Search NASA⌕ Search

SEARCH · Search NASA

Results for “Complex dynamical systems”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 415 records · Page 23
All sourcesNASA NTRSDOE OSTI
NASA NTRS1997

Dynamics of Numerics & Spurious Behaviors in CFD Computations

The global nonlinear behavior of finite discretizations for constant time steps and fixed or adaptive grid spacings is studied using tools from dynamical systems theory. Detailed analysis of commonly used temporal and spatial discretizations for simple model problems is presented. The role of dynamics in the understanding of long time behavior of numerical integration and the nonlinear stability, convergence, and reliability of using time-marching approaches for obtaining steady-state numerical solutions in computational fluid dynamics (CFD) is explored. The study is complemented with examples of spurious behavior observed in steady and unsteady CFD computations. The CFD examples were chosen to illustrate non-apparent spurious behavior that was difficult to detect without extensive grid and temporal refinement studies and some knowledge from dynamical systems theory. Studies revealed the various possible dangers of misinterpreting numerical simulation of realistic complex flows that are constrained by available computing power. In large scale computations where the physics of the problem under study is not well understood and numerical simulations are the only viable means of solution, extreme care must be taken in both computation and interpretation of the numerical data. The goal of this paper is to explore the important role that dynamical systems theory can play in the understanding of the global nonlinear behavior of numerical algorithms and to aid the identification of the sources of numerical uncertainties in CFD.

Yee, Helen C.↗
DOE OSTI2025

Real-space observation of the dissociation of a transition metal complex and its concurrent energy redistribution

Mechanistic insights into photodissociation dynamics of transition metal carbonyls, like Fe(CO) 5 , are fundamental for understanding active catalytic intermediates. Although extensively studied, the structural dynamics of these systems remain elusive. Using ultrafast X-ray scattering, we uncover the photochemistry of Fe(CO) 5 in real space and time, observing synchronous oscillations in atomic pair distances, followed by a prompt rotating CO release preferentially in the axial direction. This behavior aligns with simulations, reflecting the interplay between the axial Fe-C distances’ potential energy landscape and non-adiabatic transitions between metal-to-ligand charge-transfer states. Additionally, we characterize a secondary delayed CO release associated with a reduction of Fe-C steady state distances and structural dynamics of the formed Fe(CO) 4 . Our results quantify energy redistribution across vibration, rotation, and translation degrees of freedom, offering a microscopic view of complex structural dynamics, enhancing our grasp on Fe(CO) 5 photodissociation, and advancing our understanding of transition metal catalytic systems.

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

Space‐Time Causal Discovery in Earth System Science: A Local Stencil Learning Approach

Causal discovery tools enable scientists to infer meaningful relationships from observational data, spurring advances in fields as diverse as biology, economics, and climate science. Despite these successes, the application of causal discovery to space-time systems remains immensely challenging due to the high-dimensional nature of the data. For example, in climate sciences, modern observational temperature records over the past few decades regularly measure thousands of locations around the globe. To address these challenges, we introduce Causal Space-Time Stencil Learning (CaStLe), a novel meta-algorithm for discovering causal structures in complex space-time systems. CaStLe leverages regularities in local space-time dependencies to learn governing global dynamics. This local perspective eliminates spurious confounding and drastically reduces sample complexity, making space-time causal discovery practical and effective. For causal discovery, CaStLe flexibly accepts any appropriately adapted time series causal discovery algorithm to recover local causal structures. These advances enable causal discovery of geophysical phenomena that were previously unapproachable, including non-periodic, transient phenomena such as volcanic eruption plumes. Regularities in local space-time dependencies are transformed into informative spatial replicates, which actually improve CaStLe's performance when applied to ever-larger spatial grids. We successfully apply CaStLe to discover the atmospheric dynamics governing the climate response to the 1991 Mount Pinatubo volcanic eruption. We provide validation experiments to demonstrate the effectiveness of CaStLe over existing causal-discovery frameworks on a range of geophysics-inspired benchmarks while identifying the method's limitations and domains where its assumptions may not hold.

