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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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At least 325 records · Page 18
All sourcesNASA NTRSDOE OSTI
NASA NTRS2008

Toward Optimal Transport Networks

Strictly evolutionary approaches to improving the air transport system a highly complex network of interacting systems no longer suffice in the face of demand that is projected to double or triple in the near future. Thus evolutionary approaches should be augmented with active design methods. The ability to actively design, optimize and control a system presupposes the existence of predictive modeling and reasonably well-defined functional dependences between the controllable variables of the system and objective and constraint functions for optimization. Following recent advances in the studies of the effects of network topology structure on dynamics, we investigate the performance of dynamic processes on transport networks as a function of the first nontrivial eigenvalue of the network's Laplacian, which, in turn, is a function of the network s connectivity and modularity. The last two characteristics can be controlled and tuned via optimization. We consider design optimization problem formulations. We have developed a flexible simulation of network topology coupled with flows on the network for use as a platform for computational experiments.

Alexandrov, Natalia↗
NASA NTRS2007

Fragmentation hierarchy of bright sungrazing comets and the birth and orbital evolution of the Kreutz System. II. the case for cascading fragmentation

We examine the process of cascading fragmentation for the Kreutz sungrazer system to continue our exploration of its birth, orbital evolution, and temporal clumping. We modify and broaden the two-superfragment model from Paper I to include clusters of ~30 bright comets spanning four centuries and 1000 SOHO sungrazers from 1996 to 2006. The spectacular parent sungrazer X/1106 C1 is assumed to have tidally split shortly after perihelion into a train of major protofragments immersed in a cloud of particulate debris, which at larger heliocentric distances were breaking up nontidally over and over again. We describe potential evolutionary paths for the Kreutz system by linking X/1106 C1 in subgroup I-type orbit with the comet of February 423 in one scenario or with the comet of February 467 in another. The latter scenario accounts for sungrazer clusters in as early as the 16th century, suggests that the progenitor object may have been observed as the comet of 214 BCE, is quite consistent with the orbital distribution of the SOHO sungrazers that sample the central filament of the Kreutz system between the clusters of major sungrazers, and predicts future clusters until ~2120. Comet X/1106 C1 and the common parent of C/1882 R1 and C/1965 S1 were two first-generation fragments of the progenitor that split nontidally on the way to its 5th century perihelion, reminiscent of the superfragments in Paper I. We provide computational tools needed for solving the problem of the Kreutz system’s orbital evolution, but no unique scenarios are presented for the individual comets. Another cluster of bright sungrazers is expected to arrive in the coming decades, its earliest member possibly just several years from now.

Chodas, Paul W.↗
DOE OSTI2025

GenomeFace v1.0

GenomeFace is meta-genome binning software. Metagenomic binning, the process of grouping DNA sequences into taxonomic units, is critical for understanding the functions, interactions, and evolutionary dynamics of microbial communities. We propose a deep learning approach to binning using two neural networks, one based on composition and another on environmental abundance, dynamically weighting the contribution of each based on characteristics of the input data. Trained on over 43,000 prokaryotic genomes, our network for composition-based binning is inspired by metric learning techniques used for facial recognition. Using a task-specific, multi-GPU accelerated algorithm to cluster the embeddings produced by our network, our binner leverages marker genes observed to be universally present in nearly all taxa to grade and select optimal clusters of sequences from a hierarchy of candidates. We evaluate our approach on four simulated datasets with known ground truth. Our linear time integration of marker genes recovers more near complete genomes than state of the art but computationally infeasible solutions using them, while being over an order of magnitude faster. Finally, we demonstrate the scalability and acuity of our approach by testing it on three of the largest metagenome assemblies ever performed. Compared to other binners, we produced 47%-183% more near complete genomes. From these datasets, we find over the genomes of over 3000 new candidate species which have never been previously cataloged, representing a potential 4% expansion of the known bacterial tree of life.

Lettich, Richard [Lawrence Berkeley National Labor↗
NASA NTRS1973

Star formation and evolution in spiral galaxies.

Evolutionary models for regions of M31 and M33 and the solar neighborhood are based on a stellar birthrate suggested by the dynamics of spiral structure: we assume that stars are formed very efficiently until the gas content reaches equilibrium at its present value, which takes about 1 b.y.; thereafter, the birthrate just equals the rate at which gas enters the system from stellar mass-loss or infall of intergalactic matter. Each model represents an average around a cylindrical-shell-shaped region, which is homogeneous and closed except for possible infall. The disk and spiral-arm populations only are considered. Each star is followed in the H-R diagram from the main sequence to death as an invisible remnant. Integrated magnitudes, colors, mass-to-light ratio (M/L), gas content, helium and metal abundance (Z), are computed in steps of 1 b.y.

