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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Survey of Dynamic Mode Decomposition Methods

Dynamic mode decomposition (DMD) is a data-driven reduced order modeling (ROM) technique used for dynamic systems. The widely adopted algorithm was first introduced and demonstrated on fluid flow data by Schmid. In recent years, various other fields, such as nuclear engineering, have begun to adopt this method. For example, DMD has been used for estimating α-eigenvalues, as an ROM for pulsed neutron problems, for predicting isotopic composition in burnup calculations, as acceleration techniques for iterative methods, and in capturing dynamic behaviors in molten salt reactor transients. This report seeks to demonstrate the capabilities and limits of the standard DMD algorithm, and identify problem spaces where variants may be better suited. The primary variant this report considers is Multi-Resolution DMD (mrDMD). Because this serves as a survey, synthetically produced data is used in lieu of simulation results. The remainder of this report will go into detail on the DMD theory, outline the standard DMD and mrDMD algorithms, present test cases highlighting the applicability of each, and finally present a discussion on how to determine the best suited algorithm for a given problem. All calculations performed in this report are carried out using the open source DMD library, PyDMD.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Artificial Intelligence for Accelerating Nuclear Applications, Science, and Technology

Artificial intelligence (AI) and machine learning (ML) methods have had significant impacts in science and technology in recent years. These methods for generating models from datasets or logic-based algorithms that emulate aspects of human performance can similarly accelerate the fields of nuclear applications, science, and technology toward the IAEA goals of contributing to peace, health, and prosperity. In order to accomplish advances with AI in general and ML in particular across these fields, IAEA can play a significant role by establishing, hosting and curating centralised resources, including databases, adhering to FAIR (findable, accessible, interoperable and reusable) principles and Open Science best practices, providing stewardship of data sharing, supporting training efforts and development of relevant workforces, as well as enabling connections among the scientific, technology, mathematics, AI and ethics communities. Many areas can benefit from the use of AI in the realm of nuclear applications. In human health, these areas include clinical research, epidemiology, nutrition, medical imaging, radiotherapy and education of health professionals. AI-based tools are also being used to facilitate different clinical tasks in imaging, computer-assisted diagnosis in mammography and lung cancer screening programmes, and dose prediction in nuclear medicine procedures. ML methods in particular may also increase the efficiency and accuracy of the analysis of computerised tomography and dual-energy absorptiometry scans for body composition and bone analysis. The application of AI methods to nuclear and related technologies in food and agriculture can lead to significant advances and improved efficiency in the optimisation of agricultural production, food product development, management of supply chains, food safety and food authenticity control. In the water and environmental sector, AI can help inform policies to mitigate the world’s water problems. The application of AI techniques to hydrology and environmental sciences is expected to improve patterns identification and enable model predictions under a changing climate.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

A Physical Model Enhanced Data Driven Method for High-Resolution Residential Load Profile Generation

Residential buildings account for significant energy consumption, creating opportunities to offer grid services. As electric utilities seek to implement effective system operation strategies, understanding residential energy consumption patterns becomes essential; However, the time intervals of load profiles measured by utilities' smart meters are typically from 15 minutes to 60 minutes. The low-resolution data make it hard to extract appliance-level load information, which is critical for providing grid services. This paper presents a load profile generator designed to produce synthetic load profiles for residential buildings that emphasizes the importance of accurate representations of realistic energy consumption patterns. The generator takes realistic low-resolution residential load measurements and weather data as inputs, producing 1-minute interval profiles that match the characteristics of the original profiles. Further, this generator can be used to populate load profiles in areas where actual measurements are limited to improve the ability of utilities to analyze their distribution systems. By providing more high-resolution residential building load profiles, this tool supports electric utilities to enhance their residential building load control strategies and improve overall grid stability.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2021

Machine-learning-accelerated multimodal characterization and multiobjective design optimization of natural porous materials

