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At least 379 records · Page 21
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

McCormick envelopes in mixed-integer PDE-constrained optimization

McCormick envelopes are a standard tool for deriving convex relaxations of optimization problems that involve polynomial terms. Such McCormick relaxations provide lower bounds, for example, in branch-and-bound procedures for mixed-integer nonlinear programs but have not gained much attention in PDE-constrained optimization so far. This lack of attention may be due to the distributed nature of such problems, which on the one hand leads to infinitely many linear constraints (generally state constraints that may be difficult to handle) in addition to the state equation for a pointwise formulation of the McCormick envelopes and renders bound-tightening procedures that successively improve the resulting convex relaxations computationally intractable. We analyze McCormick envelopes for a model problem class that is governed by a semilinear PDE involving a bilinearity and integrality constraints. We approximate the nonlinearity and in turn the McCormick envelopes by averaging the involved terms over the cells of a partition of the computational domain on which the PDE is defined. This yields convex relaxations that underestimate the original problem up to an a priori error estimate that depends on the mesh size of the discretization. These approximate McCormick relaxations can be improved by means of an optimization-based bound-tightening procedure. We show that their minimizers converge to minimizers to a limit problem with a pointwise formulation of the McCormick envelopes when driving the mesh size to zero. We provide a computational example, for which we certify all of our imposed assumptions. The results point to both the potential of the methodology and the gaps in the research that need to be closed. Our methodology provides a framework first for obtaining pointwise underestimators for nonconvexities and second for approximating them with finitely many linear inequalities in an infinite-dimensional setting.

Approximations and Expansions↗
DOE OSTI2021

An optimization-based approach to parameter learning for fractional type nonlocal models

Nonlocal operators of fractional type are a popular modeling choice for applications that do not adhere to classical diffusive behavior; however, one major challenge in nonlocal simulations is the selection of model parameters. In this study we propose an optimization-based approach to parameter identification for fractional models with an optional truncation radius. We formulate the inference problem as an optimal control problem where the objective is to minimize the discrepancy between observed data and an approximate solution of the model, and the control variables are the fractional order and the truncation length. For the numerical solution of the minimization problem we propose a gradient-based approach, where we enhance the numerical performance by an approximation of the bilinear form of the state equation and its derivative with respect to the fractional order. Several numerical tests in one and two dimensions illustrate the theoretical results and show the robustness and applicability of our method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Machine-Learning Assisted Identification of Accurate Battery Lifetime Models with Uncertainty

Reduced-order battery lifetime models, which consist of algebraic expressions for various aging modes, are widely utilized for extrapolating degradation trends from accelerated aging tests to real-world aging scenarios. Identifying models with high accuracy and low uncertainty is crucial for ensuring that model extrapolations are believable, however, it is difficult to compose expressions that accurately predict multivariate data trends; a review of cycling degradation models from literature reveals a wide variety of functional relationships. Here, a machine-learning assisted model identification method is utilized to fit degradation in a stand-out LFP-Gr aging data set, with uncertainty quantified by bootstrap resampling. The model identified in this work results in approximately half the mean absolute error of a human expert model. Models are validated by converting to a state-equation form and comparing predictions against cells aging under varying loads. Parameter uncertainty is carried forward into an energy storage system simulation to estimate the impact of aging model uncertainty on system lifetime. The new model identification method used here reduces life-prediction uncertainty by more than a factor of three (86% ± 5% relative capacity at 10 years for human-expert model, 88.5% ± 1.5% for machine-learning assisted model), empowering more confident estimates of energy storage system lifetime.

