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DOE OSTI2022

On the differential representation and color-kinematics duality of AdS boundary correlators

The AdS boundary correlators and their dual correlation functions of boundary operators have been the main dynamic observables of the holographic duality relating a bulk AdS theory and a boundary conformal field theory. We show that tree-level AdS boundary correlators for generic states can be expressed as nonlocal differential operators of a certain structure acting on contact Witten diagrams. We further write the boundary correlators in a form that is very similar to flat space amplitudes, with Mandelstam variables replaced by certain combinations of single-state conformal generators, prove that all tree-level AdS boundary correlators have a differential representation, and detail the conversion of such differential expressions to position space. We illustrate the construction through the computation of the boundary correlators of scalars coupled to gluons and gravitons; when converted to position space, they reproduce known results. Color-kinematics duality and BCJ relations can be defined in analogy with their flat space counterparts, and are respected by the scalar correlators with a gluon exchange. We also discuss potential approaches to the double copy and find that its direct generalization may require nontrivial extensions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2026

Visualization of Two-phase Flow Maldistribution in Brazed Plate Heat Exchangers

Brazed plate heat exchangers (BPHEs) are widely used in refrigeration and HVAC applications, but are susceptible to two-phase flow maldistribution especially when operated as evaporators. Existing visualization approaches are either limited to idealized conditions or suffer from poor optical transparency. This paper presents a novel visualization method in which one edge of a BPHE, parallel to the refrigerant inlet or outlet port, is removed by wire electrical discharge machining and replaced with a flat, transparent plate. The planar geometry allows the use of optically and infrared (IR)-transparent materials, enabling both high-speed videography and IR thermography of the two-phase flow at the channel entrances and exits. Preliminary tests with R134a and R1234ze(Z) at saturation temperatures between 5 °C and 15 °C demonstrate that distinct two-phase flow patterns in the inlet header can be clearly identified and differentiated under realistic operating conditions. Potentials of optical flow analysis of high-speed videos are shown to provide objective, quantitative indicators for flow regime characterization and comparison. IR imaging of the outlet port reveals non-uniform temperature distributions at the channel exits, providing independent evidence of maldistribution across the channel stack. Limitations of IR temperature accuracy due to the spectral properties of the sapphire window are discussed, and directions for improvement are identified.

Hausherr, Carsten [Technical University of Berlin ↗

DOE OSTI2023

Model-parallel Fourier neural operators as learned surrogates for large-scale parametric PDEs

Fourier neural operators (FNOs) are a recently introduced neural network architecture for learning solution operators of partial differential equations (PDEs), which have been shown to perform significantly better than comparable deep learning approaches. Once trained, FNOs can achieve speed-ups of multiple orders of magnitude over conventional numerical PDE solvers. However, due to the high dimensionality of their input data and network weights, FNOs have so far only been applied to two-dimensional or small three-dimensional problems. To remove this limited problem-size barrier, we propose a model-parallel version of FNOs based on domain-decomposition of both the input data and network weights. Here, we demonstrate that our model-parallel FNO is able to predict time-varying PDE solutions of over 2.6 billion variables on Perlmutter using up to 512 A100 GPUs and show an example of training a distributed FNO on the Azure cloud for simulating multiphase CO 2 dynamics in the Earth’s subsurface.

58 GEOSCIENCES↗

DOE OSTI2021

Characterization of high thermal conductivity fuel surrogates before and after ion irradiation