Natural porous materials such as nanoporous clays are used as green and low-cost adsorbents and catalysts. The key factors determining their performance in these applications are the pore morphology and surface activity, which are typically represented by properties such as specific surface area, pore volume, micropore content and pH. The latter may be modified and tuned to specific applications through material processing and/or chemical treatment. Characterization of the material, raw or processed, is typically performed experimentally, which can become costly especially in the context of tuning of the properties towards specific application requirements and needing numerous experiments. In this work, we present an application of tree-based machine learning methods trained on experimental datasets to accelerate the characterization of natural porous materials. The resulting models allow reliable prediction of the outcomes of experimental characterization of processed materials (R2 from 0.78 to 0.99) as well as identification of key factors contributing to those properties through feature importance analysis. Furthermore, the high throughput of the models enables exploration of processing parameter–property correlations and multiobjective optimization of prototype materials towards specific applications. We have applied these methodologies to pinpoint and rationalize optimal processing conditions for clays exploitable in acid catalysis. One of such identified materials was synthesized and tested revealing appreciable acid character improvement with respect to the pristine material. Specifically, it achieved 79% removal of chlorophyll-a in acid catalyzed degradation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Constraining the phase shift of relativistic species in DESI BAOs

In the early Universe, neutrinos decouple quickly from the primordial plasma and propagate without further interactions. The impact of free-streaming neutrinos is to create a temporal shift in the gravitational potential that impacts the acoustic waves known as baryon acoustic oscillations (BAOs), resulting in a non-linear spatial shift in the Fourier-space BAO signal. In this work, we make use of and extend upon an existing methodology to measure the phase shift amplitude $\beta _{\phi }$ and apply it to the Dark Energy Spectroscopic Instrument (DESI) Data Release 1 (DR1) BAOs with an anisotropic BAO fitting pipeline. We validate the fitting methodology by testing the pipeline with two publicly available fitting codes applied to highly precise cubic box simulations and realistic simulations representative of the DESI DR1 data. We find further study towards the methods used in fitting the BAO signal will be necessary to ensure accurate constraints on $\beta _{\phi }$ in future DESI data releases. Using DESI DR1, we present individual measurements of the anisotropic BAO distortion parameters and the $\beta _{\phi }$ for the different tracers, and additionally a combined fit to $\beta _{\phi }$ resulting in $\beta _{\phi } = 2.7 \pm 1.7$. After including a prior on the distortion parameters from constraints using Planck we find $\beta _{\phi } = 2.7^{+0.60}_{-0.67}$ suggesting $\beta _{\phi } > 0$ at 4.3$\sigma$ significance. This result may hint at a phase shift that is not purely sourced from the standard model expectation for $N_{\rm {eff}}$ or could be a upwards statistical fluctuation in the measured $\beta _{\phi }$; this result relaxes in models with additional freedom beyond Lambda-cold dark matter.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Developing new analysis tools for near surface radio-based neutrino detectors

The ARIANNA experiment is an Askaryan radio detector designed to measure high-energy neutrino induced cascades within the Antarctic ice. Ultra-high-energy neutrinos above 10 16 eV have an extremely low flux, so experimental data captured at trigger level need to be classified correctly to retain as much neutrino signal as possible. We first describe two new physics-based neutrino selection methods, or "cuts", (the updown and dipole cut) that extend the previously published analysis to a specialized ARIANNA station with 8 antenna channels, which is double the number used in the prior analysis. For a standard trigger with a threshold signal to noise ratio at 4.4, the new cuts produce a neutrino efficiency of > 95% per station-year of operation, while rejecting 99.93% of the background (corresponding to 53 remaining experimental background events). When the new cuts are combined with a previously developed cut using neutrino waveform templates, all background is removed at no change of efficiency. In addition, the neutrino efficiency is extrapolated to 1,000 station-years of operation, obtaining 91%. This work then introduces a new selection method (the deep learning cut) to augment the identification of neutrino events by using deep learning methods and compares the efficiency to the physics-based analysis. The deep learning cut gives 99% signal efficiency per station-year of operation while rejecting 99.997% of the background (corresponding to 2 remaining experimental background events), which are subsequently removed by the waveform template cut at no significant change in efficiency. Here the results of the deep learning cut were verified using measured cosmic rays which shows that the simulations do not introduce artifacts with respect to experimental data. The paper demonstrates that the background rejection and signal efficiency of near surface antennas meets the requirements of a large scale future array, as considered in baseline design of the radio component of IceCube-Gen2.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Basic Research Needs for Inverse Methods for Complex Systems under Uncertainty

