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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
NASA NTRS2021

Solving Two-Equation Turbulence Models With a Perspective on Solving Transport Equations

There are three principal objectives of this report. The first objective is to investigate frequently used two-equation models when solving the RANS equations. In this study, we consider the 2006Wilcox and the 2003 Menter Shear Stress Transport (SST) models. Also, a simple change of the Wilcox model is introduced to improve computational predictions for transonic flows. Computations for flows over two different airfoils are examined to compare these turbulence models. Effects on modeling the physics of each flow due to variations in the models, such as using either strainrate or vorticity in the turbulence production term, are considered and discussed. The second objective of this report is to not only explore but also evaluate the performance of the solution algorithm for the mean flow and the transport equations. The RANS and turbulence modeling equations aresolved in a weakly coupled manner with a diagonal implicit Runge-Kutta (DIRK) solution algorithm. Throughout this report, emphasis is given to reducing the residuals to machine zero in all flow calculations, so as to eliminate the error due to numerical integration of the discrete governing equations. The final objective is to provide a perspective on solving transport equations for turbulence modeling. Aspects of solving such stiff systems of equations, as well as various numerical difficulties and possible techniques to overcome them, are considered. Discussion is also provided concerning what is called ’numerical compatibility’, which is an essential requirement when designing a solution algorithm for solving transport equations.

turbulence modeling↗
NASA NTRS2003

Comparing Model Ozone Loss during the SOLVE and SOLVE-2 Winters

Model simulations have been used to analyze the factors influencing ozone loss during the 1999-2000 and 2002-2003 js. For both winters, the evolution of the Arctic vortex from November to April has been simulated using a trajectory-based microphysical and photochemical model. Extensive PSC formation and strong ozone depletion are evident in both winters. However, the ozone loss begins earlier in the 2002-2003 winter, with significant ozone depletion by early January. Analysis of the model results shows that during December 2002 not only cold temperatures but also the vortex structure was critical, allowing PSC-processed air parcels to experience significant solar exposure. The resultant ozone loss can be differentiated from ozone loss that occurs in the springtime, in particular because of the continued exposure to PSCs. For example, chlorine reactivation by the PSCs causes ozone loss to be insensitive to denitrification. Therefore, diagnosing the extent of ozone loss early in the winter is critical In understanding the overall winter-long ozone depletion.

Drdla, K.↗
DOE OSTI2024

Decomposition and Algorithmic Approaches for Solving Large-Scale Process Family Design Problems

Our most recent work expands the water desalination case study from 76 variants to 10,897 variants using the equation-oriented model built in Pyomo as part of the PARETO project. Using the discretization formulation presented in Stinchfield (2024a), rather than solving for all 10,897 variants simultaneously, we decompose the formulation into subproblems containing subsets of variants from the process family. We solve the overall problem with Progressive Hedging (PH) deployed in parallel on a distributed HPC cluster using the open-source Python package mpi-sppy (Knueven et al., 2023). This approach allowed us to solve this process family design problem to ~1.5% relative optimality gap in about 5 hours; in comparison, Gurobi reached ~50% relative optimality gap in about 6 hours (Stinchfield et al., 2024b). However, this approach still requires discretization of the common unit module design ranges; additionally, PH acts as a heuristic for MILP’s with gap-closing capabilities. Ideally, we would not have to use ML surrogates or discretization to solve this problem, instead solving the process family design problem with the equation-oriented model directly to achieve the most accurate results. However, recall that we did not consider solving the MINLP directly due to complexity and size. In this work, we aim to decompose and solve this large-scale MINLP using a Structured Nonlinear Global Optimization algorithm presented by Cao and Zavala (2019).