High thermal conductivity nuclear fuels offer important potential advantages over traditional oxide-based fuels such as higher burnup, reduction in fission gas release, and better overall safety of the system. One proposed approach to high thermal conductivity fuels utilizes high thermal conductivity nonfissile additives with UO 2 fuel to lower the fuel operating temperature and thereby take advantage of the highly favorable radiation resistance of UO 2 at lower operating temperatures. However, differential swelling in the matrix and high conductivity additive phases during high dose irradiation could lead to internal cracking and poor performance. In the current study, ceria (CeO 2 ) and zirconia (ZrO 2 ) surrogate matrices were used to model UO2 behavior. Additives of 10 vol. % Al 2 O 3 or SiC in the form of short fibers or platelets were used for the high conductivity second phase. The nuclear fuel surrogates were sintered to achieve densities greater than 93% of the ideal values. Scanning electron microscopy (SEM) imaging and X-ray diffraction confirmed the uniform distribution of the second phase and that no intermetallic second phase was formed during sintering. The thermal conductivity of the sintered samples was measured from 50 °C to 900 °C and confirmed the desirable increase compared to pure CeO 2 /ZrO 2 pellets. Samples were irradiated with 20 MeV Ni 6+ ions at midrange doses ranging from 1 to 15 displacements per atom (dpa) and temperatures from 300 °C to 700 °C. Post irradiation characterization revealed a good stability of the samples at low to medium doses with matrix lattice parameter swelling of < 0.14 % but showed a significant microstructural deterioration and decrease of the mechanical properties at 15 dpa.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2024

Simple and General Unitarity Conserving Numerical Real-Time Propagators of the Time-Dependent Schrödinger Equation Based on Magnus Expansion

Magnus expansion (ME) provides a general way to expand the real-time propagator of a time-dependent Hamiltonian within the exponential such that the unitarity is satisfied at any order. Here, we use this property and explicit integration of Lagrange interpolation formulas for the time-dependent Hamiltonian within each time interval and derive approximations that preserve unitarity for the differential time evolution operators of general time-dependent Hamiltonians. The resulting second-order approximation is the same as using the average of Hamiltonians for two end points of time. We identify three fourth-order approximations involving commutators of Hamiltonians at different times and also derive a sixth-order expression. A test of these approximations along with other available expressions for a two-state time-dependent Hamiltonian with sinusoidal time dependences provides information on the relative performance of these approximations and suggests that the derived expressions can serve as useful numerical tools for time evolution in time-resolved spectroscopy, quantum control, quantum sensing, real-time ab initio quantum dynamics, and open system quantum dynamics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Multi-resolution partial differential equations preserved learning framework for spatiotemporal dynamics

Traditional data-driven deep learning models often struggle with high training costs, error accumulation, and poor generalizability in complex physical processes. Physics-informed deep learning (PiDL) addresses these challenges by incorporating physical principles into the model. Most PiDL approaches regularize training by embedding governing equations into the loss function, yet this depends heavily on extensive hyperparameter tuning to weigh each loss term. To this end, we propose to leverage physics prior knowledge by “baking” the discretized governing equations into the neural network architecture via the connection between the partial differential equations (PDE) operators and network structures, resulting in a PDE-preserved neural network (PPNN). This method, embedding discretized PDEs through convolutional residual networks in a multi-resolution setting, largely improves the generalizability and long-term prediction accuracy, outperforming conventional black-box models. The effectiveness and merit of the proposed methods have been demonstrated across various spatiotemporal dynamical systems governed by spatiotemporal PDEs, including reaction-diffusion, Burgers’, and Navier-Stokes equations.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

A framework for data-driven solution and parameter estimation of PDEs using conditional generative adversarial networks

We employ and adapt the image-to-image translation concept based on conditional generative adversarial networks (cGAN) for learning a forward and an inverse solution operator of partial differential equations (PDEs). We focus on steady-state solutions of coupled hydromechanical processes in heterogeneous porous media and present the parameterization of the spatially heterogeneous coefficients, which is exceedingly difficult using standard reduced-order modeling techniques. We show that our framework provides a speed-up of at least 2,000 times compared to a finite-element solver and achieves a relative root-mean-square error (r.m.s.e.) of less than 2% for forward modeling. For inverse modeling, the framework estimates the heterogeneous coefficients, given an input of pressure and/or displacement fields, with a relative r.m.s.e. of less than 7%, even for cases where the input data are incomplete and contaminated by noise. The framework also provides a speed-up of 120,000 times compared to a Gaussian prior-based inverse modeling approach while also delivering more accurate results.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Tailoring the Mass Transport to Achieve High-Performing Unitized Regenerative Fuel Cells Considering Practical Operating Conditions

