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Kolmogorov-Arnold wavefunctions
Here, this work investigates Kolmogorov-Arnold network-based (KAN) wave-function Ansätz as viable representations for quantum Monte Carlo simulations. Through systematic analysis of one-dimensional model systems, we evaluate their computational efficiency and representational power against established methods. Our numerical experiments suggest some efficient training methods and we explore how the computational cost scales with desired precision, particle number, and system parameters. Roughly speaking, KANs seem to be 10 times cheaper computationally than other neural-network-based Ansätz . We also introduce a novel approach for handling strong short-range potentials—a persistent challenge for many numerical techniques—which generalizes efficiently to higher-dimensional, physically relevant systems with short-ranged strong potentials common in atomic and nuclear physics.
Machine learning models for PDE constrained optimization
Partial differential equation (PDE)-constrained optimization problems arise in a variety of scientific and engineering applications, such as topology optimization, electrodynamics, fluid dynamics, and structural dynamics. However, these problems are often challenging and computationally expensive to solve, due to the need to solve the PDEs within the optimization loop. One approach to reducing the computational cost of these methods while providing convergence guarantees is through inexact trust region methods; this method uses lower fidelity solutions of the PDE at early stages of the optimization and adjusts the required accuracy of inexact PDE solvers as the optimization progresses. In this work, we explore the use of machine learning based surrogate models with these inexact trust region methods. We first demonstrate the potential of this approach by using Gaussian processes as the surrogate model and test this on a simple PDE-constrained optimization problem. We then document explorations into improving the computational costs of evolutional deep neural network / neural Galerkin methods, with the eventual goal of using these methods with the inexact trust region algorithms. We are able to speed up these approaches, albeit at the cost of lower accuracy.
Methods and Tools To Assess Robustness of Nuclear Plant Outages
Refueling outages are one of the most challenging phases in a nuclear power plant (NPP) operating cycle. Refueling outages are extremely costly for an NPP due to the large amount of required resources and because of lost revenue due to plant being off the grid. Outage durations have steadily decreased across the industry over that last few decades primarily due to improved planning and coordination, but there are still many plants that struggle to meet the performance metrics accomplished by other utilities. Schedule resilience is one of the issues. NPP outages require scheduling thousands of activities within 30 days on average. Despite detailed planning, once the outage starts, numerous emergent issues typically appear along with schedule delays requiring continuous replanning and adjustment. When schedule disruption occurs during an outage, plant staff make urgent efforts to recover but are often not able to maintain the planned outage duration. These outage delays can cost a utility several million dollars per day. Tools that could help outage schedulers create a more resilient schedule and allow them to optimally reschedule emergent work could significantly reduce outage delays. One key aspect of creating a resilient schedule is to have accurate estimates for activity duration. Another important outage scheduling capability is the ability to schedule emergent work with minimal disruption. This paper focuses on developing tools and methods to support NPPs with outage schedule optimization and it describes the initial development of tools to support outage management that leverage computational and machine learning methods.
MCNP ® Code Version 6.3.1 Theory & User Manual
This document acts as a repository of knowledge for the Monte Carlo N-Particle (MCNP) transport computer code. It is maintained alongside the source code and attempts to introduce new users and re-familiarize experienced users with the theory and practices of using the MCNP code for the wide range of particle transport analyses that it is appropriate for. The latest version of the MCNP code, version 6.3.1, provides the Monte Carlo particle transport community with the latest feature developments and bug fixes in the MCNP code. The MCNP code version 6.0 and later is also known as the MCNP6 code.