Quirk, W. J.↗
NASA NTRS1998

Automatic Molecular Design using Evolutionary Techniques

Molecular nanotechnology is the precise, three-dimensional control of materials and devices at the atomic scale. An important part of nanotechnology is the design of molecules for specific purposes. This paper describes early results using genetic software techniques to automatically design molecules under the control of a fitness function. The fitness function must be capable of determining which of two arbitrary molecules is better for a specific task. The software begins by generating a population of random molecules. The population is then evolved towards greater fitness by randomly combining parts of the better individuals to create new molecules. These new molecules then replace some of the worst molecules in the population. The unique aspect of our approach is that we apply genetic crossover to molecules represented by graphs, i.e., sets of atoms and the bonds that connect them. We present evidence suggesting that crossover alone, operating on graphs, can evolve any possible molecule given an appropriate fitness function and a population containing both rings and chains. Prior work evolved strings or trees that were subsequently processed to generate molecular graphs. In principle, genetic graph software should be able to evolve other graph representable systems such as circuits, transportation networks, metabolic pathways, computer networks, etc.

Globus, Al↗
DOE OSTI2024

Comparative genomic analysis of thermophilic fungi reveals convergent evolutionary adaptations and gene losses

Thermophily is a trait scattered across the fungal tree of life, with its highest prevalence within three fungal families (Chaetomiaceae, Thermoascaceae, and Trichocomaceae), as well as some members of the phylum Mucoromycota. We examined 37 thermophilic and thermotolerant species and 42 mesophilic species for this study and identified thermophily as the ancestral state of all three prominent families of thermophilic fungi. Thermophilic fungal genomes were found to encode various thermostable enzymes, including carbohydrate-active enzymes such as endoxylanases, which are useful for many industrial applications. At the same time, the overall gene counts, especially in gene families responsible for microbial defense such as secondary metabolism, are reduced in thermophiles compared to mesophiles. We also found a reduction in the core genome size of thermophiles in both the Chaetomiaceae family and the Eurotiomycetes class. The Gene Ontology terms lost in thermophilic fungi include primary metabolism, transporters, UV response, and O-methyltransferases. Comparative genomics analysis also revealed higher GC content in the third base of codons (GC3) and a lower effective number of codons in fungal thermophiles than in both thermotolerant and mesophilic fungi. Furthermore, using the Support Vector Machine classifier, we identified several Pfam domains capable of discriminating between genomes of thermophiles and mesophiles with 94% accuracy. Using AlphaFold2 to predict protein structures of endoxylanases (GH10), we built a similarity network based on the structures. We found that the number of disulfide bonds appears important for protein structure, and the network clusters based on protein structures correlate with the optimal activity temperature. Thus, comparative genomics offers new insights into the biology, adaptation, and evolutionary history of thermophilic fungi while providing a parts list for bioengineering applications.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2025

Bayesian Optimized Deep Ensemble for Uncertainty Quantification of Deep Neural Networks: a System Safety Case Study on Sodium Fast Reactor Thermal Stratification Modeling

Deep neural networks (DNNs) are increasingly important to scientific computing and engineering system simulations. Accurate uncertainty quantification (UQ) for DNNs is critical in safety-sensitive engineering domains. Traditional Deep Ensemble (DE) methods, while easy to implement, frequently suffer from poorly calibrated uncertainty estimates and limited predictive accuracy due to reliance on fixed architectures with varied weight initializations. To address these issues, we introduce a workflow that combines Bayesian Optimization (BO) and DE. The workflow is modular, scalable, and integrates parallel BO initialized with Sobol sequences to individually optimize the hyperparameters of each ensemble member. This method enhances ensemble diversity, improves predictive accuracy, and provides reliable uncertainty estimates. We evaluate the proposed BODE approach in a sodium fast reactor thermal stratification modeling case study, where we used a densely connected convolutional neural network to predict turbulent viscosity during the reactor transient with consideration of data noise. We benchmark its performance against several optimization approaches, including baseline deep ensemble, evolutionary algorithm-optimized ensemble, ensemble formed via random search combined with greedy selection, and a BO ensemble using random initialization. Here, our results demonstrate superior performance of the developed BODE approach. In noise-free scenarios, BODE notably reduces incorrect aleatoric uncertainty and significantly enhances predictive accuracy. Under conditions of 5% and 10% Gaussian noise, BODE adaptively quantifies uncertainty proportional to data noise, achieving up to an 80% reduction in root mean square error compared to baseline methods and producing well-calibrated prediction intervals.