Stinchfield, Georgia↗
NASA NTRS2001

Participation of HNO3 CIMS Instrument in the Sage III Ozone Loss and Validation Experiment (SOLVE)

This project was part of a larger SOLVE project led by Paul Wennberg at California Institute of Technology. The work completed on this project included participating in the installation and preflight testing of a new chemical ionization mass spectrometer for measuring gas and particle phase nitric acid on the ER-2. The investigators subsequently participated in SOLVE where additional instrument improvements were made and a substantial data set was generated. The two Georgia Tech investigators that participated in this work (Fred Eisele and Dave Tanner) had previously been responsible for much of the design and construction of the ion source and mass spectrometer which would be used to measure HNO3 in SOLVE, with Caltech focusing on inlets, calibration, gas supplies/pumping computer control, and overall integration. Thus, a similar focus remained during the SOLVE measurements though all investigators worked on most if not all aspects of the instrument at some point in the mission. Some of the more interesting results from the study included measurements of nitric acid on what are thought to be 5-20 microns diameter individual particles which could supply a local mechanism for HNO3 removal, Nitric acid measurements on SOLVE were completed as a collaborative effort with a great deal of overlap between this project and the larger parent project led by Paul Wennberg. As such, the instrumentation used, its operation, and the resulting measurements are far more fully discussed in the attached report (appendix A) which describes the joint SOLVE nitric acid measurement effort.

Eisele, F. L.↗
NASA NTRS2014

Novel Problem Solving - The NASA Solution Mechanism Guide

Over the past five years, the Human Health and Performance (HH&P) Directorate at the NASA Johnson Space Center (JSC) has conducted a number of pilot and ongoing projects in collaboration and open innovation. These projects involved the use of novel open innovation competitions that sought solutions from "the crowd", non-traditional problem solvers. The projects expanded to include virtual collaboration centers such as the NASA Human Health and Performance Center (NHHPC) and more recently a collaborative research project between NASA and the National Science Foundation (NSF). These novel problem-solving tools produced effective results and the HH&P wanted to capture the knowledge from these new tools, to teach the results to the directorate, and to implement new project management tools and coursework. The need to capture and teach the results of these novel problem solving tools, the HH&P decided to create a web-based tool to capture best practices and case studies, to teach novice users how to use new problem solving tools and to change project management training/. This web-based tool was developed with a small, multi-disciplinary group and named the Solution Mechanism Guide (SMG). An alpha version was developed that was tested against several sessions of user groups to get feedback on the SMG and determine a future course for development. The feedback was very positive and the HH&P decided to move to the beta-phase of development. To develop the web-based tool, the HH&P utilized the NASA Tournament Lab (NTL) to develop the software with TopCoder under an existing contract. In this way, the HH&P is using one new tool (the NTL and TopCoder) to develop the next generation tool, the SMG. The beta-phase of the SMG is planed for release in the spring of 2014 and results of the beta-phase testing will be available for the IAC meeting in September. The SMG is intended to disrupt the way problem solvers and project managers approach problem solving and to increase the use of novel and more cost and time effective problem solving tools such as open innovation, collaborative research, and virtual collaborative project centers. The HH&P envisions changing project management coursework by including the SMG in the teaching of project management problem solving tools.

Keeton, Kathryn E.↗
NASA NTRS1993

Solving modal equations of motion with initial conditions using MSC/NASTRAN DMAP. Part 1: Implementing exact mode superposition

Within the MSC/NASTRAN DMAP (Direct Matrix Abstraction Program) module TRD1, solving physical (coupled) or modal (uncoupled) transient equations of motion is performed using the Newmark-Beta or mode superposition algorithms, respectively. For equations of motion with initial conditions, only the Newmark-Beta integration routine has been available in MSC/NASTRAN solution sequences for solving physical systems and in custom DMAP sequences or alters for solving modal systems. In some cases, one difficulty with using the Newmark-Beta method is that the process of selecting suitable integration time steps for obtaining acceptable results is lengthy. In addition, when very small step sizes are required, a large amount of time can be spent integrating the equations of motion. For certain aerospace applications, a significant time savings can be realized when the equations of motion are solved using an exact integration routine instead of the Newmark-Beta numerical algorithm. In order to solve modal equations of motion with initial conditions and take advantage of efficiencies gained when using uncoupled solution algorithms (like that within TRD1), an exact mode superposition method using MSC/NASTRAN DMAP has been developed and successfully implemented as an enhancement to an existing coupled loads methodology at the NASA Lewis Research Center.

