeneous random media

In this paper, we study porous media flows in heterogeneous stochastic media. We propose an efficient forward simulation technique that is tailored for variational Bayesian inversion. As a starting point, the proposed forward simulation technique decomposes the solution into the sum of separable functions (with respect to randomness and the space), where each term is calculated based on a variational approach. This is similar to Proper Generalized Decomposition (PGD). Next, we apply a multiscale technique to solve for each term (as in ) and, further, decompose the random function into 1D fields. As a result, our proposed method provides an approximation hierarchy for the solution as we increase the number of terms in the expansion and, also, increase the spatial resolution of each term. We use the hierarchical solution distributions in a variational Bayesian approximation to perform uncertainty quantification in the inverse problem. We conduct a detailed numerical study to explore the performance of the proposed uncertainty quantification technique and show the theoretical posterior concentration.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2018

Efficient Data-Driven Geologic Feature Characterization from Pre-stack Seismic Measurements using Randomized Machine-Learning Algorithm

Conventional seismic techniques for detecting the subsurface geologic features are challenged by limited data coverage, computational inefficiency and subjective human factors. We developed a novel data-driven geological feature characterization approach based on pre-stack seismic measurements. Our characterization method employs an efficient and accurate machine learning method to extract useful subsurface geologic features automatically. Specifically, we use kernel ridge regression to account for the nonlinear relationship between seismic data and geological features. We moreover employ kernel tricks to avoid the explicit nonlinear mapping and infinite dimension of feature space. Yet, the conventional kernel ridge regression can be computationally prohibitive because of the large volume of seismic measurements. We employ a data reduction technique in combination with the conventional kernel ridge regression method to improve the computational efficiency and reduce memory usage. In particular, we utilize a randomized numerical linear algebra technique, named Nyström method, to effectively reduce the dimensionality of the feature space without compromising the information content required for accurate characterization. We provide thorough computational cost analysis to show the efficiency of our new geological feature characterization methods. We validate the performance of our method in characterizing geologic fault zones because faults play an important role in various subsurface applications. Our numerical examples demonstrate that our new characterization method significantly improves the computational efficiency while maintaining comparable accuracy. Interestingly, we demonstrate that our approach yields a speedup ratio on the order of ~102 to ~103 in a multicore computational environment.

58 GEOSCIENCES↗

DOE OSTI2014

Solving the hard problem of Bertrand's paradox

Bertrand's paradox is a famous problem of probability theory, pointing to a possible inconsistency in Laplace's principle of insufficient reason. In this article, we show that Bertrand's paradox contains two different problems: an “easy” problem and a “hard” problem. The easy problem can be solved by formulating Bertrand's question in sufficiently precise terms, so allowing for a non-ambiguous modelization of the entity subjected to the randomization. We then show that once the easy problem is settled, also the hard problem becomes solvable, provided Laplace's principle of insufficient reason is applied not to the outcomes of the experiment, but to the different possible “ways of selecting” an interaction between the entity under investigation and that producing the randomization. This consists in evaluating a huge average over all possible “ways of selecting” an interaction, which we call a universal average. Following a strategy similar to that used in the definition of the Wiener measure, we calculate such universal average and therefore solve the hard problem of Bertrand's paradox. The link between Bertrand's problem of probability theory and the measurement problem of quantum mechanics is also briefly discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2011

Green's function-stochastic methods framework for probing nonlinear evolution problems: Burger's equation, the nonlinear Schroedinger's equation, and hydrodynamic organization of near-molecular-scale vorticity