Bayesian optimization↗
DOE OSTI2025

Three-dimensional modeling of hyphal fusion, branching, and nutrient transport in filamentous fungi

Fungi exhibit behaviors distinct from other microbes. Filamentous fungi grow by extending complex networks of branched filaments collectively referred to as the mycelium. These networks can expand over large distances and traverse low-nutrient areas by translocating nutrients through the filament network. This spatial characteristic makes filamentous fungi crucial for soil ecosystems, supporting stable microbial communities and promoting plant growth. However, simulating these behaviors is complex. The elongated nature of fungal compartments results in different mechanical interactions compared to the commonly modeled spherical bacteria. These detailed hyphal mechanics require specialized consideration and are often excluded from conventional fungal simulation packages. Additionally, the extensive fungal networks in nature demand computationally intensive simulations, necessitating high-performance algorithms. Therefore, realistic fungi simulations require specialized software. Here, we introduce a fungal modeling expansion to the high-performance biological modelling and interface exchange (bmx) software suite. bmx leverages adaptive mesh refinement in AMReX for chemical diffusion and incorporates a full mechanical model for bacterial cells, accelerated by GPUs. By extending bmx to model filamentous particles, we demonstrate the formation of complex filament networks through interactions like hyphal branching and fusion (anastomosis). We show that the networks produced match real-world fungal structures through various metrics. This work supports computational studies of fungal growth dynamics and can be adapted to investigate the growth of other filamentous structures in biology or materials science. The expanded-BMX package is open-sourced and is available online.

Cell mechanics↗
NASA NTRS1990

Virtual workstations and telepresence interfaces: Design accommodations and prototypes for Space Station Freedom evolution

An advanced human-system interface is being developed for evolutionary Space Station Freedom as part of the NASA Office of Space Station (OSS) Advanced Development Program. The human-system interface is based on body-pointed display and control devices. The project will identify and document the design accommodations ('hooks and scars') required to support virtual workstations and telepresence interfaces, and prototype interface systems will be built, evaluated, and refined. The project is a joint enterprise of Marquette University, Astronautics Corporation of America (ACA), and NASA's ARC. The project team is working with NASA's JSC and McDonnell Douglas Astronautics Company (the Work Package contractor) to ensure that the project is consistent with space station user requirements and program constraints. Documentation describing design accommodations and tradeoffs will be provided to OSS, JSC, and McDonnell Douglas, and prototype interface devices will be delivered to ARC and JSC. ACA intends to commercialize derivatives of the interface for use with computer systems developed for scientific visualization and system simulation.

Mcgreevy, Michael W.↗
NASA NTRS2017

Exploring the Evolutionary Accident Hypothesis: Are Extant Protein Folds the Fittest or the Luckiest?

Considering the range of functions proteins perform, it is surprising they fold into a relatively small set of structures or "folds" that facilitate such function. One explanation is that only a minority were fit enough to emerge from Darwinian selection during the early evolution of life. Alternatively, perhaps only a fraction of all possible folds were trialed. Understanding proto-catalyst selection will aid understanding of the origins and early evolution of life. To investigate which explanation is correct, we study a protein evolved in vitro to bind ATP by Jack Szostak (Fig. 1). This protein adopts a fold which is absent from nature. We are testing whether this fold would have possessed the capability to evolve that would have been essential to survive natural selection on early Earth. Folds that couldn't improve their fitness and evolve to perform new functions would have been replaced by rivals that could. To determine whether the fold is evolvable, we are attempting to change the function of the protein by rationally redesigning to bind GTP. Two design strategies in the region of the nucleobase have been implemented to provide hydrogen bonding partners for the ligand i) an insertion ii) a MET to ASN mutation. Redesigns are being studied computationally at Ames Research Center including free energy of binding calculations. Binding affinities of promising redesigns are to be validated by experimental collaborators at ForteBio using Super Streptavidin Biosensors. If the fold is found to be non-evolvable, this may suggest that many structures were trialed, but the majority were pruned on the basis of their evolvability. Alternatively, if the fold is demonstrated to be evolvable, it would be difficult to explain its absence from nature without considering the possibility that the fold simply wasn't sampled on early Earth. This would not only further our understanding of the origins of life on Earth but also suggest a common phe-nomenon of proto-catalyst evolution.

