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DOE OSTI2024

ASGarD: Adaptive Sparse Grid Discretization

Many areas of science exhibit physical processes that are described by high dimensional partial differential equations (PDEs), e.g., the 4D, 5D and 6D models describing magnetized fusion plasmas, models describing quantum chemistry, or derivatives pricing. Such problems are affected by the so-called “curse of dimensionality” where the number of degrees of freedom (or unknowns) required to be solved for scales as N D where N is the number of grid points in any given dimension D. A simple, albeit naive, 6D example is demonstrated in the left panel of Figure 1. With N = 1000 grid points in each dimension, the memory required just to store the solution vector, not to mention forming the matrix required to advance such a system in time, would exceed an exabyte - and also the available memory on the largest of supercomputers available today. The right panel of Figure 1 demonstrates potential savings for a range of problem dimensionalities and grid resolution. While there are methods to simulate such high-dimensional systems, they are mostly based on Monte-Carlo methods, which rely on a statistical sampling such that the resulting solutions include noise. Since the noise in such methods can only be reduced at a rate proportional to $\sqrt{N_p}$ where N p is the number of Monte-Carlo samples, there is a need for continuum, or grid/mesh-based methods for high-dimensional problems, which both do not suffer from noise and bypass the curse of dimensionality. We present a simulation framework that provides such a method using adaptive sparse grids.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Real-Time Adaptive Machine Learning Platform

As part of the Cyclotron Road program, Dauntless.io, Inc. extended its existing ultrafast (0.00001 – 0.001 second) real-time, adaptive machine learning platform for modeling & control of complex, high-value physical systems. Objectives included ability to scale ubiquitously & remain differentiated on a 5+ year horizon in the highly competitive, AI / machine learning market — a rapidly growing market that (overall) is estimated to be worth $191 B by 2024 at a CAGR of 37%.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Agricultural Impacts on Nitrogen Cycling: Climate and Air Pollution (Final Technical Report)

We have successfully added a parameterization of ammonia emissions from synthetic fertilizer and manure from agriculture to Earth System Models. We have evaluated how emissions change in the future and the processes driving these changes. We have examined the impact of agricultural ammonia emissions on present-day air quality and have evaluated the impact of resolving the emissions with high temporal resolution. We have also examined the impact of how Earth System Models treat the cycling of emissions in soils. Our code, the Flows of Agricultural Nitrogen – version 2 – model (FANv2) has been run in both the CLM framework and the ELM framework. To my knowledge the code has not yet been fully implemented into ELM. Volatilization of ammonia (NH3) from fertilizers and livestock wastes forms a significant pathway of nitrogen losses in agricultural ecosystems and constitutes the largest source of atmospheric emissions of NH3. We have provided a major update to the process model FAN (Flow of Agricultural Nitrogen), which evaluates NH3 emissions interactively within an Earth system model; in this work, the Community Earth System Model (CESM) is used. The updated version (FANv2) includes a more detailed treatment of both physical and agricultural processes, which allows the model to differentiate between the volatilization losses from animal housings, manure storage, grazed pastures, and the application of manure and different types of mineral fertilizers. The modeled ammonia emissions are first evaluated at a local scale against experimental data for various types of fertilizers and manure, and they are subsequently run globally to evaluate NH3 emissions for 2010–2015 based on gridded datasets of fertilizer use and livestock populations. Comparison of regional emissions shows that FANv2 agrees with previous inventories for North America and Europe and is within the range of previous inventories for China. However, due to higher NH3 emissions in Africa, India, and Latin America, the global emissions simulated by FANv2(48 Tg N) are 30 %–40 % higher than in the existing inventories.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2023

Report for the ASCR Workshop on Basic Research Needs in Quantum Computing and Networking - 2023