Constrained nuclear–electronic orbital method for periodic density functional theory: Application to H 2 chemisorption on Si(001) surfaces
The nuclear–electronic orbital (NEO) method provides a powerful computational framework for incorporating nuclear quantum effects (NQE) in electronic structure calculations beyond the Born–Oppenheimer approximation. By incorporating additional constraints to the position operator on quantum particles like protons, the NEO method enables calculation of effective potential that accounts for NQE. Here, in this work, we present a new constrained NEO (cNEO) formulation for density functional theory (cNEO-DFT) calculations in the context of extended periodic systems. Using the nudged elastic band method, we discuss an application of the cNEO-DFT approach to studying the adsorption of a hydrogen molecule on the Si(001) surfaces. The calculation shows how NQE impacts the reaction energetics. The proton density changes are computed along the reaction pathways. This work demonstrates the capability of the new cNEO-DFT method to study a wide range of chemical processes, such as surface reactions where the quantum nature of light atoms like protons is non-negligible.
Use of Constrained Gamma Emission Computed Tomography to Evaluate Fission Product Distributions in High-Temperature Materials from a TRISO Fuel Irradiation
An image reconstruction technique was developed to overcome problems with earlier methods of gamma emission computed tomography of graphite rings surrounding the AGR-3/4 TRISO fission product transport experiment. The profiles obtained from the tomography are compared with sampling done via radially resolved destructive sampling techniques. Generally, there is good agreement between profiles measured via destructive sampling of the rings and the tomographic profiles, though at low signal strengths, the tomographic profiles appear elevated.
A Particle-in-Cell Method for Plasmas with a Generalized Momentum Formulation, Part I: Model Formulation
Here, this paper formulates a new particle-in-cell method for the Vlasov–Maxwell system. Under the Lorenz gauge condition, Maxwell’s equations for the electromagnetic fields can be written as a collection of scalar and vector wave equations. The use of potentials for the fields motivates the adoption of a Hamiltonian formulation for particles that employs the generalized (conjugate) momentum. A notable advantage offered by the Hamiltonian formulation is the elimination of time derivatives in the Lorenz gauge formulation that are required by the standard Newton–Lorentz treatment of the particles. This allows the fields to retain the full time-accuracy guaranteed by the field solver. The resulting updates for particles require only knowledge of the fields and their spatial derivatives. An analytical method for constructing these spatial derivatives is presented that exploits the underlying integral solution used in the field solver for the wave equations. Moreover, these derivatives are demonstrated to converge at the same rate as the fields in both time and space. The Method of Lines Transpose field solver we consider in this work is globally first-order accurate in time and high-order accurate in space (e.g., fourth- and fifth-order) and belongs to a larger class of methods which are unconditionally stable, can address geometry, and leverage $\mathcal {O}(N)$ fast summation methods for efficiency. We demonstrate the method on several well-established benchmark problems on bounded domains, including a plasma sheath as well as a relativistic particle beam. The efficacy of the proposed formulation is established by comparing with a second-order accurate finite-difference time-domain method that employs a leapfrog time advance for particles and a charge conserving map suitable for bounded domains. The new method shows mesh-independent numerical heating properties even in cases where the plasma Debye length is smaller than the grid spacing. This is an important feature of the new method for problems defined on bounded domains, because it permits the use of coarser grids in space in the representation of the fields. Such a capability has significant implications for the simulation of plasmas in bounded domains with complex geometry, where the ratio between the largest and smallest cells can vary significantly. The use of high-order spatial approximations in the new method also means that fewer grid points are required in order to achieve a fixed accuracy. Our results also suggest that the new method can be used with fewer simulation particles per cell compared to the benchmark explicit method, which permits further computational savings.
Computational Advances in Ionic Liquid Applications for Green Chemistry: A Critical Review of Lignin Processing and Machine Learning Approaches
The valorization and dissolution of lignin using ionic liquids (ILs) is critical for developing sustainable biorefineries and a circular bioeconomy. This review aims to critically assess the current state of computational and machine learning methods for understanding and optimizing IL-based lignin dissolution and valorization processes reported since 2022. The paper examines various computational approaches, from quantum chemistry to machine learning, highlighting their strengths, limitations, and recent advances in predicting and optimizing lignin-IL interactions. Key themes include the challenges in accurately modeling lignin’s complex structure, the development of efficient screening methodologies for ionic liquids to enhance lignin dissolution and valorization processes, and the integration of machine learning with quantum calculations. These computational advances will drive progress in IL-based lignin valorization by providing deeper molecular-level insights and facilitating the rapid screening of novel IL-lignin systems.