25 ENERGY STORAGE↗
DOE OSTI2020

An optimization-based approach to parameter learning for fractional type nonlocal models

Nonlocal operators of fractional type are a popular modeling choice for applications that do not adhere to classical diffusive behavior; however, one major challenge in nonlocal simulations is the selection of model parameters. In this work we propose an optimization-based approach to parameter identification for fractional models with an optional truncation radius. We formulate the inference problem as an optimal control problem where the objective is to minimize the discrepancy between observed data and an approximate solution of the model, and the control variables are the fractional order and the truncation length. For the numerical solution of the minimization problem we propose a gradient-based approach, where we enhance the numerical performance by an approximation of the bilinear form of the state equation and its derivative with respect to the fractional order. Several numerical tests in one and two dimensions illustrate the theoretical results and show the robustness and applicability of our method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Interpolating the ‘t Hooft model between Instant and Light-Front dynamics in the Coulomb Gauge

The 1+1D model of quantum chromodynamics (QCD) in the infinite number of colors, or 't Hooft model, can be interpolated between the instant form dynamics (IFD) and the light-front dynamics (LFD) using an interpolation parameter 0 (IFD) ≤ δ ≤ π/4 (LFD). This was realized in the interpolating axial gauge which links the axial gauge (A 1 = 0) in IFD and the light-front gauge (A + = 0) [1]. In this presentation, we discuss the corresponding realization in the interpolating Coulomb gauge which links the temporal gauge (A 0 = 0) in IFD and the light-front gauge (A + = 0) and its benefit of resolving the issue associated with the absence of the conjugate field to the gauge field A 0 in the axial gauge. In both gauges, all degrees of freedom are physical making these gauge choices ideal for finding the bound-state equations and for renormalizability. Although the gauge independence of the physical observables such as the meson mass spectra following Regge trajectories may be guaranteed due to the gauge symmetry of QCD, the realization and interpretation of the identical physical results may depend on the gauge choices. Here, we discuss such difference in the realization of the confinement phenomena ala linear potential in the two different gauges, Coulomb vs. Axial, and highlight the gauge independent physical results expected. We also comment on the utility of the interpolation which leads to an alternative quasi-PDF that can be implemented in the lattice QCD without suffering from the large momentum boost.

Duggin, Hunter↗
DOE OSTI2023

Machine-Learning Assisted Identification of Battery Life Models

Predictive battery life models are commonly utilized to extrapolate degradation trends observed during accelerated aging tests for simulation of degradation in real-world applications. Thus, fitting accelerated aging data as accurately as possible and with low uncertainty is crucial for making believable projections of battery lifetime, but it is challenging to identify algebraic expressions that accurately fit multivariate degradation trends. A review of models published in literature reveal some common expressions for fitting calendar aging data, which is only dependent on temperature and state-of-charge, but no consistency across many models for fitting cycle aging data, indicating the need for a statistically rigorous data driven approach for developing empirical models. This talk will describe a machine-learning assisted method for identification of predictive battery life models utilizing bilevel optimization and symbolic regression. Bilevel optimization with cross-validation is used to statistically determine cell- and stress-dependent model parameters, while symbolic regression identifies both linear and multiplicative candidate expressions to predict stress-dependent degradation rates by selecting low-order subsets of features from a generated feature library. Because model expressions are identified empirically, it is crucial to ensure resulting models behave according to physical expectations, so the stability of models for interpolation or extrapolation is interrogated qualitatively through simulation and quantitatively through cross-validation and uncertainty quantification via bootstrap resampling. This model identification approach substantially improves upon models identified purely using expert judgement in terms of both accuracy and uncertainty. Model simulation and validation is then conducted by deriving a state-equation form of the predictive model, enabling simulation of battery aging under dynamic stresses. This enables validation of the predictive battery model on lab-based tests with varying conditions or on drive-cycle or application-cycle testing protocols. Parameter uncertainty can be carried forward into model simulation, giving lifetime estimates and confidence windows for cell- or system-level lifetime. The financial impact of battery model uncertainty can be estimated by incorporating uncertainty into a technoeconomic model.

battery↗
DOE OSTI2024

On the Existence of Steady-State Solutions to the Equations Governing Fluid Flow in Networks