Inverse problems, which aim to infer unknown properties of a system using experimental and observational data, are central to addressing many of the U.S. Department of Energy’s (DOE) most critical scientific and engineering challenges. Accurate, computationally efficient, and data-efficient solutions to inverse problems are essential for advancing DOE mission-critical science drivers, including analyzing data from large-scale experimental facilities, optimizing fusion reactor performance, accelerating materials discovery, enhancing geophysical imaging, improving wildfire predictions, and enabling autonomous systems and digital twins. However, these problems are becoming increasingly complex, often involving nonlinear, highdimensional, and interconnected systems and models that span multiple physics and scales, while relying on data with varying quantity, quality, and information content. Compounding these challenges is the uncertainty inherent in DOE-relevant systems, where errors in inputs, noise in data, incompleteness of data, and discrepancies between models and reality constrain the accuracy and precision of solutions. At the same time, the convergence of recent scientific computing trends—scientific machine learning, artificial intelligence, and computing advances such as exascale computing—is creating unprecedented opportunities for tackling these challenges. The cross-cutting nature of inverse problems, combined with their growing complexity and rapidly evolving data and algorithmic demands, strongly motivates the formulation of a prioritized research agenda to maximize their capabilities and impact. In response to this need, DOE’s Advanced Scientific Computing Research (ASCR) program in the Office of Science convened the Workshop on Basic Research Needs for Inverse Problems for Complex Systems Under Uncertainty in June 2025. This workshop brought together experts across disciplines to identify grand challenges and major opportunities in the field. Through collaborative discussions, the workshop defined transformative research directions aimed at addressing the mathematical, statistical, and computational challenges posed by inverse problems under uncertainty. As a result of these efforts, four priority research directions (PRDs) were identified to guide future research and development in this area. These PRDs, summarized below, represent a roadmap for advancing the foundational science and mathematics of inverse problems, enabling robust, scalable, and uncertainty-aware solutions that are critical for DOE applications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Advancements in NEAMS Tool Capabilities for Multiphysics Simulation of Fast Reactor Core Bowing and Identification of Validation Test Data

Under the U.S. Department of Energy Office of Nuclear Energy Advanced Modeling and Simulation (NEAMS) Program, an integrated multiphysics approach is being developed to model the core bowing phenomena important to liquid metal-cooled fast reactors. Core bowing is an important passive safety mechanism in liquid metal-cooled fast reactors and involves Multiphysics effects including radiation transport, fluid flow, heat transfer, and mechanical response to temperature and flux gradients. This report summarizes recent progress on developing a multiphysics, MOOSE-based workflow to predict core bowing and associated reactivity feedback. Last year, thermal fluids and mechanics were coupled on a multi-assembly benchmark problem based on ABR-1000 design. This year, the reactor physics code Griffin was assessed for readiness of core bowing calculations. Preliminary integration of Griffin’s ring-heterogeneous model with thermal fluids and thermal mechanics solvers was performed. Specifically, thermal-mechanics and reactor physics were coupled for single- and multi-assembly problems, and reactor physics and subchannel methods were coupled for a single assembly model. Finally, the workflow of all three physics was preliminarily demonstrated on a single assembly model. Caveats and future development needed have been identified. To supplement the multiphysics demonstration, verification and assessment efforts of thermos-mechanical capabilities for modeling thermo-mechanical core bowing behavior were continued by analyzing IAEA Verification Problem 5 which includes radiation swelling and creep. Additionally, a small core reactor physics benchmark defined by Japan Atomic Energy Agency (JAEA) was performed to assess neutronics models for estimating reactivity feedback. Finally, Fast Flux Test Facility (FFTF) validation test data for core bowing phenomena has been identified and summarized, with a recommended path forward for validation once this capability is mature.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

Uncertainty Analysis for a Criticality Benchmark [Slides]

