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At least 1,351 records · Page 75
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Developing a remediation framework

When harmful contaminants are detected in soil, sediment, or groundwater (or suspected due to industrial activities), remediation efforts may be required to protect human health and the environment. This chapter will introduce and discuss the steps in the general site remediation process that are key when approaching any remediation strategy, regardless of the site complexity. While these steps are described in a linear fashion, in most cases, the approach is more fluid and iterative depending on the desired outcomes and success of each progressive clean-up effort along the way. This chapter will additionally articulate some key considerations which may be important to the overall remediation strategy depending on the particular needs and desired outcomes. From these more general discussions, the chapter will branch into a case-study of the remediation approach, or process steps, previously/currently/in the future taking place at the Hanford Site, as one example of a complex waste sites in the United States. As indicated earlier, while a remediation strategy can be more simply described by a progression of general process steps, it is far more likely to observe fluidity and strategy evolution over time from the first conceived strategy as remediation progress occurs. The chapter concludes with a brief discussion of how the strategy at the Hanford Site has evolved to provide a singular example of what this evolution might look like for other complex waste sites.

Muller, Katherine A.↗
DOE OSTI2022

Building Load Control Using Distributionally Robust Chance-Constrained Programs with Right-Hand Side Uncertainty and the Risk-Adjustable Variants

Aggregation of heating, ventilation, and air conditioning (HVAC) loads can provide reserves to absorb volatile renewable energy, especially solar photo-voltaic (PV) generation. In this paper, we decide HVAC control schedules under uncertain PV generation, using a distributionally robust chance-constrained (DRCC) building load control model under two typical ambiguity sets: the moment-based and Wasserstein ambiguity sets. We derive mixed integer linear programming (MILP) reformulations for DRCC problems under both sets. Especially, for the Wasserstein ambiguity set, we use the right-hand side (RHS) uncertainty to derive a more compact MILP reformulation than the commonly known MILP reformulations with big-M constants. All the results also apply to general individual chance constraints with RHS uncertainty. Furthermore, we propose an adjustable chance-constrained variant to achieve tradeoff between the operational risk and costs. We derive MILP reformulations under the Wasserstein ambiguity set and second-order conic programming (SOCP) reformulations under the moment-based set. Using real-world data, we conduct computational studies to demonstrate the efficiency of the solution approaches and the effectiveness of the solutions. Summary of Contribution: The problem studied in this paper is motivated by a building load control problem that uses the aggregation of heating, ventilation, and air conditioning (HVAC) loads as flexible reserves to absorb uncertain solar photovoltaic (PV) generation. The problem is formulated as distributionally robust chance-constrained (DRCC) programs with right-hand side (RHS) uncertainty. In addition, we propose a risk-adjustable variant of the DRCC programs, where the risk level, instead of being predetermined, is treated as a decision variable. The paper aims to provide tractable reformulations and solution algorithms for both the (general) DRCC and the (general) adjustable DRCC models with RHS uncertainty.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Data-Driven Compositional Optimization in Misspecified Regimes

With a manifold growth in the scale and intricacy of systems, the challenges of parametric misspecification become pronounced. These concerns are further exacerbated in compositional settings, which emerge in problems complicated by modeling risk and robustness. In “Data-Driven Compositional Optimization in Misspecified Regimes,” the authors consider the resolution of compositional stochastic optimization problems, plagued by parametric misspecification. In considering settings where such misspecification may be resolved via a parallel learning process, the authors develop schemes that can contend with diverse forms of risk, dynamics, and nonconvexity. They provide asymptotic and rate guarantees for unaccelerated and accelerated schemes for convex, strongly convex, and nonconvex problems in a two-level regime with extensions to the multilevel setting. Surprisingly, the nonasymptotic rate guarantees show no degradation from the rate statements obtained in a correctly specified regime and the schemes achieve optimal (or near-optimal) sample complexities for general T-level strongly convex and nonconvex compositional problems.