Research Highlights: > Systematic approach for physically probing nonlinear and random evolution problems. > Evolution of vortex sheets corresponds to evolution of an Ornstein-Uhlenbeck process. > Organization of near-molecular scale vorticity mediated by hydrodynamic modes. > Framework allows calculation of vorticity evolution within random strain fields. - Abstract: A framework which combines Green's function (GF) methods and techniques from the theory of stochastic processes is proposed for tackling nonlinear evolution problems. The framework, established by a series of easy-to-derive equivalences between Green's function and stochastic representative solutions of linear drift-diffusion problems, provides a flexible structure within which nonlinear evolution problems can be analyzed and physically probed. As a preliminary test bed, two canonical, nonlinear evolution problems - Burgers' equation and the nonlinear Schroedinger's equation - are first treated. In the first case, the framework provides a rigorous, probabilistic derivation of the well known Cole-Hopf ansatz. Likewise, in the second, the machinery allows systematic recovery of a known soliton solution. The framework is then applied to a fairly extensive exploration of physical features underlying evolution of randomly stretched and advected Burger's vortex sheets. Here, the governing vorticity equation corresponds to the Fokker-Planck equation of an Ornstein-Uhlenbeck process, a correspondence that motivates an investigation of sub-sheet vorticity evolution and organization. Under the assumption that weak hydrodynamic fluctuations organize disordered, near-molecular-scale, sub-sheet vorticity, it is shown that these modes consist of two weakly damped counter-propagating cross-sheet acoustic modes, a diffusive cross-sheet shear mode, and a diffusive cross-sheet entropy mode. Once a consistent picture of in-sheet vorticity evolution is established, a number of analytical results, describing the motion and spread of single, multiple, and continuous sets of Burger's vortex sheets, evolving within deterministic and random strain rate fields, under both viscous and inviscid conditions, are obtained. In order to promote application to other nonlinear problems, a tutorial development of the framework is presented. Likewise, time-incremental solution approaches and construction of approximate, though otherwise difficult-to-obtain backward-time GF's (useful in solution of forward-time evolution problems) are discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2026

A scalable variational method for estimating the latent infection-rate field of an outbreak

In this paper, we explore whether the infection-rate of a disease can serve as a robust monitoring variable in epidemiological surveillance algorithms. The infection-rate is dependent on population mixing patterns that do not vary erratically day-to-day; in contrast, daily case-counts used in contemporary surveillance algorithms are corrupted by reporting errors. The technical challenge lies in estimating the latent infection-rate from case-counts. Here we devise a Bayesian method to estimate the infection-rate across multiple adjoining areal units, and then use it, via an anomaly detector, to discern a change in epidemiological dynamics. We extend an existing model for estimating the infection-rate in an areal unit by incorporating a Markov random field model, so that we may estimate infection-rates across multiple areal units, while preserving spatial correlations observed in the epidemiological dynamics. To carry out the high-dimensional Bayesian inverse problem, we develop an implementation of mean-field variational inference specific to the infection model and integrate it with the random field model to incorporate correlations across counties. The method is tested on estimating the COVID-19 infection-rates across all 33 counties in New Mexico using data from the summer of 2020, and then employing them to detect the arrival of the Fall 2020 COVID-19 wave. We perform the detection using a temporal algorithm that is applied county-by-county. We also show how the infection-rate field can be used to cluster counties with similar epidemiological dynamics.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2021

Estimating Subhourly Inverter Clipping Loss From Satellite-Derived Irradiance Data

Photovoltaic system production simulations are conventionally run using hourly weather datasets. Hourly simulations are sufficiently accurate to predict the majority of long-term system behavior but cannot resolve high-frequency effects like inverter clipping caused by short-duration irradiance variability. Direct modeling of this subhourly clipping error is only possible for the few locations with high-resolution irradiance datasets. This paper describes a method of predicting the magnitude of this error using a machine learning regressor ensemble model, comprised of a random forest and an XGBoost model, and 30-minute satellite irradiance data. The method predicts a correction for each 30-minute interval with the potential to roll up into 60-minute corrections to match an hourly energy model. The model is trained and validated at locations where the error can be directly simulated from 1-minute ground data. The validation shows low bias at most ground station locations. The model is also applied to gridded satellite irradiance to produce a heatmap of the estimated clipping error across the United States. Finally, the relative importance of each predictor satellite variable is retrieved from the model and discussed.

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

DOE OSTI2013

HTR-PROTEUS Pebble Bed Experimental Program Core 4: Random Packing With a 1:1 Moderator-to-Fuel Pebble Ratio