Abdallah, Ayman A.↗
DOE OSTI2025

Graph decomposition techniques for solving combinatorial optimization problems with variational quantum algorithms

The quantum approximate optimization algorithm (QAOA) has the potential to approximately solve complex combinatorial optimization problems in polynomial time. However, current noisy quantum devices cannot solve large problems due to hardware constraints. In this work, we develop an algorithm that decomposes the QAOA input problem graph into a smaller problem and solves MaxCut using QAOA on the reduced graph. The algorithm requires a subroutine that can be classical or quantum—in this work, we implement the algorithm twice on each graph. One implementation uses the classical solver Gurobi in the subroutine and the other uses QAOA. We solve these reduced problems with QAOA. On average, the reduced problems require only approximately 1/10 of the number of vertices than the original MaxCut instances. Furthermore, the average approximation ratio of the original MaxCut problems is 0.75, while the approximation ratios of the decomposed graphs are on average of 0.96 for both Gurobi and QAOA. With this decomposition, we are able to measure optimal solutions for ten 100-vertex graphs by running single-layer QAOA circuits on the Quantinuum trapped-ion quantum computer H1-1, sampling each circuit only 500 times. This approach is best suited for sparse, particularly k-regular graphs, as k-regular graphs on n vertices can be decomposed into a graph with at most $\frac{nk}{k+1}$ vertices in polynomial time. Further reductions can be obtained with a potential trade-off in computational time. In conclusion, while this paper applies the decomposition method to the MaxCut problem, it can be applied to more general classes of combinatorial optimization problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

A Block-Structured Adaptive Mesh Framework to Solve Radiation Transfer Equation in Irregular Embedded Geometries

Radiation transport arises in various scientific, industrial, and medical fields, and understanding its effect in applications is needed to make accurate predictions, safety assessments and performance optimizations. Solving the Radiation Transport Equation (RTE) is challenging due to its integro-differential nature, which involves both differential and integral terms. The differential term describes the change in radiation intensity due to absorption and emission, while the integral term accounts for scattering. The accurate modeling of radiation is further complicated in many applications due to the complex, irregular geometries. Various methods exist for solving the RTE, including the zonal, Monte Carlo, spherical harmonics, discrete ordinates, and finite volume methods. Traditional mesh-based approaches, which rely on structured or unstructured meshes, struggle with irregular geometries due to: a) the difficulty of conforming structured grids to irregular domains, b) challenges in enforcing boundary conditions correctly, and c) the additional computational cost of unstructured mesh methods. This work presents a second-order accurate method for solving the RTE in irregular geometries. The radiation intensity is discretized using the finite-volume method in both spatial and angular directions on regular Cartesian grid blocks. Leveraging the block-structured adaptive mesh refinement (AMR) framework provided by AMReX, our method refines the grid locally to reduce spatial discretization error, ensuring a converged numerical solution while minimizing computational costs elsewhere. A two-stage deferred correction approach is employed: First, a first-order discretization on grid blocks is solved using an algebraic multigrid method in HYPRE. Second, a correction term is applied explicitly to achieve second-order accuracy. The correction term is calculated by approximating the radiation flux on cell faces using a Total Variation Diminishing (TVD) scheme. This approach ensures quick convergence of the multigrid method while preserving higher-order accuracy of the numerical solution. Irregular geometries are resolved as embedded boundaries (EB), resulting in both cut cells and regular cells. In cut cells, we modify the fluxes using face fractions and incorporate additional contributions from EB boundary conditions. To ensure higher-order convergence near the EB interface, the correction term is modified by interpolating the radiation intensity to fictitious ghost points. The implementation takes advantage of modern supercomputers by leveraging AMReX’sMPI/X parallelization strategy where X can be MPI or a GPU accelerator including CUDA, HIP and DPC++. We validate our solver using classical test cases, both with and without EB, demonstrating accuracy and efficiency. Additionally, we analyze the impact of adaptive mesh refinement on solution accuracy and computational cost, highlighting the advantages of our approach for high-resolution radiation transport simulations.

computational fluid dynamics (CFD)↗
NASA NTRS1976

An efficient numerical method for solving the time-dependent compressible Navier-Stokes equations at high Reynolds number

A fine-mesh method incorporating two new operators, which drastically reduces the computation time, has been developed for solving the time-dependent Navier-Stokes equations at flight Reynolds numbers. The approach time-splits the equations into a hyperbolic part and a parabolic part, solves the hyperbolic part by a new explicit numerical method based on characteristics theory, and solves the parabolic part by a new efficient implicit parabolic method. The method has reduced the computation time by one and two orders of magnitude from that required previously to solve for the interaction of a shock wave with a boundary layer on a flat plate.