This presentation discusses how KRUSTY was analyzed with LANL’s MCNP neutron transport code, Monte Carlo N-Particle. In the Monte Carlo method, neutrons are born in fission events and fly around the geometry having events (e.g., scatter, capture, fission, escape) according to the natural probabilities. “Natural probabilities” are given as neutron cross sections , which are measured and evaluated nuclear data. One of the goals of the benchmark project is to improve the nuclear cross sections (and the codes that use them). In this work, the response of interest is called k eff , which describes the neutron multiplication in a near critical system. Like most quantities, k eff is not measured directly; it is only inferred. In summation, MCNP results for k eff matched the measurements extremely well. The evaluated uncertainties are asymmetric and smaller than 0.00100 (e.g., + 0.00080 / – 0.00062). The largest uncertainties are due to alignment.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Indium and thallium extraction into betainium bis(trifluoromethylsulfonyl)imide ionic liquid from aqueous hydrochloric acid media

The partitioning behavior of indium and thallium ions between aqueous hydrochloric acid solutions and hydrophobic betainium bis(trifluoromethylsulfonyl)imide ionic liquid was studied using a standard liquid–liquid extraction technique. The experiments were mainly carried out by means of a radiochemical method, using 111 In and 201 Tl medical radionuclides at an ultra-trace concentration. Both mono- and trivalent thallium were utilized and the highest oxidation state (3+) was produced by adding either chlorine or bromine water to the aqueous phase prior to extraction. The metal ion transfer was optimized by varying the aqueous concentration of hydrochloric acid and by introducing zwitterionic betaine as an extracting agent into the aqueous phase. It was found that the highest D values of In(III), Tl(III) and Tl(I) in the investigated chemical systems were up to 200, 70, and 1, respectively. The influence of the addition of lithium salt, having common with the ionic liquid counterion, and the variation of mixing time on the distribution ratio of the metal ions were also studied. Finally, to understand the underlying extraction mechanism of the metal ions and to propose the predominant extracted species, mathematical models based on ion pair formation and ion exchange were developed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Analyzing Prospects for Quantum Advantage in Topological Data Analysis

Lloyd [Nat. Commun. , 10138 (2016)] were first to demonstrate the promise of quantum algorithms for computing Betti numbers, a way to characterize topological features of data sets. Here, we propose, analyze, and optimize an improved quantum algorithm for topological data analysis (TDA) with reduced scaling, including a method for preparing Dicke states based on inequality testing, a more efficient amplitude estimation algorithm using Kaiser windows, and an optimal implementation of eigenvalue projectors based on Chebyshev polynomials. We compile our approach to a fault-tolerant gate set and estimate constant factors in the Toffoli complexity. Our analysis reveals that superquadratic quantum speedups are only possible for this problem when targeting a multiplicative error approximation and the Betti number grows asymptotically. Further, we propose a dequantization of the quantum TDA algorithm that shows that having exponentially large dimension and Betti number are necessary, but insufficient conditions, for superpolynomial advantage. We then introduce and analyze specific problem examples which have parameters in the regime where superpolynomial advantages may be achieved, and argue that quantum circuits with tens of billions of Toffoli gates can solve seemingly classically intractable instances. Published by the American Physical Society 2024

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Pronghorn: A Multidimensional Coarse Mesh Application for Advanced Reactor Thermal-Hydraulics

This paper presents an overview of Pronghorn, a multiscale thermal-hydraulic (T/H) application developed by Idaho National Laboratory and the University of California, Berkeley. Pronghorn, built on the open-source finite element Multiphysics Object-Oriented Simulation Environment (MOOSE), leverages state-of-the-art physical models, numerical methods, and nonlinear solvers to deliver fast-running advanced reactor T/H simulation capabilities within a modern software engineering environment. This work summarizes the physical models, multiphysics and multiscale coupling, and numerical discretization in Pronghorn with emphasis on our initial target application to pebble bed reactors (PBRs). A diverse set of applications are shown to depressurized natural circulation in the SANA experiments, forced convection in the Pebble Bed Modular Reactor, three-dimensional (3-D)/one-dimensional coupling of Pronghorn and RELAP-7 systems T/H for loop analysis in the High Temperature Reactor Power Module, and forced convection in the Mark-1 Pebble Bed Fluoride-Salt-Cooled High-Temperature Reactor. A multiphysics coupling of Pronghorn, RELAP-7, and Griffin deterministic neutronics for a gas-cooled PBR demonstrates the capability of the MOOSE framework for reactor design calculations. These applications highlight the verification and validation underlying Pronghorn’s software development while emphasizing features that improve upon capabilities offered by legacy tools in areas such as 3-D unstructured meshing, physics modeling, and multiphysics coupling.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Dynamic PRA Methods to Evaluate the Impact on Accident Progression of Accident Tolerant Fuels