Unitized regenerative fuel cells (URFCs) convert electrical energy to chemical bonds in hydrogen during charge and convert chemical energy to output electricity during discharge, offering a promising solution to long-term energy storage. Recent studies indicate that the round-trip-voltaic efficiency (RTE) and longevity of URFCs are limited by complex mass transport during charging and discharging. Here, we first investigate how different porous transport layer (PTL) structures can impact URFC performance. The preferred PTL has a low tortuosity and high porosity, leading to a high RTE above 50% at 1 A cm −2 using Nafion 212. Moreover, thicker membranes, such as Solvay 90, are required to ensure mechanical stability and minimize H 2 crossover when operating under high differential pressure. Although this assembly inevitably leads to a higher ohmic loss, the RTE can be improved by further tailoring the electrode structures to facilitate mass transport by using supported catalyst, which still achieves over 50% RTEs at 1 A cm −2 . Optimization of porous structure to mitigate mass transport resistance with appropriate materials down selection considering practical application requirements can be a key design principle for achieving high-performing URFCs.

25 ENERGY STORAGE↗

DOE OSTI2025

Graph-based Reversible Evaluation and Tangents Library

GRETL is a C++ library for evaluation, re-evaluation and algorithmic differentiation of functional operations on an arbitrary computational graph with limited memory usage. Similar to popular machine learning frameworks in Python, like PyTorch and JAX, it tracks and stores both operations and output data as functions are evaluated. Once this composition of functions is built up, the entire chain of operations can be back propagated to compute sensitivities of the final result with respect to any number of inputs. In contrast to most machine learning applications, memory usage becomes the bottleneck for back propagation in many physics applications, especially for time-dependent PDEs. Dynamic check pointing becomes essential. An important distinguishing feature of GRETL is its ability to limit the maximum memory usage by automatically dynamic checkpointing the data output for each graph operation (see Wang, Moin, Iaccarino, 2009). During backpropagation, parts of the graph that are no longer in memory are automatically re-evaluated from upstream checkpointed states as needed for derivative sensitivity calculations (or more precisely, for vector-Jacobian products). GRETL is particularly beneficial for applications, such as coupled multi-physics, where deriving adjoint-based sensitivities and managing checkpoint memory across modules becomes onerous. Cases which can be readily handled by the GRETL library include: different time-integration algorithms per physics (e.g., coupled predictor-corrector algorithms, IMEX, etc.), sub-cycling, asynchronous integrators, state dependent timestep sizes, iterative solvers and coupling algorithms, controller algorithms, and more.

Tupek, MichaelR [Lawrence Livermore National Labor↗

DOE OSTI2020

SRS Composite Analysis Monitoring Plan (FY2019 Model Validation)

Using a projected end-state date of 2065 (SRNS 2015b), the Savannah River Site (SRS) Composite Analysis (CA) modeling for each facility and waste site began on the inventory year assigned to it so that source depletion and radionuclide transport out of the system could be appropriately captured. Some SRS waste sites that have already achieved their end states (i.e. end-state inventories and end-state configuration) are currently contributing to the potential off-site public dose through source release, groundwater transport, discharge to on-site surface streams, and stream transport to the CA point of assessments (POAs). The inventory year assigned to these waste sites is 2002 or before. This means that SRS CA results from 2002 and beyond are a reasonable representation for these waste sites that have already achieved their end states and are currently contributing to the potential off-site public dose. The SRS Annual Environmental Report (AER) monitoring can differentiate and separate liquid pathway data allowing the data representing only waste sites at their end state to be produced. Because the SRS CA has projected reasonable end-state impacts from 2002 and beyond, and the AER monitoring can differentiate and separate operating and end-state contributions to annual liquid pathway release, an opportunity exists to use the AER monitoring data to validate the SRS CA model. The CA model validation program uses a graded and systematic approach for taking corrective action, starting with an SRS established administrative dose limit of 15 mrem/yr, below which no action is required. Based on the location of the 2010 SRS CA POAs, the only potential exposure pathway for the public is through surface water. The completion of the FY2019 CA model validation indicates that the SRS CA projected dose, while generally conservative, provides a reasonable representation of the maximum annual doses. These doses are well below the administrative limit; therefore, no additional action is required.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2021