Maccormack, R. W.↗
NASA NTRS1986

An efficient method for solving the steady Euler equations

An efficient numerical procedure for solving a set of nonlinear partial differential equations is given, specifically for the steady Euler equations. Solutions of the equations were obtained by Newton's linearization procedure, commonly used to solve the roots of nonlinear algebraic equations. In application of the same procedure for solving a set of differential equations we give a theorem showing that a quadratic convergence rate can be achieved. While the domain of quadratic convergence depends on the problems studied and is unknown a priori, we show that firstand second-order derivatives of flux vectors determine whether the condition for quadratic convergence is satisfied. The first derivatives enter as an implicit operator for yielding new iterates and the second derivatives indicates smoothness of the flows considered. Consequently flows involving shocks are expected to require larger number of iterations. First-order upwind discretization in conjunction with the Steger-Warming flux-vector splitting is employed on the implicit operator and a diagonal dominant matrix results. However the explicit operator is represented by first- and seond-order upwind differencings, using both Steger-Warming's and van Leer's splittings. We discuss treatment of boundary conditions and solution procedures for solving the resulting block matrix system. With a set of test problems for one- and two-dimensional flows, we show detailed study as to the efficiency, accuracy, and convergence of the present method.

Liou, M. S.↗
NASA NTRS1994

Understanding the determinants of problem-solving behavior in a complex environment

It is often argued that problem-solving behavior in a complex environment is determined as much by the features of the environment as by the goals of the problem solver. This article explores a technique to determine the extent to which measured features of a complex environment influence problem-solving behavior observed within that environment. In this study, the technique is used to determine how complex flight deck and air traffic control environment influences the strategies used by airline pilots when controlling the flight path of a modern jetliner. Data collected aboard 16 commercial flights are used to measure selected features of the task environment. A record of the pilots' problem-solving behavior is analyzed to determine to what extent behavior is adapted to the environmental features that were measured. The results suggest that the measured features of the environment account for as much as half of the variability in the pilots' problem-solving behavior and provide estimates on the probable effects of each environmental feature.

Casner, Stephen A.↗
NASA NTRS2009

Workflow Agents vs. Expert Systems: Problem Solving Methods in Work Systems Design

During the 1980s, a community of artificial intelligence researchers became interested in formalizing problem solving methods as part of an effort called "second generation expert systems" (2nd GES). How do the motivations and results of this research relate to building tools for the workplace today? We provide an historical review of how the theory of expertise has developed, a progress report on a tool for designing and implementing model-based automation (Brahms), and a concrete example how we apply 2nd GES concepts today in an agent-based system for space flight operations (OCAMS). Brahms incorporates an ontology for modeling work practices, what people are doing in the course of a day, characterized as "activities." OCAMS was developed using a simulation-to-implementation methodology, in which a prototype tool was embedded in a simulation of future work practices. OCAMS uses model-based methods to interactively plan its actions and keep track of the work to be done. The problem solving methods of practice are interactive, employing reasoning for and through action in the real world. Analogously, it is as if a medical expert system were charged not just with interpreting culture results, but actually interacting with a patient. Our perspective shifts from building a "problem solving" (expert) system to building an actor in the world. The reusable components in work system designs include entire "problem solvers" (e.g., a planning subsystem), interoperability frameworks, and workflow agents that use and revise models dynamically in a network of people and tools. Consequently, the research focus shifts so "problem solving methods" include ways of knowing that models do not fit the world, and ways of interacting with other agents and people to gain or verify information and (ultimately) adapt rules and procedures to resolve problematic situations.