Shannon, G.↗
DOE OSTI2024

Fate of supernova progenitors in massive binary systems

ABSTRACT How massive stars end their lives depends on the core mass, core angular momentum, and hydrogen envelopes at death. However, these key physical facets of stellar evolution can be severely affected by binary interactions. In turn, the effectiveness of binary interactions itself varies greatly depending on the initial conditions of the binaries, making the situation much more complex. We investigate systematically how binary interactions influence core–collapse progenitors and their fates. Binary evolution simulations are performed to survey the parameter space of supernova progenitors in solar metallicity binary systems and to delineate major evolutionary paths. We first study fixed binary mass ratios ($q=M_2/M_1$ = 0.5, 0.7, and 0.9) to elucidate the impacts of initial mass and initial separation on the outcomes, treating separately Type Ibc supernova, Type II supernova, accretion-induced collapse (AIC), rapidly rotating supernova (Ibc-R), black hole formation, and long gamma ray burst (long GRB). We then conduct 12 binary population synthesis model calculations, varying the initial condition distributions and binary evolution parameters, to estimate various supernova fractions. We obtain a Milky Way supernova rate $R_{\rm SN} = (1.78$–$2.47) \times 10^{-2} \, {\rm yr}^{-1}$ which is consistent with observations. We find the rates of AIC, Ibc-R, and long GRB to be $\sim 1/100$ the rate of regular supernovae. Our estimated long GRB rates are higher than the observed long GRB rate and close to the low luminosity GRB rate, although care must be taken considering our models are computed with solar metallicity. Furthering binary modelling and improving the inputs one by one will enable more detailed studies of these and other transients associated with massive stars.

Astronomy & Astrophysics↗
NASA NTRS1981

The estimation of genetic divergence

Consideration is given to the criticism of Nei and Tateno (1978) of the REH (random evolutionary hits) theory of genetic divergence in nucleic acids and proteins, and to their proposed alternative estimator of total fixed mutations designated X2. It is argued that the assumption of nonuniform amino acid or nucleotide substitution will necessarily increase REH estimates relative to those made for a model where each locus has an equal likelihood of fixing mutations, thus the resulting value will not be an overestimation. The relative values of X2 and measures calculated on the basis of the PAM and REH theories for the number of nucleotide substitutions necessary to explain a given number of observed amino acid differences between two homologous proteins are compared, and the smaller values of X2 are attributed to (1) a mathematical model based on the incorrect assumption that an entire structural gene is free to fix mutations and (2) the assumptions of different numbers of variable codons for the X2 and REH calculations. Results of a repeat of the computer simulations of Nei and Tateno are presented which, in contrast to the original results, confirm the REH theory. It is pointed out that while a negative correlation is observed between estimations of the fixation intensity per varion and the number of varions for a given pair of sequences, the correlation between the two fixation intensities and varion numbers of two different pairs of sequences need not be negative. Finally, REH theory is used to resolve a paradox concerning the high rate of covarion turnover and the nature of general function sites as permanent covarions.

Holmquist, R.↗
NASA NTRS1992

Distributed digital signal processors for multi-body flexible structures

Multi-body flexible structures, such as those currently under investigation in spacecraft design, are large scale (high-order) dimensional systems. Controlling and filtering such structures is a computationally complex problem. This is particularly important when many sensors and actuators are located along the structure and need to be processed in real time. This report summarizes research activity focused on solving the signal processing (that is, information processing) issues of multi-body structures. A distributed architecture is developed in which single loop processors are employed for local filtering and control. By implementing such a philosophy with an embedded controller configuration, a supervising controller may be used to process global data and make global decisions as the local devices are processing local information. A hardware testbed, a position controller system for a servo motor, is employed to illustrate the capabilities of the embedded controller structure. Several filtering and control structures which can be modeled as rational functions can be implemented on the system developed in this research effort. Thus the results of the study provide a support tool for many Control/Structure Interaction (CSI) NASA testbeds such as the Evolutionary model and the nine-bay truss structure.