The steady-state solution of fluid flow in pipeline infrastructure networks driven by junction/node potentials is a crucial ingredient in various decision-support tools for system design and operation. While the nonlinear system is known to have a unique solution (when one exists), the absence of a definite result on the existence of solutions hobbles the development of computational algorithms, for it is not possible to distinguish between algorithm failure and non-existence of a solution. In this letter, we show that for any fluid whose equation of state is a scaled monomial, a unique solution exists for such nonlinear systems if the term solution is interpreted in terms of potentials and flows rather than pressures and flows. However, for gases following the CNGA equation of state, while the question of existence remains open, we construct an alternative system that always has a unique solution and show that the solution to this system is a good approximant of the true solution. Further, the existence result for flow of natural gas in networks also applies to other fluid flow networks such as water distribution networks or networks that transport carbon dioxide in carbon capture and sequestration. Most importantly, our result enables correct diagnosis of algorithmic failure, problem stiffness, and non-convergence in computational algorithms.

42 ENGINEERING↗
DOE OSTI2020

Stringent constraints on neutron-star radii from multimessenger observations and nuclear theory

The properties of neutron stars are determined by the nature of the matter that they contain. These properties can be constrained by measurements of the star’s size. We obtain stringent constraints on neutron-star radii by combining multimessenger observations of the binary neutron-star merger GW170817 with nuclear theory that best accounts for density-dependent uncertainties in the equation of state. We construct equations of state constrained by chiral effective field theory and marginalize over these using the gravitational-wave observations. Combining this with the electromagnetic observations of the merger remnant that imply the presence of a short-lived hypermassive neutron star, we find that the radius of a 1.4 M⊙ neutron star is $R_{1.4M_⊙} = 11.0^{+0.9}_{-0.6} km$ (90% credible interval). Finally, using this constraint, we show that neutron stars are unlikely to be disrupted in neutron star–black hole mergers; subsequently, such events will not produce observable electromagnetic emission.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Simulation of Methane Oxycombustion in Supercritical Carbon Dioxide

The Allam-Fetvedt Cycle (AFC) offers the potential for electricity generation with minimal or even negative carbon emissions by using oxycombustion in supercritical carbon dioxide (sCO2). Because of the extreme high temperatures and pressures encountered in these systems, simulation of oxycombustion requires use of a complex equation of state such as the modified Soave-Redlich-Kwong (SRK) equation, coupled with equally complex correlations for transport properties. The current work simulates a model combustor using both an ideal gas equation of state and the SRK equation of state. The model combustor features a jet of CH4 mixing with and reacting with O2 in the sCO2 ambient. Two jet configurations are considered: one of pure CH4, and one of CH4 mixed with sCO2. Comparison of results shows that key output properties such as combustor temperature and flow distribution are impacted by the choice of equations of state. Inspection of simulation results shows that mixing and reaction rates, as well as the uniformity of the flow, are impacted by the choice of equation of state. These results show that even though use of a complex equation of state greatly increases the computational costs of these simulations, it is critical to accurately capturing the physics of these systems.

computational fluid dynamics↗
DOE OSTI2024

Axion baryogenesis puts a new spin on the Hubble tension

We show that a rotating axion field that makes a transition from a matterlike equation of state to a kinationlike equation of state around the epoch of recombination can significantly ameliorate the Hubble tension, i.e., the discrepancy between the determinations of the present-day expansion rate H 0 from observations of the cosmic microwave background on one hand and type Ia supernovae on the other. We consider a specific, UV-complete model of such a rotating axion and find that it can relax the Hubble tension without exacerbating tensions in determinations of other cosmological parameters, in particular the amplitude of matter fluctuations S 8 . We subsequently demonstrate how this rotating axion model can also generate the baryon asymmetry of our Universe, by introducing a coupling of the axion field to right-handed neutrinos. This baryogenesis model predicts heavy neutral leptons that are most naturally within reach of future lepton colliders, but in finely tuned regions of parameter space may also be accessible at the high-luminosity LHC and the beam dump experiment SHiP. Published by the American Physical Society 2024

Co, Raymond T. (ORCID:0000000283957056)↗
DOE OSTI2023

ARES v1.x - Performance Portable Tool to Simulate Supernovae based on Parthenon Framework