Clancey, William J.↗
NASA NTRS2011

Technique for Solving Electrically Small to Large Structures for Broadband Applications

Fast iterative algorithms are often used for solving Method of Moments (MoM) systems, having a large number of unknowns, to determine current distribution and other parameters. The most commonly used fast methods include the fast multipole method (FMM), the precorrected fast Fourier transform (PFFT), and low-rank QR compression methods. These methods reduce the O(N) memory and time requirements to O(N log N) by compressing the dense MoM system so as to exploit the physics of Green s Function interactions. FFT-based techniques for solving such problems are efficient for spacefilling and uniform structures, but their performance substantially degrades for non-uniformly distributed structures due to the inherent need to employ a uniform global grid. FMM or QR techniques are better suited than FFT techniques; however, neither the FMM nor the QR technique can be used at all frequencies. This method has been developed to efficiently solve for a desired parameter of a system or device that can include both electrically large FMM elements, and electrically small QR elements. The system or device is set up as an oct-tree structure that can include regions of both the FMM type and the QR type. The system is enclosed with a cube at a 0- th level, splitting the cube at the 0-th level into eight child cubes. This forms cubes at a 1st level, recursively repeating the splitting process for cubes at successive levels until a desired number of levels is created. For each cube that is thus formed, neighbor lists and interaction lists are maintained. An iterative solver is then used to determine a first matrix vector product for any electrically large elements as well as a second matrix vector product for any electrically small elements that are included in the structure. These matrix vector products for the electrically large and small elements are combined, and a net delta for a combination of the matrix vector products is determined. The iteration continues until a net delta is obtained that is within the predefined limits. The matrix vector products that were last obtained are used to solve for the desired parameter. The solution for the desired parameter is then presented to a user in a tangible form; for example, on a display.

Jandhyala, Vikram↗
NASA NTRSDate not supplied

Students Solving Problems for ISS and Beyond: Inspiring the Next-Generation

Students Solving Problems for ISS and Beyond: Inspiring the Next-Generation Session Title: Students Solving Problems for ISS and Beyond: Inspiring the Next-Generation Session Description: NASA High school students United with NASA to Create Hardware (HUNCH) mission is to empower and inspire students through a Project-Based Learning program where 7-12 grade students learn 21st century skills and can launch their careers through participation in the design and fabrication of real-world valued products for NASA. With six different tracks consisting of Design & Prototype, Culinary Challenge, Softgoods, Precision Machining, Software, and Video Challenge, students are given the opportunity to create solutions for the International Space Station (ISS), the Moon, and beyond. Many projects are requested by the Crew to help ease living conditions, giving students the opportunity to make an impact on the lives of Astronauts. Other projects come directly from NASA and its partners. Join our session to learn how NASA is working with teachers across the country to mentor the next generation of scientists and engineers to solve some of NASA’s greatest challenges. Learning Outcomes: 1. Describe the NASA HUNCH Program, including the program objectives, goals, and strategic partnerships for middle school and high school outreach and advocacy efforts. 2. Identify the innovative strategies NASA is using to work with middle and high school students to solve real-world problems 3. Use the knowledge gained to inspire the next generation of scientists and engineers Session Track: Advocacy & Outreach Specialized Focus Area: Women in Government and Military Learning Level: Foundational Session Format: Listen & Learn Speaker Qualifications: 1. Deboshri Sadhukhan • Current Job Title: Deputy Project Manager • Topic Experience (years of experience related to proposed topic): 1-5 years • Biography: Deboshri Sadhukhan is an engineer for NASA Glenn Research Center (GRC). She has worked on numerous projects — from International Space Station (ISS) fluid technologies, to Orion European Service Module propulsion, to planetary science missions and other game-changing technologies. Her roles have ranged from Project Manager to System Safety Lead. She currently serves as a GRC Regional Mentor for the High school students United with NASA to Create Hardware (HUNCH) program. She also serves as Deputy Project Manager for an ISS payload and Safety & Mission Assurance Lead for a Radioisotope Power Systems project. In these roles, she oversees each phase of a project from beginning to end and provides leadership to increase the reliability, maintainability and system safety of hardware and personnel throughout the system life cycle. She holds a Bachelor of Science in Electrical Engineering from The University of Akron. 2. Nancy Hall • Current Job Title: Project Manager • Topic Experience: 20+ years • Biography: Nancy Rabel Hall earned a B.S. degree in Space Sciences from Florida Institute of Technology and a M.S. degree in Mechanical Engineering from the University of Toledo. She has been at NASA Glenn for over 30 years. She has led several International Space Station experiments that studied how the behavior of fluids and fluid systems behave differently in microgravity as compared to here on Earth. She is also the High school students United with NASA to Create Hardware (HUNCH) project manager, a program that allows students to design and fabricate hardware and softgoods for NASA as well as participate in a culinary and video challenge. She enjoys talking to the public and students about the work being done at NASA as well as showing students how math and science can be fun. She is an amateur radio operator, enjoys playing golf, and reading science fiction and fantasy books.