Business & Economics↗
DOE OSTI2024

Challenges of COVID-19 Case Forecasting in the US, 2020–2021

During the COVID-19 pandemic, forecasting COVID-19 trends to support planning and response was a priority for scientists and decision makers alike. In the United States, COVID-19 forecasting was coordinated by a large group of universities, companies, and government entities led by the Centers for Disease Control and Prevention and the US COVID-19 Forecast Hub ( https://covid19forecasthub.org ). We evaluated approximately 9.7 million forecasts of weekly state-level COVID-19 cases for predictions 1–4 weeks into the future submitted by 24 teams from August 2020 to December 2021. We assessed coverage of central prediction intervals and weighted interval scores (WIS), adjusting for missing forecasts relative to a baseline forecast, and used a Gaussian generalized estimating equation (GEE) model to evaluate differences in skill across epidemic phases that were defined by the effective reproduction number. Overall, we found high variation in skill across individual models, with ensemble-based forecasts outperforming other approaches. Forecast skill relative to the baseline was generally higher for larger jurisdictions (e.g., states compared to counties). Over time, forecasts generally performed worst in periods of rapid changes in reported cases (either in increasing or decreasing epidemic phases) with 95% prediction interval coverage dropping below 50% during the growth phases of the winter 2020, Delta, and Omicron waves. Ideally, case forecasts could serve as a leading indicator of changes in transmission dynamics. However, while most COVID-19 case forecasts outperformed a naïve baseline model, even the most accurate case forecasts were unreliable in key phases. Further research could improve forecasts of leading indicators, like COVID-19 cases, by leveraging additional real-time data, addressing performance across phases, improving the characterization of forecast confidence, and ensuring that forecasts were coherent across spatial scales. In the meantime, it is critical for forecast users to appreciate current limitations and use a broad set of indicators to inform pandemic-related decision making.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2021

Quantifying the effects of multiple land management practices, land cover change, and wildfire on the California landscape carbon budget with an empirical model

The effectiveness of land-based climate mitigation strategies is generally estimated on a case-by-case basis without considering interactions with other strategies or influencing factors. Here we evaluate a new, comprehensive approach that incorporates interactions among multiple management strategies, land use/cover change, wildfire, and climate, although the potential effects of climate change are not evaluated in this study. The California natural and working lands carbon and greenhouse gas model (CALAND) indicates that summing individual practice estimates of greenhouse gas impacts may underestimate emission reduction benefits in comparison with an integrated estimate. Annual per-area estimates of the potential impact of specific management practices on landscape emissions can vary based on the estimation period, which can be problematic for extrapolating such estimates over space and time. Furthermore, the actual area of implementation is a primary factor in determining potential impacts of management on landscape emissions. Nonetheless, less intensive forest management, avoided conversion to urban land, and urban forest expansion generally create the largest annual per-area reductions, while meadow restoration and forest fuel reduction and harvest practices generally create the largest increases with respect to no management. CALAND also shows that data uncertainty is too high to determine whether California land is a source or a sink of carbon emissions, but that estimating effects of management with respect to a baseline provides valid results. Important sources of this uncertainty are initial carbon density, net ecosystem carbon accumulation rates, and land use/cover change data. The appropriate choice of baseline is critical for generating valid results.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Non-invertible symmetries in finite-group gauge theory

We investigate the invertible and non-invertible symmetries of topological finite-group gauge theories in general spacetime dimensions, where the gauge group can be abelian or non-abelian. We focus in particular on the 0-form symmetry. The gapped domain walls that generate these symmetries are specified by boundary conditions for the gauge fields on either side of the wall. We investigate the fusion rules of these symmetries and their action on other topological defects including the Wilson lines, magnetic fluxes, and gapped boundaries. We illustrate these constructions with various novel examples, including non-invertible electric-magnetic duality symmetry in 3+1d \mathbb{Z}_2 ℤ 2 gauge theory, and non-invertible analogs of electric-magnetic duality symmetry in non-abelian finite-group gauge theories. In particular, we discover topological domain walls that obey Fibonacci fusion rules in 2+1d gauge theory with dihedral gauge group of order 8. We also generalize the Cheshire string defect to analogous defects of general codimensions and gauge groups and show that they form a closed fusion algebra.