Historically, codes for simulating supernovae (such as Arepo, FLASH or LEAFS) have been at the forefront of scientific high-performance computing to the immense computational resources required for full 3D simulations. However, given the shift towards heterogenous HPC architectures, many current-generation codes are at the risk of losing their competitiveness as they are only designed to run on homogeneous CPU-only systems. There exist several efforts to enable these codes for GPU’s, however, these efforts only consider specific architectures or vendors (e.g., implement only CUDA or HIP), limiting themselves to a small range of exascale computing systems. Frameworks such as Kokkos aim to provide a framework which is agnostic of the targeted architecture, enabling the development of performant and portable code. In the Ares code, we develop a performance portable tool to simulate supernovae based on the Parthenon Framework, which in turn uses Kokkos in the background. Here, the Parthenon Framework provides an interface to the underlying mesh-refinement routines, which form the backbone of our code. In addition, we incorporate the already existing Singularity-EOS toolkit to provide us with various equations of state, primarily the Helmholtz equation of state. We also include the JINA Reaclib as a basis for our nuclear network solver. Finally, we implement a gravity solver to complete the required physics. This setup will provide us with a minimal code base to simulate supernova in a similar style to the tried-and-tested Arepo code, but in a futureproof performance portable framework.

Lim, Hyun↗
DOE OSTI2021

A non‐intrusive domain‐decomposition model reduction method for linear steady‐state partial differential equations with random coefficients

Abstract Domain decomposition methods have been proved to be an effective strategy to reduce the dimension of parametric partial differential equations (PDEs). However, existing domain decomposition methods for parametric PDEs are usually intrusive, which means domain decomposition based solvers need to be implemented from scratch for each target parametric PDE. To address this issue, we develop a new non‐intrusive domain‐decomposition model reduction method for linear steady‐state PDEs with random‐field coefficients. As a variant of our previous work by Mu and Zhang, the new method only needs access to the final linear system, that is, the global stiffness matrix and the right hand side, of a deterministic PDE solver, in order to build a domain‐decomposition‐based reduced model without intrusive implementation from scratch. The key idea is to remove the interface condition between sub‐domains and rely on the correlation between columns of the linear system to couple the sub‐domains. The non‐intrusive feature enables the applicability of the proposed method to a broader class of uncertainty quantification problems, where many legacy codes/solvers can be fully reused by our method. Two numerical examples including diffusion equations with random diffusivity and convection‐dominated transport with random velocity, are provided to demonstrate the effectiveness and efficiency of our method.

Zhang, Guannan↗
DOE OSTI2024

Density dependence of the symmetry energy in the post–PREX-CREX era

The recently published CREX results suggest a rather peculiar picture for the density dependence of the symmetry energy. Whereas PREX favors a large neutron skin thickness in 208 Pb, thereby suggesting a stiff equation of state, CREX suggests instead a much softer equation of state. This discrepancy has caused a large spur in the theoretical community, since no model has been able to simultaneously reproduce within 1σ the PREX and CREX results. Motivated by a novel correlation between a CREX observable and a combination of bulk symmetry energy parameters, we calibrate three new covariant energy density functionals that reproduce binding energies and charge radii of spherical nuclei—and also accommodate the constraints imposed by PREX and CREX. Given that these models suggest a stiff equation of state at high densities, predictions for neutron star properties are also discussed.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Density dependence of the symmetry energy in the post–PREX-CREX era

The recently published CREX results suggest a rather peculiar picture for the density dependence of the symmetry energy. Whereas PREX favors a large neutron skin thickness in 208 Pb, thereby suggesting a stiff equation of state, CREX suggests instead a much softer equation of state. Here, this discrepancy has caused a large spur in the theoretical community, since no model has been able to simultaneously reproduce within 1σ the PREX and CREX results. Motivated by a novel correlation between a CREX observable and a combination of bulk symmetry energy parameters, we calibrate three new covariant energy density functionals that reproduce binding energies and charge radii of spherical nuclei—and also accommodate the constraints imposed by PREX and CREX. Given that these models suggest a stiff equation of state at high densities, predictions for neutron star properties are also discussed.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Hierarchical Network Partitioning for Solution of Potential-Driven, Steady-State Nonlinear Network Flow Equations