HUNCH↗
NASA NTRSDate not supplied

Content and Representation of Information Needed to Support Time-Constrained Problem Solving

NASA’s current mission-operations paradigm originated with Project Mercury and endured with minimum evolution through the Apollo Program, Space Shuttle Program, and ISS missions. At its foundation is a near-complete real-time dependence on a ground team to manage the combined state of the mission, vehicle, and crew. Utilizing many engineers and operators with broad and deep expertise; large, distributed datasets including extensive telemetry; and expansive analytical and computing power, this ground team has served as the safety net for crewed spaceflight missions over the past 60 years. This approach must change to address challenges associated with missions beyond low Earth orbit (BLEO), including infrequent resupply, reduced ability to evacuate, and delayed communications that prohibit real-time operational support. We anticipate that a necessary part of this change will be increased independence for the crew, as roles and responsibilities traditionally performed by ground teams move on board the vehicle. While many risks are associated with Earth-independent operations, one particular concern is ensuring that the crew will have adequate onboard support to perform urgent problem solving when communication with the ground is delayed or intermittent. A key resource that enables the ground team to respond to anomalies quickly and effectively is the extraordinary expertise and experience it possesses. It is comprised of 80+ experts on at any given time, with a combined 600+ years of system-specific experience across 22 unique console disciplines. A small crew will face the unprecedented challenge of independently responding to anomalies that have historically been handled by a team 20 times their size. Another important resource upon which the ground heavily relies to support procedure execution and anomaly response is data. The amount of telemetry data that each flight controller monitors is extensive. In addition, as the ground team works to further assess impacts, trouble shoot, identify workarounds, and oversee procedure execution, it accesses and synthesizes engineering and procedure information, as well as system build, test, and configuration documentation. It is not feasible nor useful to put all these data onboard as crews become more Earth independent. Each member of a small Mars mission small crew will have multiple roles beyond monitoring telemetry and data gathering, and multiple roles within anomaly resolution processes, thereby limiting their capacity for copious amounts of information. Moreover, while access is necessary, it alone is insufficient. Information will need to be compiled, refined, and represented appropriately to support the crew’s reduced attention and expertise. This work seeks to understand the content and representation of information needed to support time-constrained problem solving and decision making by the crew without real-time ground support. To build this understanding, we first surveyed the literature, focusing on how expert problem solvers construct and manipulate their mental models. Next, we interviewed expert problem solvers in spaceflight and analogous domains and surveyed industry solutions for data presentation. Finally, we analyzed current spaceflight operations by investigating flight controller anomaly resolution processes during ISS training simulations and real operational events. These methods led to creating a problem-solving framework that details common themes and features of attending to, assessing, analyzing, and acting on problems in complex, time-constrained domains. Using this framework and the results of our analysis, we identified conceptual data representations needed for crew-led problem-solving. Preliminary onboard user interface concepts to meet identified needs will be presented.

anomaly response↗
DOE OSTI2025

DS-TIDE: Harnessing Dynamical Systems for Efficient Time-Independent Differential Equation Solving