Córdova, Clay↗
DOE OSTI2020

Performance Limits for Maritime Wide-Area Search (MWAS) Radar

One of the earliest applications for radar was to search for and find maritime vessels on the open sea. Proper design and operation of an airborne Maritime Wide Area Search (MWAS) radar requires an understanding of system performance characteristics and limitations, and furthermore understanding the trades amongst a large number of interdependent system parameters. This report identifies and explores those characteristics and limits, and how they depend on hardware system parameters and environmental conditions. Ultimately, this leads to a characterization of parameters that offer optimum performance for the overall MWAS radar system. While the information herein is not new to the literature, its collection into a single report hopes to offer some value in reducing the 'seek time'. Acknowledgements This report was funded by General Atomics Aeronautical Systems, Inc. (GA-ASI) Mission Systems under Cooperative Research and Development Agreement (CRADA) SC08/01749 between Sandia National Laboratories and GA-ASI. General Atomics Aeronautical Systems, Inc. (GA-ASI), an affiliate of privately-held General Atomics, is a leading manufacturer of Remotely Piloted Aircraft (RPA) systems, radars, and electro-optic and related mission systems, including the Predator/Gray Eagle-series and Lynx Multi-mode Radar. -

42 ENGINEERING↗
DOE OSTI2020

Characterization of Hanford LAW Phase 3 Glasses

This report provides analyses of glass compositions, wash solution compositions, and Product Consistency Test (PCT) leachate compositions for a series of simulated low-activity waste (LAW) glasses fabricated at the Pacific Northwest National Laboratory (PNNL). These data will be used in the development of improved property/composition models for LAW glass at Hanford. Chemical analyses were performed on a representative sample of each of the quenched and sulfur saturated glasses to allow for comparisons with the targeted compositions. For some of the quenched glasses, measured concentrations of Cr₂O₃, K₂O, Na₂O, P₂O₅, and ZrO₂ were below the targeted values. For some of the sulfur saturated glasses, the measured concentrations of Al₂O₃, Cl⁻, Cr₂O₃, F⁻, K₂O, Na₂O, P₂O₅, V₂O₅, and ZrO₂ were generally low relative to the targeted values. A comparison of the measured compositions of the quenched and sulfur saturated versions of the study glasses showed that the measured concentrations of Al₂O₃, Cl⁻, and F⁻ were lower for most of the sulfur saturated glasses. The measured Cr₂O₃ and K₂O concentrations were markedly lower for the sulfur saturated versions of the glasses as compared to the quenched versions, which may indicate that these elements partitioned to the soluble sulfur salts. A set of modified glasses was received from PNNL later in this study. Chemical analysis showed that these glasses generally met their targeted compositions. The measured SO₃ concentrations were higher for most of the sulfur saturated glasses relative to those of the quenched versions, as expected. Chemical analysis of the wash solutions that resulted from preparation of the sulfur saturated melts identified Cr, K, Na, P, S, and V as the major elements in solution. With the exception of sulfur, this may explain why the measured concentrations of these components in the study glasses were generally below the targeted values. PNNL performed PCTs on quenched and canister centerline cooled (CCC) versions of the study glasses, as well as the modified glasses. The leachates were sent to SRNL for chemical analysis. Minor scatter in the measured values among the triplicate samples for each glass was noted. Several of the study glasses, both quenched and CCC, have NCi values that are greater than the immobilized LAW constraint of 4 g/L for B, Na, and Si.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2020