Lee, Gordon K. F.↗
NASA NTRS1992

System model development for nuclear thermal propulsion

A critical enabling technology in the evolutionary development of nuclear thermal propulsion (NTP) is the ability to predict the system performance under a variety of operating conditions. This is crucial for mission analysis and for control subsystem testing as well as for the modeling of various failure modes. Performance must be accurately predicted during steady-state and transient operation, including startup, shutdown, and post operation cooling. The development and application of verified and validated system models has the potential to reduce the design, testing, and cost and time required for the technology to reach flight-ready status. Since Oct. 1991, the U.S. Department of Energy (DOE), Department of Defense (DOD), and NASA have initiated critical technology development efforts for NTP systems to be used on Space Exploration Initiative (SEI) missions to the Moon and Mars. This paper presents the strategy and progress of an interagency NASA/DOE/DOD team for NTP system modeling. It is the intent of the interagency team to develop several levels of computer programs to simulate various NTP systems. The first level will provide rapid, parameterized calculations of overall system performance. Succeeding computer programs will provide analysis of each component in sufficient detail to guide the design teams and experimental efforts. The computer programs will allow simulation of the entire system to allow prediction of the integrated performance. An interagency team was formed for this task to use the best capabilities available and to assure appropriate peer review.

Walton, James T.↗
NASA NTRS1998

Classification and evolution of EF-hand proteins

Forty-five distinct subfamilies of EF-hand proteins have been identified. They contain from two to eight EF-hands that are recognizable by amino acid sequence as being statistically similar to other EF-hand domains. All proteins within one subfamily are congruent to one another, i.e. the dendrogram computed from one of the EF-hand domains is similar, within statistical error, to the dendrogram computed from another(s) domain. Thirteen subfamilies--including Calmodulin, Troponin C, Essential light chain, Regulatory light chain--referred to collectively as CTER, are congruent with one another. They appear to have evolved from a single ur-domain by two cycles of gene duplication and fusion. The subfamilies of CTER subsequently evolved by gene duplications and speciations. The remaining 32 subfamilies do not show such general patterns of congruence; however, some--such as S100, intestinal calcium binding protein (calbindin 9 kd), and trichohylin--do not form congruent clusters of subfamilies. Nearly all of the domains 1, 3, 5, and 7 are most similar to other ODD domains. Correspondingly the EVEN numbered domains of all 45 subfamilies most closely resemble EVEN domains of other subfamilies. Many sequence and chemical characteristics do not show systemic trends by subfamily or species of host organisms; such homoplasy is widespread. Eighteen of the subfamilies are heterochimeric; in addition to multiple EF-hands they contain domains of other evolutionary origins.

Non-NASA Center↗
NASA NTRS2021

Generation-based Evolutionary Tool for the Optimization of Constellations (GenETOC)

With the rapid growth in the capabilities of smaller satellites, satellite architectures that replace a single, extremely capable spacecraft with multiple, cheaper ones are gaining in popularity. Unfortunately, the orbit design process for constellations can be significantly more involved, especiallywhen the relative placement of the individual spacecraft within the constellation is not constrained by mission and/or science objectives. Optimizing a satellite constellation in the presence of multiple, competing objectives is a highly complex problem to which many traditional mathematical optimization methods cannot be applied and few tools exist to help mission designers search for promising candidate mission designs. The Generation-based Evolutionary Tool for the Optimization of Constellations (GenETOC) has been created to search for near-optimal constellation design options. GenETOC combines a modified version of the Non-dominated Sorting Genetic Algorithm II (NSGA II) with STK Components libraries (a 3rdparty .NET package created by Analytical Graphics Inc.) to create a framework that enables a mission designer to generate a simulation that models the design problem and obtain a family of potential, near-optimal solutions that can be investigated more in detail. GenETOC was developed in C# using the .NET framework with Windows Presentation Foundation (WPF) serving as the framework from which to create the graphical user interface (GUI). GenETOC user inputs can be categorized into three major data components: definition of the problem (areas of interest, satellite decision parameters, and sensor configurations), definition of performance objectives, and specification of the genetic algorithm (GA) parameters. In the problem definition component, the user is prompted to define the areas of interest against which the performance metrics will be computed, define the sensor parameters and attach them to specific spacecraft, select which satellite orbital parameters will be added to the decision space of the GA, and specify the range of desired values for each optimization parameter. For performance objectives, the user is presented with a list of available coverage and revisit performance based calculation options from which two metrics are chosen to serve as the objective functions that the GA will use to evaluate solutions during the optimization process. Finally, the definition of the GA parameters provides user control over the number of generations (number of optimization iterations), the population size (number of candidate constellations created in each generation), and the adaptive mutation and crossover threshold values (control parameters for how frequently each process occurs during the optimization). GenETOC has been extensively tested to verify the individual components of the optimization process. The GA has been tested against a suite of GA test problems to confirm convergence to the known two and three-dimensional Pareto fronts. The coverage and revisit performance metrics obtained in GenETOC are compared with STK desktop scenarios, confirming the constellations are being appropriately modeled within GenETOC simulations. A walkthrough of a simple, example problem is provided to illustrate the workings of GenETOC and to demonstrate the output available to the mission designer.