Tritiated Sulfur Hexafluoride Disposition Strategies

Tritium (T 2 ) is a radioactive isotope of hydrogen that is produced in nuclear fission reactions and is often used in nuclear fusion reactions and accelerator-based applications for medical isotope production. As a hydrogen isotope, tritium can readily bind to hydroxyl radicals (OH), forming tritiated water (HTO or T 2 0), and to carbon atoms. Tritium decays to helium-3 ( 3 He) via beta-decay with max decay energy of 18.6 keV. While it is not an external radiation hazard, it can be an internal radiation hazard if tritium is inhaled, ingested, or absorbed through the skin. In applications where tritium is handled, tritium confinement is performed using different barriers to minimize releases to the environment. For gaseous (elemental), liquid (oxide), and metal (hydride) tritium, process piping and components provide the primary confinement function. Secondary tritium confinement is typically provided by inert (i.e. non-flammable gases such as nitrogen, argon, or helium) gloveboxes which are connected to a tritium stripper system. Primary tritium confinement barriers typically produce low volumes of high tritium concentrations of tritiated methane from carbon in steels or organic materials along with tritiated water/tritium oxide (e.g. HTO) and tritiated ammonia from reactions with oxygen and nitrogen. Tritium escaping primary confinement into secondary confinement atmospheres (e.g. gloveboxes) produce higher volumes of lower activity contamination than found in process piping. Tritium contamination also occurs by leaks or tritium permeation/diffusion through confinement materials. Tritium from inside primary confinement barriers will diffuse or leak out of the primary confinement barrier and usually into the air, if the system is inside an air hood or ventilated hot cell, or into the secondary confinement (e.g. glovebox) atmosphere which is either exhausted or stripped based on the function of the secondary confinement (glovebox) system. Accelerator based processes for medical isotope production represent an atypical tritium contamination challenge. In medical isotope production, deuterium supply gas is ionized and accelerated to a tritium gas target to produce neutrons that are then used to produce the medical isotopes through additional nuclear fission reactions. To create large voltage differentials for accelerator operations, an electrical insulation medium is needed to prevent or rapidly quench electric discharges. A common electrical insulation medium utilized in accelerator applications is sulfur hexafluoride (SF 6 ) gas. SF 6 has a high dielectric strength and allows for the construction of smaller accelerator systems compared to other electrical insulation mediums such as air or dry nitrogen. Due to tritium permeation/diffusion through accelerator process and confinement materials, there is the possibility that tritium can contaminate the electrical insulation medium of the accelerator. Tritium contaminated SF 6 creates a material without any obvious processes for managing the contamination, reuse, or disposal of the used SF 6 . This document will discuss possible management strategies for tritium contaminated SF 6 for accelerator-based processes for Molybdenum-99 (Mo-99) production.