Employing quantum mechanical resources in computing and networking opens the door to new computation and communication models and potential disruptive advantages over classical counterparts. However, quantifying and realizing such advantages face extensive scientific and engineering challenges. Investments by the Department of Energy (DOE) have driven progress toward addressing such challenges. Quantum algorithms have been recently developed, in some cases offering asymptotic exponential advantages in speed or accuracy, for fundamental scientific problems such as simulating physical systems, solving systems of linear equations, or solving differential equations. Empirical demonstrations on nascent quantum hardware suggest better performance than classical analogs on specialized computational tasks favorable to the quantum computing systems. However, demonstration of an end-to-end, substantial and rigorously quantifiable quantum performance advantage over classical analogs remains a grand challenge, especially for problems of practical value. The definition of requirements for quantum technologies to exhibit scalable, rigorous, and transformative performance advantages for practical applications also remains an outstanding open question, namely, what will be required to ultimately demonstrate practical quantum advantage?

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Report for the ASCR Workshop on Basic Research Needs in Quantum Computing and Networking - 2023

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

An improved mechanistic model for ammonia volatilization in Earth system models: Flow of Agricultural Nitrogen version 2 (FANv2)

Abstract. Volatilization of ammonia (NH 3 ) from fertilizers and livestock wastes forms a significant pathway of nitrogen losses in agricultural ecosystems and constitutes the largest source of atmospheric emissions of NH 3 . This paper describes a major update to the process model FAN (Flow of Agricultural Nitrogen), which evaluates NH 3 emissions interactively within an Earth system model; in this work, the Community Earth System Model (CESM) is used. The updated version (FANv2) includes a more detailed treatment of both physical and agricultural processes, which allows the model to differentiate between the volatilization losses from animal housings, manure storage, grazed pastures, and the application of manure and different types of mineral fertilizers. The modeled ammonia emissions are first evaluated at a local scale against experimental data for various types of fertilizers and manure, and they are subsequently run globally to evaluate NH3 emissions for 2010–2015 based on gridded datasets of fertilizer use and livestock populations. Comparison of regional emissions shows that FANv2 agrees with previous inventories for North America and Europe and is within the range of previous inventories for China. However, due to higher NH 3 emissions in Africa, India, and Latin America, the global emissions simulated by FANv2 (48 Tg N) are 30 %–40 % higher than in the existing inventories.

Vira, Julius↗

DOE OSTI2022

Differentiable, Learnable, Regionalized Process-Based Models With Multiphysical Outputs can Approach State-Of-The-Art Hydrologic Prediction Accuracy

Predictions of hydrologic variables across the entire water cycle have significant value for water resources management as well as downstream applications such as ecosystem and water quality modeling. Recently, purely data-driven deep learning models like long short-term memory (LSTM) showed seemingly insurmountable performance in modeling rainfall runoff and other geoscientific variables, yet they cannot predict untrained physical variables and remain challenging to interpret. Here, we show that differentiable, learnable, process-based models (called δ models here) can approach the performance level of LSTM for the intensively observed variable (streamflow) with regionalized parameterization. We use a simple hydrologic model HBV as the backbone and use embedded neural networks, which can only be trained in a differentiable programming framework, to parameterize, enhance, or replace the process-based model's modules. Without using an ensemble or post-processor, δ models can obtain a median Nash-Sutcliffe efficiency of 0.732 for 671 basins across the USA for the Daymet forcing data set, compared to 0.748 from a state-of-the-art LSTM model with the same setup. For another forcing data set, the difference is even smaller: 0.715 versus 0.722. Meanwhile, the resulting learnable process-based models can output a full set of untrained variables, for example, soil and groundwater storage, snowpack, evapotranspiration, and baseflow, and can later be constrained by their observations. Both simulated evapotranspiration and fraction of discharge from baseflow agreed decently with alternative estimates. The general framework can work with models with various process complexity and opens up the path for learning physics from big data.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2020

DOE/NNSA Nuclear Criticality Safety Program – Brief Overview [Slides]

This presentation discusses nuclear data measurements and evaluation work for the NCSP. The objective of the NCSP is to provide measured and evaluated thermal, resonance, unresolved resonance, and fast region cross section data to address the priority NCSP nuclear data needs. It also discusses its vision which is to address multiple Nuclear Data 5- and 10-year goals and attributes identified in the NCSP. The intended final product is for rigorous ENDF/B evaluations to be produced from cross section measurements and analyses. It also discusses NCSP integral experiments and differential experiments in addition to NCSP support of SCALE in the future.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2025