The solution of potential-driven steady-state flow in large networks is a task which manifests in various engineering applications, such as transport of natural gas or water through pipeline networks. The resultant system of nonlinear equations depends on the network topology, and in general, there is no numerical algorithm that offers guaranteed convergence to the solution (assuming a solution exists). Some methods offer guarantees in cases where the network topology satisfies certain assumptions, but these methods fail for larger networks. On the other hand, the Newton-Raphson algorithm offers a convergence guarantee if the starting point lies close to the (unknown) solution. It would be advantageous to compute the solution of the large nonlinear system through the solution of smaller nonlinear sub-systems wherein the solution algorithms (Newton-Raphson or otherwise) are more likely to succeed. Here, this letter proposes and describes such a procedure, a hierarchical network partitioning algorithm that enables the solution of large nonlinear systems corresponding to potential-driven steady-state network flow equations.

42 ENGINEERING↗
DOE OSTI2021

Validation and Comparison of HyRAM Physics Models

The Hydrogen Risk Assessment Models (HyRAM) software version 3 uses a real gas equation of state rather than the Abel-Noble equation of state that is used in 2.0 and previous versions. This change enables the use of HyRAM 3 for cryogenic hydrogen flows, whereas the Abel-Noble equation of state is not accurate at low temperatures. HyRAM 3.1 results were compared to experimental data from the literature in order to demonstrate the accuracy of the physics models. HyRAM 3.1 results were also compared to HyRAM 2.0 for high-pressure, non-cryogenic flows to highlight the differences in predictions between the two major versions of HyRAM. Validation data sets are from multiple groups and span the range of HyRAM physics models, including tank blowdown, unignited dispersion jet plume, ignited jet flame, and accumulation and overpressure inside an enclosure. Both versions 2.0 and 3.1 of HyRAM are accurate for predictions of blowdowns, diffusion jets, and diffusion flames of hydrogen at pressures up to 900 bar, and HyRAM 3.1 also shows good agreement with cryogenic hydrogen data. Overall, HyRAM 3.1 improves on the accuracy of the physical models relative to HyRAM 2.0. In most cases, this reduces the conservatism in risk calculations using HyRAM.

08 HYDROGEN↗
DOE OSTI2020

C HIMERA : A Massively Parallel Code for Core-collapse Supernova Simulations

Herein we provide a detailed description of the C HIMERA code, a code developed to model core collapse supernovae (CCSNe) in multiple spatial dimensions. The CCSN explosion mechanism remains the subject of intense research. Progress to date demonstrates that it involves a complex interplay of neutrino production, transport, and interaction in the stellar core, three-dimensional stellar core fluid dynamics and its associated instabilities, nuclear burning, and the fundamental physics of the neutrino–stellar core weak interactions and the equations of state of all stellar core constituents—particularly, the nuclear equation of state associated with core nucleons, both free and bound in nuclei. C HIMERA , by incorporating detailed neutrino transport, realistic neutrino–matter interactions, three-dimensional hydrodynamics, realistic nuclear, leptonic, and photonic equations of state, and a nuclear reaction network, along with other refinements, can be used to study the role of neutrino radiation, hydrodynamic instabilities, and a variety of input physics in the explosion mechanism itself. It can also be used to compute observables such as neutrino signatures, gravitational radiation, and the products of nucleosynthesis associated with CCSNe. The code contains modules for neutrino transport, multidimensional compressible hydrodynamics, nuclear reactions, a variety of neutrino interactions, equations of state, and modules to provide data for post-processing observables such as the products of nucleosynthesis, and gravitational radiation. C HIMERA is an evolving code, being updated periodically with improved input physics and numerical refinements. We detail here the current version of the code, from which future improvements will stem, which can in turn be described as needed in future publications.

79 ASTRONOMY AND ASTROPHYSICS↗