07 ISOTOPE AND RADIATION SOURCES↗

DOE OSTI2022

Model Validation for the FY2021 SRS Composite Analysis Monitoring Plan

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2024

Open Call LDRD: Physically Informed Autoencoders for Galactic Redshift Regression

Physical constraints have been suggested to make neural network models more generalizable, act scientifically plausible, and be more data-efficient over unconstrained baselines. In this report, we present preliminary work on evaluating the effects of adding soft physical constraints to computer vision neural networks trained to estimate the conditional density of redshift on input galaxy images for the Sloan Digital Sky Survey. We introduce physically motivated soft constraint terms that are not implemented with differential or integral operators. We frame this work as a simple ablation study where the effect of including soft physical constraints is compared to an unconstrained baseline. We compare networks using standard point estimate metrics for photometric redshift estimation, as well as metrics to evaluate how faithful our conditional density estimate represents the probability over the ensemble of our test dataset. We find no evidence that the implemented soft physical constraints are more effective regularizers than augmentation.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Cloud Condensation Nuclei and Printed Optical Particle Spectrometer Measurements at Mt. Soledad during EPCAPE 2023-24

These measurements are provided by a differential mobility analyzer operated as a scanning mobility particle sizer, a printed particle optical spectrometer (POPS), and a continuous flow diffusion cloud condensation nuclei (CCN) counter. The instruments sample from either a counterflow virtual impactor inlet or an isokinetic inlet. The measurements provide the mobility aerosol size distribution (30-360 nm), optical size distribution (150 - 6000 nm), size-resolved CCN distribution (30-360 nm) at 0.2, 0.4, 0.6, 0.8, and 1.0% supersaturation. CCN measurements are performed in denuded and undenuded configuration, where denuded refers to the removal of low molecular weight organic vapors. A detailed NetCDF header is included with the datafiles. Users of these measurements are encouraged to consult with the authors about appropriate interpretation before submitting for publication, offering coauthorship where appropriate.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2025

Aerosol Microphysics and Chemical Measurements at Mt. Soledad and Scripps Pier during the Eastern Pacific Cloud Aerosol Precipitation Experiment (EPCAPE) from February 2023 to February 2024 UCSD Library Collection

This dataset includes guest instrument measurements and other PI products for aerosol microphysics and chemical measurements collected at Mt. Soledad and Scripps Pier during the Eastern Pacific Cloud Aerosol Precipitation Experiment (EPCAPE) from February 2023 to February 2024. The measurements include the following instruments at Mt. Soledad: High-Resolution Time-of-Flight Aerosol Mass Spectrometer (HR-ToF-AMS, Aerodyne), Scanning Electrical Mobility Spectrometer (SEMS, Brechtel Manufacturing Inc.), Aerodynamic Particle Sizer (APS, Droplet Measurements Technologies), Single Particle Soot Photometer (SP2, Drople Measurements Technologies), Meteorological Station (WXT520, Vaisala), Ozone (Teco), and trace gas proxies (Teledyne). In addition, the analyses of particle filters collected at Mt. Soledad for three dry-diameter size cuts (<1 micron, <0.5 micron, <0.18 micron) and at Scripps Pier for one dry-diameter size cut (<1 micron) by Fourier Transform Infrared (FTIR) and X-ray Fluorescence (XRF) are reported. A differential mobility analyzer operated as a scanning mobility particle sizer (SMPS, TSI Inc.), a printed particle optical spectrometer (POPS, Grimm), and a continuous flow diffusion cloud condensation nuclei (CCN, DMT) counter provide the mobility aerosol size distribution (30-360 nm), optical size distribution (150 - 6000 nm), size-resolved CCN distribution (30-360 nm) at 0.2, 0.4, 0.6, 0.8, and 1.0% supersaturation. Measurements are reported for both sampling from an isokinetic aerosol inlet and from a Counterflow Virtual Impactor (CVI, Brechtel Manufacturing Inc.). The data are available at the following link: https://library.ucsd.edu/dc/collection/bb0898306q

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2023

Residual-based error correction for neural operator accelerated infinite-dimensional Bayesian inverse problems