Description of di-hadron saturation signals within a universal nuclear parton distribution function approach

Di-hadron and di-jet correlation measurements in proton-nucleus (𝑝+𝐴) and electron-nucleus collisions are widely motivated as sensitive probes of novel, nonlinear quantum chromodynamices saturation dynamics in hadrons, which are particularly accessible in the dense nuclear environment at low values of Bjorken-𝑥 (𝑥 A ). Current measurements at the BNL Relativistic Heavy Ion Collider (RHIC) and the CERN Large Hadron Collider (LHC) observe a significant suppression in the per-trigger yield at forward rapidities compared to that in proton-proton collisions, nominally consistent with the “mono-jet” production expected in a saturation scenario. However, the width of the azimuthal correlation remains unmodified, in contradiction to the qualitative expectations from this physics picture. I investigate whether the construction of these observables leaves them sensitive to effects from simple nuclear shadowing as captured by, for example, universal nuclear parton distribution function (nPDF) analyses. I find that modern nPDF sets, informed by recent precision measurements sensitive to the shadowing of low-𝑥 A gluon densities in LHC and other data, can describe all or the majority of the di-hadron/jet suppression effects in 𝑝+𝐴 data at both RHIC and the LHC, while giving a natural explanation for why the azimuthal correlation width is unmodified. Notably, this is achieved via a (𝑥 A ,𝑄 2 )-differential suppression of overall cross sections only, without requiring additional physics dynamics which alter the interevent correlations.

Jets & heavy flavor physics↗

DOE OSTI2025

Self-adaptive weights based on balanced residual decay rate for physics-informed neural networks and deep operator networks

Physics-informed deep learning has emerged as a promising alternative for solving partial differential equations. However, for complex problems, training these networks can still be challenging, often resulting in unsatisfactory accuracy and efficiency. In this work, we demonstrate that the failure of plain physics-informed neural networks arises from the significant discrepancy in the convergence rate of residuals at different training points, where the slowest convergence rate dominates the overall solution convergence. Based on these observations, we propose a pointwise adaptive weighting method that balances the residual decay rate across different training points. The performance of our proposed adaptive weighting method is compared with current state-of-the-art adaptive weighting methods on benchmark problems for both physics-informed neural networks and physics-informed deep operator networks. In conclusion, through extensive numerical results we demonstrate that our proposed approach of balanced residual decay rates offers several advantages, including bounded weights, high prediction accuracy, fast convergence rate, low training uncertainty, low computational cost, and ease of hyperparameter tuning.

Balanced convergence rate↗

DOE OSTI2020

Differentiating and Quantifying Gas-Phase Conformational Isomers Using Coulomb Explosion Imaging

Conformational isomerism plays a crucial role in defining the physical and chemical properties and biological activity of molecules ranging from simple organic compounds to complex biopolymers. However, it is often a significant challenge to differentiate and separate these isomers experimentally as they can easily interconvert due to their low rotational energy barrier. Here, we use the momentum correlation of fragment ions produced after inner-shell photoionization to distinguish conformational isomers of 1,2-dibromoethane (C 2 H 4 Br 2 ). We demonstrate that the three-body breakup channel, C 2 H 4 + + Br + + Br + , contains signatures of both sequential and concerted breakup, which are decoupled to distinguish the geometries of two conformational isomers and to quantify their relative abundance. The sensitivity of our method to quantify these yields is established by measuring the relative abundance change with sample temperature, which agrees well with calculations. Finally, our study paves the way for using Coulomb explosion imaging to track subtle molecular structural changes.