Accident tolerant fuels (ATFs) are new nuclear fuels developed in response to the accident at the Fukushima power station in March 2011. The goal of ATFs is to withstand accident scenarios through better performance compared to currently employed fuels (e.g., small-scale hydrogen generation). This paper targets a method for evaluating and comparing ATF performance from a probabilistic risk assessment (PRA) perspective by employing a newly developed combination of event trees and dynamic PRA methods. Compared to classical PRA methods based on event trees and fault trees, dynamic PRA can evaluate with higher resolution the safety impacts of physics dynamics and the timing/sequencing of events on the accident progression without the need to introduce overly conservative modeling assumptions and success criteria. In this paper, we analyze the impact on the accident progression of three different cladding configurations for two initiating events [a large break loss-of-coolant accident (LB-LOCA) and a station blackout (SBO)] by employing dynamic PRA methods. The goal is to compare the safety performance of ATFs (FeCrAl and Cr-coated cladding) and the currently employed Zr-based clad fuel. We employ two different strategies. The first focuses on the identification of success criteria discrepancies between the accident sequences generated by the classical PRA model and the set of simulation runs generated by dynamic PRA using ATF. The second one, on the other hand, directly uses dynamic PRA to evaluate the impact of timing of events (e.g., recovery actions) on accident progression. In conclusion, by applying these methods to the LB-LOCA and SBO initiating events, we show how dynamic PRA methods can provide analysts with detailed and quantitative information on the safety impact of ATFs.

97 - MATHEMATICS AND COMPUTING↗
DOE OSTI2025

SAGIPS: a physics-inspired scalable asynchronous generative inverse-problem solver

Abstract Solving large-scale inverse problems using deep-learning algorithms have become an essential part of modern research and industrial applications. The complexity of the underlying inverse problem may require the utilization of high performance computing systems which poses a challenge on the algorithmic design of the inverse problem solver. Most deep learning algorithms require, due to their design, custom parallelization techniques in order to be resource efficient while showing a reasonable convergence. In this paper we introduce a S calable A synchronous G enerative I nverse P roblem S olver (SAGIPS) on high-performance computing systems. We present a workflow that utilizes an asynchronous ring-allreduce algorithm to transfer the gradients of the generator network across multiple GPUs. Experiments with a scientific proxy application demonstrate that SAGIPS shows near linear weak scaling, together with a convergence quality that is comparable to traditional methods. The approach presented here allows leveraging Generative Adverserial Network across multiple GPUs, promising advancements in solving complex inverse problems at scale.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Solving Inverse Stochastic Problems from Discrete Particle Observations Using the Fokker--Planck Equation and Physics-Informed Neural Networks

The Fokker--Planck (FP) equation governing the evolution of the probability density function (PDF) is applicable to many disciplines, but it requires specification of the coefficients for each case, which can be functions of space-time and not just constants and hence require the development of a data-driven modeling approach. When the data available is directly on the PDF, there exist methods for inverse problems that can be employed to infer the coefficients and thus determine the FP equation and subsequently obtain its solution. Herein, we address a more realistic scenario, where only sparse data are given on the particles' positions at a few time instants, which are not sufficient to accurately construct directly the PDF even at those times from existing methods, e.g., kernel estimation algorithms. To this end, we develop a general framework based on physics-informed neural networks (PINNs) that introduces a new loss function using the Kullback--Leibler divergence to connect the stochastic samples with the FP equation to simultaneously learn the equation and infer the multidimensional PDF at all times. In particular, we consider two types of inverse problems, type I, where the FP equation is known but the initial PDF is unknown, and type II, in which, in addition to the unknown initial PDF, the drift and diffusion terms are also unknown. In both cases, we investigate problems with either Brownian or Lévy noise or a combination of both. Here, we demonstrate the new PINN framework in detail in the one-dimensional (1D) case, but we also provide results for up to five dimensions demonstrating that we can infer both the FP equation and dynamics simultaneously at all times with high accuracy using only very few discrete observations of the particles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Vibrational Signatures of Electronic Properties in Renewable-Energy Catalysis