Storm Water Pollution Prevention Plan Middle DP Road Recovery Effort, June 26, 2020

The United States Environmental Protection Agency (EPA) has issued a final 2017 Construction General Permit (CGP) that covers discharges of stormwater from construction sites. The 2017 National Pollutant Discharge Elimination System (NPDES) General Permit for Storm Water Discharges from Construction Activity (Appendix D) includes the following requirements:(1) conduct a critical habitat and threatened/endangered species study; (2) develop and implement a Storm Water Pollution Prevention Plan (SWPPP) in accordance with good engineering practices; (3) submit a Notice of Intent (NOI); (4) install and maintain erosion and stormwater controls; (5) perform and document storm water inspections during construction and site stabilization; (6) amend the SWPPP as necessary; and (7) submit a Notice of Termination (NOT) following project completion and final stabilization of disturbed areas. Authorization to discharge storm water is required under this Permit for both large and small construction projects disturbing more than one (1) acre or part of a larger common plan of development that collectively disturbs more than one (1) acre. All parties that meet the definition of Operator must be permitted. Each permittee is not required to develop and implement a separate SWPP Plan. It is required that there be at least one SWPP Plan for a site that incorporates the required elements for all Operators. The 2017 CGP number for New Mexico (Region 6) is NMR100000. This Plan, which has been developed for Triad National Security, LLC (Triad), describes the nature and sequencing of construction activities, potential sources of pollution, and identifies the Best Management Practices (BMPs) to minimize the potential for erosion and storm water pollution. The Plan was developed in accordance with the provisions of the Clean Water Act (33 U.S.C. § §1251 et seq., as amended by the Water Quality Act of 1987, P.L. 100-4), and the regulations established by the U.S. Environmental Protection Agency (EPA) for National Pollutant Discharge Elimination System (NPDES) General Permits for Storm Water Discharges From Construction Activities.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Storm Water Pollution Prevention Plan Middle DP Road Recovery Effort, June 26, 2020 (Copy for Informational Puproses Only)

The United States Environmental Protection Agency (EPA) has issued a final 2017 Construction General Permit (CGP) that covers discharges of stormwater from construction sites. The 2017 National Pollutant Discharge Elimination System (NPDES) General Permit for Storm Water Discharges from Construction Activity (Appendix D) includes the following requirements: (1) conduct a critical habitat and threatened/endangered species study; (2) develop and implement a Storm Water Pollution Prevention Plan (SWPPP) in accordance with good engineering practices; (3) submit a Notice of Intent (NOI); (4) install and maintain erosion and stormwater controls; (5) perform and document storm water inspections during construction and site stabilization; (6) amend the SWPPP as necessary; and (7) submit a Notice of Termination (NOT) following project completion and final stabilization of disturbed areas. Authorization to discharge storm water is required under this Permit for both large and small construction projects disturbing more than one (1) acre or part of a larger common plan of development that collectively disturbs more than one (1) acre. All parties that meet the definition of Operator must be permitted. Each permittee is not required to develop and implement a separate SWPP Plan. It is required that there be at least one SWPP Plan for a site that incorporates the required elements for all Operators. The 2017 CGP number for New Mexico (Region 6) is NMR100000. This Plan, which has been developed for Triad National Security, LLC (Triad), describes the nature and sequencing of construction activities, potential sources of pollution, and identifies the Best Management Practices (BMPs) to minimize the potential for erosion and storm water pollution. The Plan was developed in accordance with the provisions of the Clean Water Act (33 U.S.C. § §1251 et seq., as amended by the Water Quality Act of 1987, P.L. 100-4), and the regulations established by the U.S. Environmental Protection Agency (EPA) for National Pollutant Discharge Elimination System (NPDES) General Permits for Storm Water Discharges From Construction Activities.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Composition Measurements of the LAW Phase 4 Glasses