Photoionization↗

DOE OSTI2021

Machine learning and algebraic approaches towards complete matter spectra in 4d F-theory

Motivated by engineering vector-like (Higgs) pairs in the spectrum of 4d F-theory compactifications, we combine machine learning and algebraic geometry techniques to analyze line bundle cohomologies on families of holomorphic curves. To quantify jumps of these cohomologies, we first generate 1.8 million pairs of line bundles and curves embedded in dP 3 , for which we compute the cohomologies. A white-box machine learning approach trained on this data provides intuition for jumps due to curve splittings, which we use to construct additional vector-like Higgs-pairs in an F-Theory toy model. We also find that, in order to explain quantitatively the full dataset, further tools from algebraic geometry, in particular Brill-Noether theory, are required. Using these ingredients, we introduce a diagrammatic way to express cohomology jumps across the parameter space of each family of matter curves, which reflects a stratification of the F-theory complex structure moduli space in terms of the vector-like spectrum. Furthermore, these insights provide an algorithmically efficient way to estimate the possible cohomology dimensions across the entire parameter space.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Generative Ensemble Regression: Learning Particle Dynamics from Observations of Ensembles with Physics-informed Deep Generative Models

Here, we propose a new method for inferring the governing stochastic ordinary differential equations (SODEs) by observing particle ensembles at discrete and sparse time instants, i.e., multiple “snapshots.” Particle coordinates at a single time instant, possibly noisy or truncated, are recorded in each snapshot but are unpaired across the snapshots. By training a physics-informed generative model that generates “fake” sample paths, we aim to fit the observed particle ensemble distributions with a curve in the probability measure space, which is induced from the inferred particle dynamics. We employ different metrics to quantify the differences between distributions, e.g., the sliced Wasserstein distances and the adversarial losses in generative adversarial networks. We refer to this method as generative “ensemble-regression” (GER), in analogy to the classic “point-regression,” where we infer the dynamics by performing regression in the Euclidean space. We illustrate the GER by learning the drift and diffusion terms of particle ensembles governed by SODEs with Brownian motions and Lévy processes up to 100 dimensions. We also discuss how to treat cases with noisy or truncated observations. Apart from systems consisting of independent particles, we also tackle nonlocal interacting particle systems with unknown interaction potential parameters by constructing a physics-informed loss function. Finally, we investigate scenarios of paired observations and discuss how to reduce the dimensionality in such cases by proving a convergence theorem that provides theoretical support.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Improvements of Nuclear Data Evaluations for Lead Isotopes in Support of Next Generation Lead-Cooled Fast Systems

The neutron evaluation of the isotopes that comprise natural lead were undertaken as a part of DOE-NEUP Project #19-16739. The goal of the project was to update the neutron cross sections to account for new differential measurements and incorporate the most up-to-date physics. Shortcomings in the lead cross sections was made known by several independent reports. The work performed here repeated the simulation of all the “benchmark” validation systems and concluded that the major issue is the scattering cross sections in the major lead isotopes above 100 keV. Re-evaluation of 206,207,208 Pb included both the resolved resonance region and fast region evaluations of the cross sections. Combined these regions cover energies from thermal to 20 MeV. The most drastic improvement is the resolved resonance region evaluation of 208 Pb which is now extended from 1.0 to 1.5 MeV. Parameterization of these resonances in the R-matrix provides a superior reconstruction of not only the experimental cross section but also the scattering distributions via the Blatt-Biedenharn formalism. Fast region evaluations of the three major isotopes were done to include new inelastic experimental data from the neutron Time-of-Flight facility at CERN. The culmination of all the changes to the cross section is a drastic improvement in the scattering kernel as shown in Rensselaer Polytechnic Institute (RPI) Quasi-Differential scattering measurements and improved prediction of keff for fast integral experiments. Alongside the new cross sections, new nuclear data covariance (uncertainties) have been computed and are included in the evaluation. Little is changed in the magnitude of the uncertainties but the correlations within the covariance display non-trivial changes. The new evaluations of 206,207,208 Pb have been submitted to the National Nuclear Data Center to be included in the ENDF/B-VIII.1 library. While the cross sections have been updated extensively, knowledge and modeling of the cross sections between 1.0 and 3.0 MeV for the isotopes remain a challenge. Most notably is the double differential elastic cross section for 208 Pb and 206 Pb. New quasi-differential measurements for pure samples of these two nuclei would go a long way in reducing compensating errors in the evaluations. Qualitatively, the project has produced a prosperous collaboration between the nuclear data group at RPI with staff scientists at Brookhaven National Laboratory, Naval Nuclear Laboratory, Oak Ridge National Laboratory, Los Alamos National Laboratory, Lawrence Livermore National Laboratory, and Sandia National Laboratories. Quantitatively this is reflected in seven conference presentations, at least one journal submission, and one doctoral thesis.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2021