The objective of this research program is to discover and develop new approaches for ab initio computational simulations of molecular motion. Specifically, this program aims to decipher the connection between the underlying electronic structure and the accordant molecular vibrations in reactive ions and radicals for renewable-energy purposes. Recent experimental progress in ion sources and optical spectroscopies has unearthed considerable new inner-sphere detail for these complexes, but the connection between these spectral signatures and mechanistic information often remains elusive, to the continued frustration of experimentalists. For this purpose, new anharmonic vibrational frequency methods, along with a publicly deployed software package, will be developed. Working closely with committed experimental collaborators, this conceptual and computational framework will be used to explain the results of new spectroscopy experiments, focusing specifically on the inner-shell mechanisms of renewable-energy catalysis. The oxidation half of catalytic water-splitting chemistry will be a central focus, along with fundamental studies of the manner in which strong ions and radicals activate solvent as a chemical species. The resulting products of the research program will include openly available software and algorithms for the ab initio simulation of challenging vibrational spectra, as well as critical mechanistic insight into energy-focused catalytic processes that are opaque to other existing analytical techniques.

42 ENGINEERING↗
DOE OSTI2024

c-HAND: near real-time coastal flood mapping

The Texas Gulf Coast region contains significant centers of population, infrastructure, and economy and is threatened by intensifying tropical storms. The flooding from these tropical storms often has multiple compounding drivers. This characteristic presents a complex numerical problem where a simulation must consider multiple hydrologic forcings. While several procedures exist for addressing this problem numerically, they tend to be resource-intensive and cannot be conducted in near real-time. We extend GeoFlood, a reduced physics approach for fluvial flood forecasting, to rapidly predict coastal and compound fluvial-coastal inundation. This method is validated against a numerical ocean circulation model (ADCIRC) simulation of Hurricane Ike, a major coastal flooding event that happened on the Texas Gulf Coast in 2008. We show that the inundation map generated by coastal HAND (c-HAND) has reasonable agreement with the ADCIRC simulation while taking about 1.7% of the time currently needed to run ADCIRC on a supercomputer. While our model correctly predicts 99% of ADCIRC-inundated DEM cells, it also overpredicts inundated area by a factor of approximately 27%. We combine c-HAND with the GeoFlood framework for fluvial flood forecasting to create a compound fluvial-coastal inundation mapping workflow that can be run in near real-time. c-HAND's fast wall-clock time and low CPU requirements can support decision making by first response personnel. The method provides timely and convenient access to crucial information, such as the locations of flooded roads and inundated coastal areas.

42 ENGINEERING↗
DOE OSTI2025

A Quantum Approach for Implementing Fixed-Point Arithmetic in Solving Ordinary Differential Equations

Differential equations (DEs) serve as fundamental tools in mathematical modeling across scientific disciplines, yet classical numerical solvers face limitations with large-scale or computationally intensive problems. This study explores a quantum-inspired approach to solving DEs, combining quantum- inspired techniques with classical methods. It focuses on fixed- point arithmetic on quantum circuits, utilizing basic quantum gates to manipulate DE solutions. We expand upon the techniques introduced by Zanger et al. [Quantum, 5, 502 (2021)] by offering a precise computation for a fixed-point signed multiplication scheme, while also presenting a quantum circuit capable of executing the fixed-point division algorithm. We demonstrate the feasibility of our approach through the simulation of a linear Ordinary Differential Equation (ODE), where initial conditions and parameters are encoded into quantum circuits using fixed- point representation. By executing sequences of quantum gates mimicking numerical integration steps, we obtain approximate solutions to the ODE with specified fixed-point precision.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