In this report, the Savannah River National Laboratory provides results from the analyses of glass compositions for a series of simulated nuclear waste glasses fabricated at the Pacific Northwest National Laboratory. The series included quenched versions of the glasses. The resulting data will be used in the development of enhanced property/composition models for waste vitrification at Hanford. Chemical analyses were performed on a representative sample of each of the quenched glasses to allow for comparisons with the targeted compositions. For the quenched glasses from Set 1, measured concentrations of B 2 O 3 and SiO 2 were generally above the targeted values. Measured concentrations for MgO and P 2 O 5 were generally low for glasses. Measured concentrations of ZrO 2 were both below and above the targeted values for glasses. For the quenched glasses from Set 2, measured concentrations of AL 2 O 3 , B 2 O 3 , P 2 O 5 , SiO 2 , and ZrO 2 were generally below the targeted values. Measured concentrations of Na 2 0 were both below and above the targeted values for glasses. The measured concentrations of chlorine, fluorine, and SO 3 were below the targeted values for most of the study glasses, likely because of volatility during melting. Overall, there were no indications of errors in batching of the simulated waste glasses. These results can be used in further characterization of this series of glasses, including the normalization of Product Consistency Test results.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2020

An Updated Analysis of Clad Degradation

This report provides an analysis of the clad barrier function associated with the direct disposal of dual purpose canisters (DPCs) under hypothetical conditions in a shale repository and in an alluvial repository, including the effect of a postulated criticality event inside a disposed DPC. Should a postulated criticality event occur in a hypothetical shale repository, cladding will primarily degrade by general corrosion. Stress corrosion cracking, hydride cracking, creep failure, pitting and crevice corrosion, rod pressurization, and clad unzipping are calculated to have little impact on cladding persistence. At the higher temperature expected during a postulated criticality event in a saturated shale repository, general corrosion of cladding would be rapid - on the order of 0.034 microns/yr. A few hundred years after onset of a postulated criticality event in a shale repository complete general corrosion of fuel assembly grid spacer walls and guide tubes will likely result in settling of fuel rods upon each other. This rod consolidation should displace the water moderator and possibly terminate a postulated criticality. The primary potential degradation pathway for cladding in a hypothetical alluvial repository is localized corrosion by fluoride, which cannot occur in a shale repository. Fluoride-enhanced corrosion of cladding would be accelerated under the slightly higher (< 100°C) temperatures associated with a postulated criticality event. The impact of criticality in both cases (shale and alluvial) would be to increase the amount of failed cladding. But it would require very specialized transport pathways.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2021

Modeling Study of Reduced Tubing Size Effects on Flow in Depleted Reservoir Natural Gas Storage Wells

This report explores the effects of tubing size reductions on natural gas flow from representative depleted reservoir underground storage wells and fields using basic models for coupled reservoir and pipe flow. This work was motivated by interest at the U.S. Department of Transportation, Pipeline and Hazardous Materials Safety Administration, in evaluating the effects of tubing and packer as a potential safety upgrade to implement double-barrier systems to existing underground natural gas storage wells. Reservoir and well flow models were developed from widely accepted industry equations, verified against a commercial process simulator model, and validated against field data. The study utilized U.S. operator survey data to provide context and assure that modeling parameters including aver age deliverability rates for wells and fields, operating pressures, well depths, and storage capacities were all carefully considered to keep the modeling relevant to the known range of U.S. operations. The models generally found that wells and fields with inherently low deliverability were relatively insensitive to reductions in tubing diameter, primarily because the hydraulics in those cases were controlled by reservoir properties. For the high-producing wells and fields, the models found that reducing tubing diameter could produce significant reductions in deliverability, both at the field- and well-level. When put into context with occurrence data regarding average deliverability of fields and wells, it appears that most wells and most fields across the U.S. would experience deliverability reductions on the low end of what was simulated here, generally below 20%. For fields with moderate to high deliverability, reductions were generally larger, and could reach as high as 60% for the highest-producing wells and fields.