Nichol, J. Jake [Univ. of New Mexico, Albuquerque,↗
DOE OSTI2026

Latent Twins

Over the past decade, scientific machine learning has transformed the development of mathematical and computational frameworks for analyzing, modeling, and predicting complex systems. From inverse problems to numerical partial differential equations (PDEs), dynamical systems, and model reduction, these advances have pushed the boundaries of what can be simulated. Yet they have often progressed in parallel, with representation learning and algorithmic solution methods evolving largely as separate pipelines. With Latent Twins, we propose a unifying mathematical framework that creates a hidden surrogate in latent space for the underlying equations. Whereas digital twins mirror physical systems in the digital world, Latent Twins mirror mathematical systems in a learned latent space governed by operators. Through this lens, classical modeling, inversion, model reduction, and operator approximation all emerge as special cases of a single principle. We establish the fundamental approximation properties of Latent Twins for both ordinary differential equations (ODEs) and PDEs and demonstrate the framework across three representative settings: (i) canonical ODEs, capturing diverse dynamical regimes; (ii) a PDE benchmark using the shallow-water equations, contrasting Latent Twin simulations with deep operator network and forecasts with a four-dimensional variational method baseline; and (iii) a challenging real-data geopotential reanalysis dataset, reconstructing and forecasting from sparse, noisy observations. Latent Twins provide a compact, interpretable surrogate for solution operators that evaluate across arbitrary time gaps in a single-shot, while remaining compatible with scientific pipelines such as assimilation, control, and uncertainty quantification. Looking forward, this framework offers scalable, theory-grounded surrogates that bridge data-driven representation learning and classical scientific modeling across disciplines.

Latent Twins↗
DOE OSTI2025

Efficient Streaming Dynamic Mode Decomposition

We propose a reformulation of the streaming dynamic mode decomposition method that requires maintaining a single orthonormal basis, thereby reducing computational redundancy. The proposed efficient streaming dynamic mode decomposition method results in a constant-factor reduction in computational complexity and memory storage requirements. Numerical experiments on representative canonical dynamical systems show that the enhanced computational efficiency does not compromise the accuracy of the proposed method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

The scientific case for concurrent neutron and X-ray scattering and spectroscopy

The interrogation of materials with X-rays or neutrons to determine structure, energetics, and dynamics is fundamental to advancing physical and chemical materials science and enabling innovative material technologies. A persistent challenge in materials development is that progress depends on understanding structure and dynamics across multiple length and time scales in increasingly complex, multicomponent systems featuring interfaces, heterogeneity, and hierarchical organization. Despite rapidly growing demands on materials characterization, current experimental approaches are almost exclusively based on isolated X-ray or neutron scattering and spectroscopy, reflecting a paradigm largely unchanged for decades. To assess the scientific need for a new experimental paradigm, a 3-day workshop sponsored by the U.S. National Science Foundation (NSF) was held at the SpringHill Suites, San Jose, California, from June 2 to 4, 2022. The workshop brought together 70 national and international experts who critically evaluated opportunities enabled by concurrent neutron and X-ray (NeX) scattering, spectroscopy, and imaging experiments. The participants reached a clear consensus that establishing NeX capabilities is crucial for advancing the science of complex materials in the United States. This report illustrates the scientific drivers for NeX experiments through representative examples spanning biomaterials, energy materials, soft matter, nanomaterials, quantum materials, geoscience, and applied materials research. The complementarity of neutrons and X-rays is essential for robust model development and refinement, particularly in multiphase and multicomponent systems. While joint refinement of data from separate experiments is valuable, concurrent measurements uniquely eliminate uncertainties arising from sample evolution, environmental drift, and irreproducibility associated with experiments performed at different locations and times. Realizing NeX capabilities will require the development of new instrumentation, data analysis frameworks, and robust sample environments compatible with both neutron and X-ray probes. Addressing these challenges will enable unambiguous interpretation of complex materials behavior and open new frontiers in materials research.

X-ray↗
NASA NTRS1987

Commit your works to the Lord, and your thoughts shall be established (Prov. 16:3). Inter-stable control systems

Algebraic structures are discussed for control systems that maintain stability in the presence of resonance uncertainties. Dual algebraic operations serve as elementary connections that propagate the stability of inter-stable subsystems. Frequency responses within complex half-planes define different types of inter-stability. Dominance between incompatible types is discussed. Inter-stability produces sufficient but unnecessary stability conditions, except for conservative systems where the conditions become also necessary. Multivariable systems, colocation of actuator and sensor, and virtual colocation are treated. Instead of passivity, inter-stability relates stability to the mapping of poles and zeros by transfer functions and transfer matrices. Inter-stability determines stability on the subsystem level, is less complex even for multivariable systems, adds design flexibility, and relaxes the dynamic data problem of large systems such as space stations.