A Scalable Approach to Minimize Charging Costs for Electric Bus Fleets
Incorporating battery electric buses into bus fleets faces three primary challenges: a BEB’s extended refuel time, the cost of charging, both by the consumer and the power provider, and large compute demands for planning methods. When BEBs charge, the additional demands on the grid may exceed hardware limitations, so power providers divide a consumer’s energy needs into separate meters even though doing so is expensive for both power providers and consumers. Prior work has developed a number of strategies for computing charge schedules for bus fleets; however, prior work has not worked to reduce costs by aggregating meters. Additionally, because many works use mixed integer linear programs, their compute needs make planning for commercial-sized bus fleets intractable. This work presents a multi-program approach to computing charge plans for electric bus fleets. The proposed method solves a series of subproblems where the solution to the charge problem becomes more refined with each problem, moving closer to the optimal schedule. The results demonstrate how runtimes are reduced by using intermediate subproblems to refine the bus charge solution so that the proposed method can be applied to large bus fleets of 100+ buses. Not only will we demonstrate that runtimes scale linearly with the number of buses but we will also show how the proposed method scales to large bus fleets of over 100 buses while managing the monthly cost of energy.
Data-driven discovery of dynamics from time-resolved coherent scattering
Coherent X-ray scattering (CXS) techniques are capable of interrogating dynamics of nano- to mesoscale materials systems at time scales spanning several orders of magnitude. However, obtaining accurate theoretical descriptions of complex dynamics is often limited by one or more factors—the ability to visualize dynamics in real space, computational cost of high-fidelity simulations, and effectiveness of approximate or phenomenological models. In this work, we develop a data-driven framework to uncover mechanistic models of dynamics directly from time-resolved CXS measurements without solving the phase reconstruction problem for the entire time series of diffraction patterns. Our approach uses neural differential equations to parameterize unknown real-space dynamics and implements a computational scattering forward model to relate real-space predictions to reciprocal-space observations. This method is shown to recover the dynamics of several computational model systems under various simulated conditions of measurement resolution and noise. Moreover, the trained model enables estimation of long-term dynamics well beyond the maximum observation time, which can be used to inform and refine experimental parameters in practice. Finally, we demonstrate an experimental proof-of-concept by applying our framework to recover the probe trajectory from a ptychographic scan. Our proposed framework bridges the wide existing gap between approximate models and complex data.
A Diffusion‐Based Uncertainty Quantification Method to Advance E3SM Land Model Calibration
Abstract Calibrating land surface models and accurately quantifying their uncertainty are crucial for improving the reliability of simulations of complex environmental processes. This, in turn, advances our predictive understanding of ecosystems and supports climate‐resilient decision‐making. Traditional calibration methods, however, face challenges of high computational costs and difficulties in accurately quantifying parameter uncertainties. To address these issues, we develop a diffusion‐based uncertainty quantification (DBUQ) method. Unlike conventional generative diffusion methods, which are computationally expensive and memory‐intensive, DBUQ innovates by formulating a parameterized generative model and approximates this model through supervised learning, which enables quick generation of parameter posterior samples to quantify its uncertainty. DBUQ is effective, efficient, and general‐purpose, making it suitable for site‐specific ecosystem model calibration and broadly applicable for parameter uncertainty quantification across various earth system models. In this study, we applied DBUQ to calibrate the Energy Exascale Earth System Model land model at the Missouri Ozark AmeriFlux forest site. Results indicated that DBUQ produced accurate parameter posterior distributions similar to those from Markov Chain Monte Carlo sampling but with 30 times less computing time. This significant improvement in efficiency suggests that DBUQ can enable rapid, site‐level model calibration at a global scale, enhancing our predictive understanding of climate impacts on terrestrial ecosystems.