03 NATURAL GAS↗
DOE OSTI2021

Algebraic Multigrid with Optimal Interpolation and Adaptive Smoothers (Final Report)

The project team continued with work on developing new bootstrap AMG techniques for solving symmetric and non-symmetric PDE systems. The focus of this work is to derive more reliable measures of the quality of the coarse space set than the convergence rate of the standard F-relaxation form of CR and a more robust form of interpolation than the so-called ideal form. We have successfully derived a sharp variant of CR that gives the precise convergence rate of the two-grid method using this optimal interpolation and, in addition, we derived a new Generalized Bootstrap AMG setup algorithm that uses as its main tool a multilevel eigensolver for the generalized eigenvalue problem involving the system matrix and the symmetrized smoother. In addition, the approach allows for general block smoothers with overlap. We have applied the method to scalar diffusion problems, linear elasticity, and Maxwell’s and the method shows marked improvements over existing AMG methods for these problems. In addition, the team worked with CASC members on new forms of ideal AMG interpolation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Creep-fatigue Behavior and Damage Accumulation of a Candidate Structural Material for Concentrating Solar Power Solar Thermal Receiver (Final Technical Report)

Creep-fatigue deformation is an important consideration for a thermal receiver in Concentrating Solar Power systems due to the constant static stress or pressure, diurnal cycling, and elevated service temperatures required for efficient operation. An accurate description of the creep-fatigue behavior, not available for five of the six candidate materials, is important for assessment of preliminary designs. This project has provided a detailed analysis of the creep-fatigue behavior and damage accumulation of Alloy 740H, a candidate structural material for a CSP solar thermal receiver to address a critical knowledge barrier for receiver designs identified in the CSP Gen3 Demonstration Roadmap. This project was divided in to three tasks, split between two general categories: Experimental and design methodology. Tasks 1 and 3, relating to the collection of data on Alloy 740H plate and sheet forms, respectively, were performed at the Idaho National Laboratory and used as input to Task 2, the development of design methodology performed at Argonne National Laboratory. Experimental work covered limited tensile and creep testing to fill gaps in available data that is currently available and to demonstrate how the plate of Alloy 740H tested in this work compared to historical data. A more substantial testing program for fatigue and creep-fatigue was performed, with particular emphasis on creep-fatigue as there is little available data and it is necessary to understand the creep-fatigue interaction and develop related design models. This effort includes the development of rules for the design of solar receiver components against high temperature creep-fatigue and ratcheting failure modes. The ASME Code rules for high temperature nuclear components was used to the basis of the method but adjustments will be made to reflect the generally shorter, diurnal operating cycles of thermal receivers and the relative consequences of failure, comparing nuclear to solar components. This work has provided guidance for the design of components for concentrating power facilities operating at high temperatures and undergoing high, secondary thermal stresses relative to the applied primary pressure stress. The design rules were developed for the design of Generation 3 CSP tubular receivers manufactured from Alloy 740H, but are generally applicable to a wide range of component types undergoing similar loads. Procedural design rules for components to be used in conjunction with the 2019 edition of the ASME Boiler & Pressure Vessel Code and the corresponding design data for Alloy 740H have been developed. A commentary describing the rationale behind the design rules and the data underlying the design material properties, as well as an extensive set of worked sample problems detailing the application of the rules to CSP components were developed as a part of this project, with a separate report covering these aspects in detail and included in the Appendix of this report.