We explore using neural operators, or neural network representations of nonlinear maps between function spaces, to accelerate infinite-dimensional Bayesian inverse problems (BIPs) with models governed by nonlinear parametric partial differential equations (PDEs). Neural operators have gained significant attention in recent years for their ability to approximate the parameter-to-solution maps defined by PDEs using as training data solutions of PDEs at a limited number of parameter samples. The computational cost of BIPs can be drastically reduced if the large number of PDE solves required for posterior characterization are replaced with evaluations of trained neural operators. However, reducing error in the resulting BIP solutions via reducing the approximation error of the neural operators in training can be challenging and unreliable. We provide an a priori error bound result that implies certain BIPs can be ill-conditioned to the approximation error of neural operators, thus leading to inaccessible accuracy requirements in training. To reliably deploy neural operators in BIPs, we consider a strategy for enhancing the performance of neural operators: correcting the prediction of a trained neural operator by solving a linear variational problem based on the PDE residual. We show that a trained neural operator with error correction can achieve a quadratic reduction of its approximation error, all while retaining substantial computational speedups of posterior sampling when models are governed by highly nonlinear PDEs. The strategy is applied to two numerical examples of BIPs based on a nonlinear reaction–diffusion problem and deformation of hyperelastic materials. We demonstrate that posterior representations of the two BIPs produced using trained neural operators are greatly and consistently enhanced by error correction.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Uncertainty quantification in scientific machine learning: Methods, metrics, and comparisons

Neural networks (NNs) are currently changing the computational paradigm on how to combine data with mathematical laws in physics and engineering in a profound way, tackling challenging inverse and ill-posed problems not solvable with traditional methods. However, quantifying errors and uncertainties in NN-based inference is more complicated than in traditional methods. This is because in addition to aleatoric uncertainty associated with noisy data, there is also uncertainty due to limited data, but also due to NN hyperparameters, overparametrization, optimization and sampling errors as well as model misspecification. Although there are some recent works on uncertainty quantification (UQ) in NNs, there is no systematic investigation of suitable methods towards quantifying the total uncertainty effectively and efficiently even for function approximation, and there is even less work on solving partial differential equations and learning operator mappings between infinite-dimensional function spaces using NNs. In this work, we present a comprehensive framework that includes uncertainty modeling, new and existing solution methods, as well as evaluation metrics and post-hoc improvement approaches. Further, to demonstrate the applicability and reliability of our framework, we present an extensive comparative study in which various methods are tested on prototype problems, including problems with mixed input-output data, and stochastic problems in high dimensions. In the Appendix, we include a comprehensive description of all the UQ methods employed. Further, to help facilitate the deployment of UQ in Scientific Machine Learning research and practice, we present and develop in [1] an open-source Python library (github.com/Crunch-UQ4MI/neuraluq), termed NeuralUQ, that is accompanied by an educational tutorial and additional computational experiments.

11 physics-informed neural networks↗

DOE OSTI2022

Automatic Differentiation of C++ Codes on Emerging Manycore Architectures with Sacado

Automatic differentiation (AD) is a well-known technique for evaluating analytic derivatives of calculations implemented on a computer, with numerous software tools available for incorporating AD technology into complex applications. However, a growing challenge for AD is the efficient differentiation of parallel computations implemented on emerging manycore computing architectures such as multicore CPUs, GPUs, and accelerators as these devices become more pervasive. In this work, we explore forward mode, operator overloading-based differentiation of C++ codes on these architectures using the widely available Sacado AD software package. In particular, we leverage Kokkos, a C++ tool providing APIs for implementing parallel computations that is portable to a wide variety of emerging architectures. Here we describe the challenges that arise when differentiating code for these architectures using Kokkos, and two approaches for overcoming them that ensure optimal memory access patterns as well as expose additional dimensions of fine-grained parallelism in the derivative calculation. We describe the results of several computational experiments that demonstrate the performance of the approach on a few contemporary CPU and GPU architectures. We then conclude with applications of these techniques to the simulation of discretized systems of partial differential equations.

97 MATHEMATICS AND COMPUTING↗