A comprehensive study on three typical photoacid generators using photoelectron spectroscopy and ab initio calculations
Conducting a comprehensive molecular-level evaluation of a photoacid generator (PAG) and its subsequent impact on lithography performance can facilitate the rational design of a promising 193 nm photoresist tailored to specific requirements. In this study, we integrated spectroscopy and computational techniques to meticulously investigate the pivotal factors of three prototypical PAG anions, p-toluenesulfonate (pTS - ), 2-(trifluoromethyl)benzene-1-sulfonate (TFMBS - ), and triflate (TF - ), in the lithography process. Our findings reveal a significant redshift in the absorption spectra caused by specific PAG anions, attributed to their involvement in electronic transition processes, thereby enhancing the transparency of the standard PAG cation, triphenylsulfonium (TPS + ), particularly at ~193 nm. Furthermore, the electronic stability of PAG anions can be enhanced by solvent effects with varying degrees of strength. Here we observed the lowest vertical detachment energy of 6.6 eV of pTS - in PGMEA solution based on the polarizable continuum model, which prevents anion loss at 193 nm lithography. In addition, our findings indicate gas-phase proton affinity values of 316.4 kcal/mol for pTS - , 308.1 kcal/mol for TFMBS - , and 303.2 kcal/mol for TF - , which suggest the increasing acidity strength, yet even the weakest acid pTS - is still stronger than strong acid HBr. The photolysis of TPS + -based PAG, TPS + ·pTS - , generated an excited state leading to homolysis bond cleavage with the lowest reaction energy of 83 kcal/mol. Overall, the PAG anion pTS - displayed moderate acidity, possessed the lowest photolysis reaction energy, and demonstrated an appropriate redshift. These properties collectively render it a promising candidate for an effective acid producer.
Approximating accelerator impedances with resonator networks
It is common in the accelerator community to use the impedance of accelerator components to describe wake interactions in the frequency domain. However, it is often desirable to understand such wake interactions in the time domain in a general manner for excitations that are not necessarily Gaussian in nature. Here, the conventional method for doing this involves taking the inverse Fourier Transform of the component impedance, obtaining the Green's Function, and then convolving it with the desired excitation distribution. This method can prove numerically cumbersome, for a convolution integral must be evaluated for each individual point in time when the wake function is desired. An alternative to this method would be to compute the wake function analytically, which would sidestep the need for repetitive integration. Only a handful of cases, however, are simple enough for this method to be tenable. One of these cases is the case where the component in question is an RLC resonator, which has a closed-form analytical wake function solution. This means that a component which can be represented in terms of resonators can leverage this solution. As it happens, common network synthesis techniques may be used to map arbitrary impedance profiles to RLC resonator networks in a manner the accelerator community has yet to take advantage of. In this work, we will use Foster Canonical Resonator Networks and partial derivative descent optimization to develop a technique for synthesizing resonator networks that well approximate the impedances of real-world accelerator components. We will link this synthesis to the closed-form resonator wake function solution, giving rise to a powerful workflow that may be used to streamline beam dynamics simulations.
Chemistry Informed Machine Learning-Based Heat Capacity Prediction of Solid Mixed Oxides
Knowing heat capacity is crucial for modeling temperature changes with the absorption and release of heat and for calculating the thermal energy storage capacity of oxide mixtures with energy applications. The current prediction methods (ab initio simulations, computational thermodynamics, and the Neumann–Kopp rule) are computationally expensive, not fully generalizable, or inaccurate. Machine learning has the potential of being fast, accurate, and generalizable, but it has been scarcely used to predict mixture properties, particularly for mixed oxides. Here, we demonstrate a method for the generalizable prediction of heat capacity of solid oxide pseudobinary mixtures using heat capacity data obtained from computational thermodynamics and descriptors from ab initio databases. Further, models trained through this workflow achieved an error (mean absolute error of 0.43 J mol –1 K –1 ) lower than the uncertainty in differential scanning calorimetry measurements, and the workflow can be extended to predict other properties derived from the Gibbs free energy and for higher-order oxide mixtures.