Vonpragenau, George L.↗
NASA NTRS1989

Causal simulation and sensor planning in predictive monitoring

Two issues are addressed which arise in the task of detecting anomalous behavior in complex systems with numerous sensor channels: how to adjust alarm thresholds dynamically, within the changing operating context of the system, and how to utilize sensors selectively, so that nominal operation can be verified reliably without processing a prohibitive amount of sensor data. The approach involves simulation of a causal model of the system, which provides information on expected sensor values, and on dependencies between predicted events, useful in assessing the relative importance of events so that sensor resources can be allocated effectively. The potential applicability of this work to the execution monitoring of robot task plans is briefly discussed.

Doyle, Richard J.↗
NASA NTRS1994

Wavelets, period-doubling, and time-frequency localization with application to organization of convection over the tropical western Pacific

In this paper, preliminary results in using orthogonal and continuous wavelet transform (WT) to identify period doubling and time-frequency localization in both synthetic and real data are presented. First, the Haar WT is applied to synthetic time series derived from a simple nonlinear dynamical system- a first-order quadratic difference equation. Second, the complex Morlet WT is used to study the time-frequency localization of tropical convection based on a high-resolution Japanese Geostationary Meteorological Satellite infrared (IR) radiance dataset. The Haar WT of the synthetic time series indicates the presence and distinct separation of multiple frequencies in a period-doubling sequence. The period-doubling process generates a multiplicity of intermediate frequencies, which are manifested in the nonuniformity in time with respect to the phase of oscillations in the lower frequencies. Wavelet transform also enables the detection of extremely weak signals in high-order subharmonics resulting from the period-doubling bifurcations. These signals are either undetected or considered statistically insignificant by traditional Fourier analysis. The Morlet WT of the IR radiance dataset indicates the presence of multiple timescales, which are localized in both frequency and time. There are two regimes in the variation of IR radiance, corresponding to the wet and dry periods. Multiple timescales, ranging from semidiurnal, diurnal, synoptic, to intraseasonal with embedding structures, are active in the wet regime. In particular, synoptic variability is more prominent during the wet phase of an intensive intraseasonal cycle. These are not only consistent with, but also show more details than, previous findings by using other techniques. The phase-locking relationships among the oscillations with different time-scales suggest that both synoptic and intraseasonal variations may be mixed oscillations due to the interaction of self-excited oscillations in the tropical atmosphere and external forcings such as annual and diurnal solar radiation variations. Both examples show that WT is a powerful tool for analysis of phenomena involving multiscale interactions that exhibit localization in both frequency and time. A discussion on the caveats in the use of WT in geophysical data analysis is also presented.

Weng, Hengyi↗
NASA NTRS1997

HARV ANSER Flight Test Data Retrieval and Processing Procedures

Under the NASA High-Alpha Technology Program the High Alpha Research Vehicle (HARV) was used to conduct flight tests of advanced control effectors, advanced control laws, and high-alpha design guidelines for future super-maneuverable fighters. The High-Alpha Research Vehicle is a pre-production F/A-18 airplane modified with a multi-axis thrust-vectoring system for augmented pitch and yaw control power and Actuated Nose Strakes for Enhanced Rolling (ANSER) to augment body-axis yaw control power. Flight testing at the Dryden Flight Research Center (DFRC) began in July 1995 and continued until May 1996. Flight data will be utilized to evaluate control law performance and aircraft dynamics, determine aircraft control and stability derivatives using parameter identification techniques, and validate design guidelines. To accomplish these purposes, essential flight data parameters were retrieved from the DFRC data system and stored on the Dynamics and Control Branch (DCB) computer complex at Langley. This report describes the multi-step task used to retrieve and process this data and documents the results of these tasks. Documentation includes software listings, flight information, maneuver information, time intervals for which data were retrieved, lists of data parameters and definitions, and example data plots.