14 SOLAR ENERGY↗
DOE OSTI2021

Simple Acceptance Decisions and Acceptance Risk

Acceptance risk may be estimated using cumulative probability distribution functions applied to populations of measurands and test measurement values. “Simple acceptance” is a decision rule that sets the acceptance range of a test result equal to the tolerance range specification. While acceptance risk is comprised of both consumer risk and producer risk, this paper compares the effects of simple acceptance decision rules and guardbanding decision rules on consumer risk. Consumer risk is also known as the probability of false acceptance. The terms describe the risk of accepting test results as passing when the actual values exceed specification limits. False acceptance is only possible when the true value of a measurand is out of tolerance and the test result indicates that the measurand is within tolerance. Metrologists generally have some information about the test uncertainty regarding a specific acceptance test result. Along with a general lack of knowledge regarding the measurand population parameters, the complicated interplay between risk, dispersion, and central values generally prevents calibration laboratories from fully characterizing acceptance probabilities. Organizations that model the measurand populations can reduce consumer risk by avoiding certification of items whose measurand populations are not well centered. The models in this paper present a recurring trend: guardbanding reduces nonnegligible risks of false acceptance when compared to simple acceptance. However, guardbanding is not the most effective means of acceptance risk mitigation. Systematic characterization of measurand populations can provide the information a calibration laboratory needs to reliably control acceptance risk.

42 ENGINEERING↗
DOE OSTI2022

Permutation-adapted complete and independent basis for atomic cluster expansion descriptors

In many recent applications, particularly in the field of atom-centered descriptors for interatomic potentials, tensor products of spherical harmonics have been used to characterize complex atomic environments. When coupled with a radial basis, the atomic cluster expansion (ACE) basis is obtained. However, symmetrization with respect to both rotation and permutation results in an overcomplete set of ACE descriptors with linear dependencies occurring within blocks of functions corresponding to particular generalized Wigner symbols. All practical applications of ACE employ semi-numerical constructions to generate a complete, fully independent basis. While computationally tractable, the resultant basis cannot be expressed analytically, is susceptible to numerical instability, and thus has limited reproducibility. Here we present a procedure for generating explicit analytic expressions for a complete and independent set of ACE descriptors. The procedure uses a coupling scheme that is maximally symmetric w.r.t. permutation of the atoms, exposing the permutational symmetries of the generalized Wigner symbols, and yields a permutation-adapted rotationally and permutationally invariant basis (PA-RPI ACE). Theoretical support for the approach is presented, as well as numerical evidence of completeness and independence. A summary of explicit enumeration of PA-RPI functions up to rank 6 and polynomial degree 32 is provided. The PA-RPI blocks corresponding to particular generalized Wigner symbols may be either larger or smaller than the corresponding blocks in the simpler rotationally invariant basis. Finally, we demonstrate that basis functions of high polynomial degree persist under strong regularization, indicating the importance of not restricting the maximum degree of basis functions in ACE models a priori.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2022

Hypothesis testing via AI: Generating physically interpretable models of scientific data with machine learning (Full Technical Report)

Deep learning has demonstrated an exceptional ability to solve complex tasks (an engineering success); however, it has done so at the expense of the ability to generate new knowledge (a scientific failure). We propose an alternative framework—entitled Deep Symbolic Regression (DSR)—in which artificial neural networks (NNs) rapidly generate hypotheses about physical relationships among inputs. This framework bypasses the need to interpret an NN altogether, while still leveraging the representational power of deep learning. The resulting models are tractable mathematical expressions, which are inherently and readily human interpretable and can provide insights into underlying physical phenomena. Further, we fold this methodology into the scientific process by allowing the scientist to directly integrate a priori knowledge and beliefs to accelerate learning. We demonstrate this methodology on symbolic regression—the problem of rediscovering underlying expressions describing a dataset—and achieve state-of-the-art performance across a wide variety of symbolic regression problems. Further, we generalize our DSR framework to apply to the more general class of symbolic optimization problems, in which one seeks to optimize a sequence of symbols or “tokens” under a black-box reward function. Examples of other symbolic optimization problems include neural architecture search and computational antibody design. Our generalized tool, Deep Symbolic Optimization (DSO), has been demonstrated on the task of learning symbolic control policies for reinforcement learning environments, and has been adopted as an enabling capability for computational antibody design.

97 MATHEMATICS AND COMPUTING↗