In its deployment as a pebble bed reactor (PBR) critical facility from 1992 to 1996, the PROTEUS facility was designated as HTR-PROTEUS. This experimental program was performed as part of an International Atomic Energy Agency (IAEA) Coordinated Research Project (CRP) on the Validation of Safety Related Physics Calculations for Low Enriched HTGRs. Within this project, critical experiments were conducted for graphite moderated LEU systems to determine core reactivity, flux and power profiles, reaction-rate ratios, the worth of control rods, both in-core and reflector based, the worth of burnable poisons, kinetic parameters, and the effects of moisture ingress on these parameters. One benchmark experiment was evaluated in this report: Core 4. Core 4 represents the only configuration with random pebble packing in the HTR-PROTEUS series of experiments, and has a moderator-to-fuel pebble ratio of 1:1. Three random configurations were performed. The initial configuration, Core 4.1, was rejected because the method for pebble loading, separate delivery tubes for the moderator and fuel pebbles, may not have been completely random; this core loading was rejected by the experimenters. Cores 4.2 and 4.3 were loaded using a single delivery tube, eliminating the possibility for systematic ordering effects. The second and third cores differed slightly in the quantity of pebbles loaded (40 each of moderator and fuel pebbles), stacked height of the pebbles in the core cavity (0.02 m), withdrawn distance of the stainless steel control rods (20 mm), and withdrawn distance of the autorod (30 mm). The 34 coolant channels in the upper axial reflector and the 33 coolant channels in the lower axial reflector were open. Additionally, the axial graphite fillers used in all other HTR-PROTEUS configurations to create a 12-sided core cavity were not used in the randomly packed cores. Instead, graphite fillers were placed on the cavity floor, creating a funnel-like base, to discourage ordering effects during pebble loading. Core 4 was determined to be acceptable benchmark experiment.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2014

HTR-proteus pebble bed experimental program core 4: random packing with a 1:1 moderator-to-fuel pebble ratio

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2014

Tensor hypercontracted ppRPA: Reducing the cost of the particle-particle random phase approximation from O(r {sup 6}) to O(r {sup 4})

In recent years, interest in the random-phase approximation (RPA) has grown rapidly. At the same time, tensor hypercontraction has emerged as an intriguing method to reduce the computational cost of electronic structure algorithms. In this paper, we combine the particle-particle random phase approximation with tensor hypercontraction to produce the tensor-hypercontracted particle-particle RPA (THC-ppRPA) algorithm. Unlike previous implementations of ppRPA which scale as O(r{sup 6}), the THC-ppRPA algorithm scales asymptotically as only O(r{sup 4}), albeit with a much larger prefactor than the traditional algorithm. We apply THC-ppRPA to several model systems and show that it yields the same results as traditional ppRPA to within mH accuracy. Our method opens the door to the development of post-Kohn Sham functionals based on ppRPA without the excessive asymptotic cost of traditional ppRPA implementations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Differentially Private Synthesis and Sharing of Network Data Via Bayesian Exponential Random Graph Models

Abstract Network data often contain sensitive relational information. One approach to protecting sensitive information while offering flexibility for network analysis is to share synthesized networks based on the information in originally observed networks. We employ differential privacy (DP) and exponential random graph models (ERGMs) and propose the DP-ERGM method to synthesize network data. We apply DP-ERGM to two real-world networks. We then compare the utility of synthesized networks generated by DP-ERGM, the DyadWise Randomized Response (DWRR) approach, and the Synthesis through Conditional distribution of Edge given nodal Attribute (SCEA) approach. In general, the results suggest that DP-ERGM preserves the original information significantly better than two other approaches in network structural statistics and inference for ERGMs and latent space models. Furthermore, DP-ERGM satisfies node DP through modeling the global network structure with ERGM, a stronger notion of privacy than the edge DP under which DWRR and SCEA operate.

graph synthesis↗

DOE OSTI2016

Hexagonal boron nitride and water interaction parameters

The study of hexagonal boron nitride (hBN) in microfluidic and nanofluidic applications at the atomic level requires accurate force field parameters to describe the water-hBN interaction. In this work, we begin with benchmark quality first principles quantum Monte Carlo calculations on the interaction energy between water and hBN, which are used to validate random phase approximation (RPA) calculations. We then proceed with RPA to derive force field parameters, which are used to simulate water contact angle on bulk hBN, attaining a value within the experimental uncertainties. This paper demonstrates that end-to-end multiscale modeling, starting at detailed many-body quantum mechanics and ending with macroscopic properties, with the approximations controlled along the way, is feasible for these systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2010

Theory of weak scattering of stochastic electromagnetic fields from deterministic and random media

The theory of scattering of scalar stochastic fields from deterministic and random media is generalized to the electromagnetic domain under the first-order Born approximation. The analysis allows for determining the changes in spectrum, coherence, and polarization of electromagnetic fields produced on their propagation from the source to the scattering volume, interaction with the scatterer, and propagation from the scatterer to the far field. An example of scattering of a field produced by a {delta}-correlated partially polarized source and scattered from a {delta}-correlated medium is provided.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