Yeager, Jessie C.↗
NASA NTRS2002

Alternative Metrics for Evaluating the Resilence of Advanced Life Support Systems

Ensuring the safety of the crew is a key performance requirement of a life support system. However, a number of conceptual and practical difficulties arise when devising metrics to concretely measure the ability of a life support system to maintain critical functions in the presence of anticipated and unanticipated faults. Resilience is a dynamic property of a life support system that depends on the complex interactions between faults, controls and system hardware. We review some of the approaches to understanding the robustness or resilience of complex systems being developed in diverse fields such as ecology, software engineering and cell biology and discuss their applicability to regenerative life support systems. We also consider how approaches to measuring resilience vary depending on system design choices such as the definition and choice of the nominal operating regime. Finally, we explore data collection and implementation issues such as the key differences between the instantaneous or conditional and average or overall measures of resilience. Extensive simulation of a hybrid computational model of a water revitalization subsystem (WRS) with probabilistic, component-level faults provides data about off-nominal behavior of the system. The data are used to consider alternative measures of resilience as predictors of the system's ability to recover from component-level faults.

Bell, Ann Maria↗
DOE OSTI2024

Tracking the dynamics of catalytic Pt/CeO2 active sites during water-gas-shift reaction

Abstract Understanding the atomistic structure of the active site during catalytic reactions is of paramount importance in both fundamental studies and practical applications, but such studies are challenging due to the complexity of heterogeneous systems. Here, we use Pt/CeO 2 as an example to study the dynamic nature of active sites during the water-gas-shift reaction (WGSR) by combining multiple in situ characterization tools. We show that the different concentrations of interfacial Pt δ+ – O – Ce 4+ moieties at Pt/CeO 2 interfaces are responsible for the rank of catalytic performance of Pt/CeO 2 catalysts: Pt/CeO 2 -rod > Pt/CeO 2 -cube > Pt/CeO 2 -oct. For all the catalysts, metallic Pt is formed during the WGSR, leading to the transformation of the active sites to Pt 0 – O v – Ce 3+ and interface reconstruction. These findings shed light on the nature of the active site for the WGSR on Pt/CeO 2 and highlight the importance of combining complementary in situ techniques for establishing structure-performance relationships.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Practical and Optimal Sequential Bayesian Experimental Design for Complex Systems Incorporating Human Experimenter Preferences (Final Scientific/Technical Report)

Experiments are indispensable for developing models of complex systems. Carefully designed experiments can provide substantial savings for these expensive data-acquisition opportunities. However, designs based on heuristics are often suboptimal for systems with multiphysics, nonlinear dynamics, and uncertain and noisy environments. Optimal experimental design, while leveraging predictive models, seeks to systematically quantify and maximize the value of experiments. In this project, we focused on the design of multiple experiments, where current approaches are largely suboptimal: batch-design does not adapt to new data acquired during the experiment campaign (no feedback), and greedy/myopic design ignores future dynamics and consequences (no lookahead). We developed the mathematical framework and computational methods for sequential optimal experimental design (sOED) for complex systems. We enabled tractable model-based sOED in a rigorous manner through novel algorithms based on reinforcement learning, and investigated the effects of human experimenters on the design process. Our methods are fully Bayesian, able to quantify and update uncertainty in a principled manner. The traits aimed by our approach—mathematical rigor and optimality, human effects and uncertainty quantification, computational practicality—are crucial for elevating the standards of artificial intelligence (AI) to support decision-making in scientific domains, and contribute toward trust and realistic adoption of AI in experimental design practice.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2005

Development of the Architectural Simulation Model for Future Launch Systems and its Application to an Existing Launch Fleet