Equilibrium Core Model for Micro Pebble Bed Reactors Using OpenMC
Estimating the equilibrium state for pebble bed reactors (PBRs) presents complex challenges as it requires simultaneous consideration of changes in the pebbles’ movement as well as their fuel compositions. Whereas traditional approaches use multigroup diffusion codes for neutronics calculations of PBRs’ equilibrium state, the double-heterogeneity of PBRs complicates neutron cross-section generation. Continuous-energy Monte Carlo (MC) methods are better suited for detailed PBR analysis because of their natural handling of double-heterogeneity, but they demand substantially more computational resources. Here, this study introduces a novel method for efficiently estimating the equilibrium state in small and micro PBRs with reduced computational cost. The method is anticipated to accelerate the processes of core design and performing parametric studies for utilizing advanced fuel and structural materials. The HTR-10 reactor design was used for validating the method’s predictions and evaluating its computational efficiency. When compared to reference calculation values from the literature, criticality (k-effective) was predicted to be approximately within the margin of error of the MC transport calculation, average core power density (in megawatts per cubic meter) was predicted within 2.5% relative error, and maximum thermal flux (10 13 n/cm 2 .s −1 ) was predicted within 1.8% relative error. The calculated inventory of fission products and fuel composition in the equilibrium core were within 15% and 16.6%, respectively, when compared to reported values from the literature. The difference is attributed to variance in the considered values of the core temperature, which was found to significantly affect the depletion analyses.
Iterative methods in GPU-resident linear solvers for nonlinear constrained optimization
Linear solvers are major computational bottlenecks in a wide range of decision support and optimization computations. The challenges become even more pronounced on heterogeneous hardware, where traditional sparse numerical linear algebra methods are often inefficient. For example, methods for solving ill-conditioned linear systems have relied on conditional branching, which degrades performance on hardware accelerators such as graphical processing units (GPUs). To improve the efficiency of solving ill-conditioned systems, our computational strategy separates computations that are efficient on GPUs from those that need to run on traditional central processing units (CPUs). Our strategy maximizes the reuse of expensive CPU computations. Iterative methods, which thus far have not been broadly used for ill-conditioned linear systems, play an important role in our approach. In particular, we extend ideas from Arioli et al., (2007) to implement iterative refinement using inexact LU factors and flexible generalized minimal residual (FGMRES), with the aim of efficient performance on GPUs. In conclusion, we focus on solutions that are effective within broader application contexts, and discuss how early performance tests could be improved to be more predictive of the performance in a realistic environment.
An evaluation of multi-fidelity methods for quantifying uncertainty in projections of ice-sheet mass change
Abstract. This study investigated the computational benefits of using multi-fidelity statistical estimation (MFSE) algorithms to quantify uncertainty in the mass change of Humboldt Glacier, Greenland, between 2007 and 2100 using a single climate change scenario. The goal of this study was to determine whether MFSE can use multiple models of varying cost and accuracy to reduce the computational cost of estimating the mean and variance of the projected mass change of a glacier. The problem size and complexity were chosen to reflect the challenges posed by future continental-scale studies while still facilitating a computationally feasible investigation of MFSE methods. When quantifying uncertainty introduced by a high-dimensional parameterization of the basal friction field, MFSE was able to reduce the mean-squared error in the estimates of the statistics by well over an order of magnitude when compared to a single-fidelity approach that only used the highest-fidelity model. This significant reduction in computational cost was achieved despite the low-fidelity models used being incapable of capturing the local features of the ice-flow fields predicted by the high-fidelity model. The MFSE algorithms were able to effectively leverage the high correlation between each model's predictions of mass change, which all responded similarly to perturbations in the model inputs. Consequently, our results suggest that MFSE could be highly useful for reducing the cost of computing continental-scale probabilistic projections of sea-level rise due to ice-sheet mass change.