Geometry optimization speedup through a geodesic approach to internal coordinates

We present a new geodesic-based method for geometry optimization in a basis set of redundant internal coordinates. Overall, our method updates the molecular geometry by following the geodesic generated by a displacement vector on the internal coordinate manifold, which dramatically reduces the number of steps required to converge to a minimum. Our method can be implemented in any existing optimization code, requiring only implementation of derivatives of the Wilson B-matrix and the ability to numerically solve an ordinary differential equation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Learning effective stochastic differential equations from microscopic simulations: Linking stochastic numerics to deep learning

We identify effective stochastic differential equations (SDEs) for coarse observables of fine-grained particle- or agent-based simulations; these SDEs then provide useful coarse surrogate models of the fine scale dynamics. We approximate the drift and diffusivity functions in these effective SDEs through neural networks, which can be thought of as effective stochastic ResNets. The loss function is inspired by, and embodies, the structure of established stochastic numerical integrators (here, Euler–Maruyama and Milstein); our approximations can thus benefit from backward error analysis of these underlying numerical schemes. They also lend themselves naturally to “physics-informed” gray-box identification when approximate coarse models, such as mean field equations, are available. Existing numerical integration schemes for Langevin-type equations and for stochastic partial differential equations can also be used for training; we demonstrate this on a stochastically forced oscillator and the stochastic wave equation. Our approach does not require long trajectories, works on scattered snapshot data, and is designed to naturally handle different time steps per snapshot. We consider both the case where the coarse collective observables are known in advance, as well as the case where they must be found in a data-driven manner.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Stability-preserving Lossy Compression for Large-scale Partial Differential Equations

Checkpoint/Restart (C/R) strategies are vital for fault tolerance in PDE-based scientific simulations, yet traditional checkpointing incurs significant I/O overhead. Lossy compression offers a scalable solution by reducing checkpoint data size, but conventional methods often lack control over physical invariants (e.g., energy), leading to instability such as oscillations or divergence in Partial Differential Equations (PDE) systems. This paper introduces a stability-preserving compression approach tailored for PDE simulations by explicitly controlling kinetic and potential energy perturbations to ensure stable restarts. Extensive experiments conducted across diverse PDE configurations demonstrate that our method maintains numerical stability with minimal error magnification—even across multiple checkpoint-restart cycles—outperforming state-of-the-art lossy compressors. Parallel evaluations on the Frontier supercomputer show up to 8.4× improvement in checkpoint write performance and 6.3× in read performance, while maintaining relative L2 errors ∼ 2e-6 throughout continued simulation. These results provide practical guidance for balancing compression accuracy, stability, and computational efficiency in large-scale PDE applications.

Gong, Qian [ORNL] (ORCID:0000000235704142)↗

DOE OSTI2024

Cosmology meets cohomology

The cosmological polytope and bootstrap programs have revealed interesting connections between positive geometries, modern on-shell methods and bootstrap principles studied in the amplitudes community with the wavefunction of the Universe in toy models of FRW cosmologies. To compute these FRW correlators, one often faces integrals that are too difficult to evaluate by direct integration. Borrowing from the Feynman integral community, the method of (canonical) differential equations provides an efficient alternative for evaluating these integrals. Moreover, we further develop our geometric understanding of these integrals by describing the associated relative twisted cohomology. Leveraging recent progress in our understanding of relative twisted cohomology in the Feynman integral community, we give an algorithm to predict the basis size and simplify the computation of the differential equations satisfied by FRW correlators.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