A significant portion of lifecycle costs for launch vehicles are generated during the operations phase. Research indicates that operations costs can account for a large percentage of the total life-cycle costs of reusable space transportation systems. These costs are largely determined by decisions made early during conceptual design. Therefore, operational considerations are an important part of vehicle design and concept analysis process that needs to be modeled and studied early in the design phase. However, this is a difficult and challenging task due to uncertainties of operations definitions, the dynamic and combinatorial nature of the processes, and lack of analytical models and the scarcity of historical data during the conceptual design phase. Ultimately, NASA would like to know the best mix of launch vehicle concepts that would meet the missions launch dates at the minimum cost. To answer this question, we first need to develop a model to estimate the total cost, including the operational cost, to accomplish this set of missions. In this project, we have developed and implemented a discrete-event simulation model using ARENA (a simulation modeling environment) to determine this cost assessment. Discrete-event simulation is widely used in modeling complex systems, including transportation systems, due to its flexibility, and ability to capture the dynamics of the system. The simulation model accepts manifest inputs including the set of missions that need to be accomplished over a period of time, the clients (e.g., NASA or DoD) who wish to transport the payload to space, the payload weights, and their destinations (e.g., International Space Station, LEO, or GEO). A user of the simulation model can define an architecture of reusable or expendable launch vehicles to achieve these missions. Launch vehicles may belong to different families where each family may have it own set of resources, processing times, and cost factors. The goal is to capture the required resource levels of the major launch elements and their required facilities. The model s output can show whether or not a certain architecture of vehicles can meet the launch dates, and if not, how much the delay cost would be. It will also produce aggregate figures of missions cost based on element procurement cost, processing cost, cargo integration cost, delay cost, and mission support cost. One of the most useful features of this model is that it is stochastic where it accepts statistical distributions to represent the processing times mimicking the stochastic nature of real systems.

Rabadi, Ghaith↗
NASA NTRSDate not supplied

Predictive Modeling to Assess and Address Challenges and Limitations Associated with Clinical Care and Decision Support in Deep Space

Probabilistic risk assessment (PRA) is a method for assessing and integrating the risk of failure in a multivariate system. While it is often applied by engineers designing complex machines, it could also be applied to humans to assess the probability of a health “failure” treating diseases as the multiple “variables” and the human as the “complex machine.” The Medical Extensible Dynamic Probabilistic Risk Assessment Tool (MEDPRAT) was developed to apply PRA to assess medical risk for exploration spaceflight and inform the design of medical systems for space flight. The NASA engineering community utilizes event-driven and fault tree probabilistic techniques to classify risk in the space flight environment by leveraging the inherent knowledge of complex space flight system design and testing to quantify risk. However, in harmonizing the risk of human space flight, answering the question of “How do we balance astronaut health, performance and resource risks with other engineering risks on exploration space missions?” remains a profoundly challenging and largely qualitative practice. The Medical Extensible Dynamic Probabilistic Risk Assessment Tool (MEDPRAT) is one aspect of the Human Research Program’s efforts to represent space fight human health and performance risks quantitatively.

L Mcintyre↗
NASA NTRSDate not supplied

Adaptive Optimization for System Performance and Combined Bernstein Polynomial, Optimal Reciprocal Collision Avoidance, Differential Dynamic Programming for Trajectory Replanning and Collision Avoidance for UAM Vehicles

The emerging urban air mobility (UAM) sector in aerospace is driving development of unconventional multi-modal vehicle configurations and autonomous flight. The combination of multi-modal vehicle dynamics, complex environment, requirements to deal with flight contingencies in an efficient and safe manner, as well as necessity for precise trajectory following and performance, are the driving influence behind adaptive optimization for system performance. We are interested in trajectory optimization algorithm that would system parameter estimation and identifying the optimal switching time between modes of hybrid dynamical systems. This presentation discusses a parameterized optimal control trajectory optimization algorithm that is an extended and generalized version of Differential Dynamic Programming (DDP), titled Parameterized Differential Dynamic Programming (PDDP). DDP is an efficient trajectory optimization algorithm relying on second order approximations of a system’s dynamics and cost function and has recently been applied to optimize systems with time invariant parameters. Experiments are presented applying PDDP to solve model predictive control (MPC) and moving horizon estimation (MHE) tasks simultaneously. In particular, PDDP is used to determine the optimal transition point between flight regimes of a complex urban air mobility (UAM) class vehicle exhibiting multiple phases of flight and to identify and compensate for actuation faults.

optimization↗
NASA NTRS1985

A modal parameter extraction procedure applicable to linear time-invariant dynamic systems

Modal analysis has emerged as a valuable tool in many phases of the engineering design process. Complex vibration and acoustic problems in new designs can often be remedied through use of the method. Moreover, the technique has been used to enhance the conceptual understanding of structures by serving to verify analytical models. A new modal parameter estimation procedure is presented. The technique is applicable to linear, time-invariant systems and accommodates multiple input excitations. In order to provide a background for the derivation of the method, some modal parameter extraction procedures currently in use are described. Key features implemented in the new technique are elaborated upon.

Kurdila, A. J.↗