Time-Independent Differential Equations (TIDEs) are central to modeling equilibrium behavior across a wide range of scientific and engineering domains, from electrostatics to porous media flow. Conventional numerical solvers offer reliable solutions but incur significant computational costs due to fine-grained discretization and iterative procedures. Machine learning-based approaches address this by replacing iterative solving processes with one-time inference; however, their sophisticated models require extensive training resources that often exceed those of traditional solvers. Consequently, designing a TIDE solver that achieves high accuracy, broad applicability, and exceptional computational efficiency remains a fundamental challenge. In this paper, we propose DS-TIDE, a novel hardware solver that is inspired by, and subsequently leverages, the intrinsic connection between Dynamical Systems (DS) and Differential Equations (DEs) to efficiently and accurately solve TIDEs. DS-TIDE employs a CMOS-compatible DS-based processor, whose physical states evolve under carefully designed DE-driven dynamics and naturally converge to equilibrium -- the solution of the target TIDE -- within ~1µs on a ~1-watt DS-TIDE processor. To enhance expressivity, DS-TIDE incorporates Heterogeneous Dynamics with Temporal Layering (HDTL), which solves TIDEs through a three-stage DS evolution -- conditioning, solving, and decoding -- each governed by specialized dynamics. The entire evolution process is analogous to an infinitely deep neural network temporally unrolled, offering the system the capability of representing complex equations. Furthermore, DS-TIDE is equipped with an on-device DS-DE Auto-Alignment mechanism that dynamically adapts intrinsic hardware dynamics within milliseconds, effectively aligning the system’s dynamics to diverse target DEs. Experimental results across TIDEs from a wide range of scientific and engineering domains demonstrate that DS-TIDE achieves ~10^3× speedup, ~10^5× energy savings, and competitive or superior accuracy compared to state-of-the-art numerical and ML-based solvers.

Liu, Chuan↗
DOE OSTI2026

Solutions for Lasting, Viable Energy Infrastructure Technologies (SOLVE IT) Prize Final Technical Report

This is a final technical report for the American-Made The Solutions for Lasting, Viable Energy Infrastructure Technologies (SOLVE IT) Prize, funded by the Infrastructure Investments and Jobs Act through the Technology Commercialization Fund, administered by the U.S. Department of Energy (DOE) Office of Technology Commercialization (OTC) in collaboration with the Office of Clean Energy Demonstrations (OCED) and the Office of Energy Efficiency and Renewable Energy (EERE) with support from the National Laboratory of the Rockies (NLR). The SOLVE IT Prize aimed to enable local organizations to identify and implement innovative energy solutions in a way that works for their unique needs and challenges. The competition awarded $3,740,000 to winning teams across two phases. The prize was designed to support local stakeholders and organizations as they identified and implemented innovative energy solutions. In doing so, the SOLVE IT Prize looked to promote the commercialization of promising energy technologies that will lead to reliable, affordable energy across the U.S.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2025

Optical neural engine for solving scientific partial differential equations

Abstract Solving partial differential equations (PDEs) is the cornerstone of scientific research and development. Data-driven machine learning (ML) approaches are emerging to accelerate time-consuming and computation-intensive numerical simulations of PDEs. Although optical systems offer high-throughput and energy-efficient ML hardware, their demonstration for solving PDEs is limited. Here, we present an optical neural engine (ONE) architecture combining diffractive optical neural networks for Fourier space processing and optical crossbar structures for real space processing to solve time-dependent and time-independent PDEs in diverse disciplines, including Darcy flow equation, the magnetostatic Poisson’s equation in demagnetization, the Navier-Stokes equation in incompressible fluid, Maxwell’s equations in nanophotonic metasurfaces, and coupled PDEs in a multiphysics system. We numerically and experimentally demonstrate the capability of the ONE architecture, which not only leverages the advantages of high-performance dual-space processing for outperforming traditional PDE solvers and being comparable with state-of-the-art ML models but also can be implemented using optical computing hardware with unique features of low-energy and highly parallel constant-time processing irrespective of model scales and real-time reconfigurability for tackling multiple tasks with the same architecture. The demonstrated architecture offers a versatile and powerful platform for large-scale scientific and engineering computations.

Tang, Yingheng (ORCID:0009000153622546)↗