mission design↗
DOE OSTI2025

Web-Based Tools for Data-Informed Remedy Optimization: Software Theory and User Guide

This report documents the development and application of two web-based decision-support tools for pump-and-treat (P&T) groundwater remediation systems: PTOLEMY (Pump-and-Treat Optimized Location Evaluation to Maximize Yields) and OPTIMA (Optimization for Pump-and-Treat Implementation, Management, & Assessment). These tools enhance remedy design and management by leveraging advanced computational methods – specifically deep learning and multi-objective optimization – within a user-friendly platform. By integrating data-driven models with established hydrogeological knowledge, PTOLEMY and OPTIMA enable more efficient evaluation of well placement and operational strategies, helping site managers balance multiple remediation objectives under complex conditions. Both tools are implemented as modules within the SOCRATES (Suite Of Comprehensive Rapid Analysis Tools for Environmental Sites) web platform, which provides data access, visualization, and analytics to support remedy optimization across sites in the U.S. Department of Energy Office of Environmental Management complex. PTOLEMY is a rapid screening module designed to identify promising locations for new extraction wells. It employs a multi-channel three-dimensional convolutional neural network (MC3D-CNN) trained on high-fidelity simulation data to predict the relative performance (in terms of contaminant mass recovery) of potential well sites. Through an interactive web interface, PTOLEMY visualizes the probability of high performance across a site, highlighting areas where an extraction well is likely to yield above-threshold contaminant removal over a multi-year period. PTOLEMY’s map-based displays and exportable results support transparent communication of screening analyses. By focusing attention on the most favorable candidate locations, the tool augments traditional engineering judgment and physics-based modeling, providing a data informed basis for subsequent detailed evaluations. OPTIMA is a multi objective optimization module designed to find wellfield layouts and operating schedules that meet various cleanup goals. It quickly evaluates thousands of candidate setups – combinations of well locations, timing, and rates – and returns a small set of best trade-off options for comparison. At its core, OPTIMA uses a U-Net-based surrogate model – a deep-learning emulator of a groundwater flow and transport simulator – to dramatically accelerate scenario evaluations. Coupling this fast surrogate with the NSGA-II (Non-dominated Sorting Genetic Algorithm II) evolutionary algorithm, OPTIMA explores a wide decision space of well locations and schedules to identify Pareto-optimal solutions that trade off key objectives (e.g., minimizing cleanup time, maximizing contaminant mass removal, and minimizing plume extent). The tool outputs a family of optimal configurations and visualizes their trade-offs (Pareto frontiers of cleanup metrics and maps of optimized well placements). Site managers can use these results to understand the range of viable strategies and to select candidate designs for more detailed verification. OPTIMA is currently under active development and not yet fully released; this guide provides early documentation to support planning and gather user feedback.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

On Properties of Adjoint Systems for Evolutionary PDEs

We investigate the geometric structure of adjoint systems associated with evolutionary partial differential equations at the fully continuous, semi-discrete, and fully discrete levels and the relations between these levels. We show that the adjoint system associated with an evolutionary partial differential equation has an infinite-dimensional Hamiltonian structure, which is useful for connecting the fully continuous, semi-discrete, and fully discrete levels. We subsequently address the question of discretize-then-optimize versus optimize-then-discrete for both semi-discretization and time integration, by characterizing the commutativity of discretize-then-optimize methods versus optimize-then-discretize methods uniquely in terms of an adjoint-variational quadratic conservation law. For Galerkin semi-discretizations and one-step time integration methods in particular, we explicitly construct these commuting methods by using structure-preserving discretization techniques.

97 MATHEMATICS AND COMPUTING↗