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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 145 records · Page 8

Fluid & Thermal Analysis of a Manifold Microchannel Heat Sink

A three-dimensional (3-D) numerical model has been developed to study the fluid flow and heat transfer through a manifold-microchannel (MMC) heat sink, a microfluidic cooling system designed as a heat dissipation solution for compact, high-powered electronic systems. An MMC consists of a 3-D manifold structure that distributes working fluid through alternating inlet and outlet manifold channels that guide the fluid to and from the microchannels, shortening the flow length and thereby, reducing the pressure drop across the system. Wide bandgap semiconductors such as silicon carbide (SiC) are increasingly utilized due to their ability to enable smaller electronic devices and components to operate more efficiently at higher frequencies. These semiconductors can greatly benefit from the MMC, which can extract all the heat produced by compact, high-powered electronics, enabling them to achieve optimal performance. The MMC also utilizes an embedded cooling approach which allows for fabrication directly within SiC-based electronics, resulting in significant mass and weight savings and lower thermal resistance than conventional heat sink designs. This paper outlines the methods used to conduct fluid and thermal analysis of different MMC configurations for flow parameters such as flow rate and inlet flow conditions. This study involves both steady state and transient thermal analysis as a gradually increasing heat flux is applied to the system over time, which is representative of the heat dissipation from the electronics over a given period. Results from the analysis show that the MMC is capable of effectively dissipating heat flux of ~100 W/cm2 while maintaining considerably low pressure drop (< 1 kPa) and thermal resistance (< 1 K/W) for certain single-phase working fluids.

manifold microchannel↗

Fluid & Thermal Analysis of a Manifold Microchannel Heat Sink

A three-dimensional (3-D) numerical model has been developed to study the fluid flow and heat transfer through a manifold-microchannel (MMC) heat sink, a microfluidic cooling system designed as a heat dissipation solution for compact, high-powered electronic systems. An MMC consists of a 3-D manifold structure that distributes working fluid through alternating inlet and outlet manifold channels that guide the fluid to and from the microchannels, shortening the flow length and thereby, reducing the pressure drop across the system. Wide bandgap semiconductors such as silicon carbide (SiC) are increasingly utilized due to their ability to enable smaller electronic devices and components to operate more efficiently at higher frequencies. These semiconductors can greatly benefit from the MMC, which can extract all the heat produced by compact, high-powered electronics, enabling them to achieve optimal performance. The MMC also utilizes an embedded cooling approach which allows for fabrication directly within SiC-based electronics, resulting in significant mass and weight savings and lower thermal resistance than conventional heat sink designs. This paper outlines the methods used to conduct fluid and thermal analysis of different MMC configurations for flow parameters such as flow rate and inlet flow conditions. This study involves both steady state and transient thermal analysis as a gradually increasing heat flux is applied to the system over time, which is representative of the heat dissipation from the electronics over a given period. Results from the analysis show that the MMC is capable of effectively dissipating heat flux of ~100 W/cm2 while maintaining considerably low pressure drop (< 1 kPa) and thermal resistance (< 1 K/W) for certain single-phase working fluids.

manifold microchannel↗

Exhaust emission reduction for intermittent combustion aircraft engines

Three concepts for optimizing the performance, increasing the fuel economy, and reducing exhaust emission of the piston aircraft engine were investigated. High energy-multiple spark discharge and spark plug tip penetration, ultrasonic fuel vaporization, and variable valve timing were evaluated individually. Ultrasonic fuel vaporization did not demonstrate sufficient improvement in distribution to offset the performance loss caused by the additional manifold restriction. High energy ignition and revised spark plug tip location provided no change in performance or emissions. Variable valve timing provided some performance benefit; however, even greater performance improvement was obtained through induction system tuning which could be accomplished with far less complexity.

Moffett, R. N.↗

Development of a High Output Fluorescent Light Module for the Commercial Plant Biotechnology Facility

To maximize the use of available resources provided onboard the International Space Station, the development of an efficient lighting 1 system is critical to the overall performance of the CPBF. Not only is it important to efficiently generate photon energy, but thermal loads on the CPBF Temperature and Humidity Control System must be minimized. By utilizing optical coatings designed to produce highly diffuse reflectance in the visible wavelengths while minimizing reflectance in the infrared region, the design of the fluorescent light module for the CPBF is optimized for maximum photon flux, spatial uniformity and energy efficiency. Since the Fluorescent Light Module must be fully enclosed to meet (ISS) requirements for containment of particulates and toxic materials, heat removal from the lights presented some unique design challenges. By using the Express Rack moderate C, temperature-cooling loop, heat is rejected by means of a liquid/air coolant manifold. Heat transfer to the manifold is performed by conduction using copper fins, by forced air convection using miniature fans, and by radiation using optically selective coatings that absorb in the infrared wavelengths. Using this combination of heat transfer mechanisms builds in redundancy to prevent thermal build up and premature bulb failure.

Turner, Mark↗

Dual-Fuel Ammonia Equivalence Ratio Sweep Data

Ammonia (NH3) has garnered significant interest as an alternative fuel for meeting international emissions reduction mandates in sectors with high weight and distance requirements, such as shipping. Technical barriers and unanswered questions remain on the combustion strategies that can maximize ammonia utilization and minimize emissions. Prior research studies at the US Department of Energy’s Oak Ridge National Laboratory have shown strong performance with NH3 under dual-fuel mode using conventional diesel combustion (CDC) manifold air pressure settings. Diesel airflow was initially used to simplify retrofitting (no turbocharger modification), which resulted in air-fuel equivalence ratios (λ) greater than 1.5. To characterize potential improvements in dual-fuel NH3 combustion performance at richer in-cylinder conditions, a global λ sweep compared the use of early (E-pilot) and late (L-pilot) single diesel injections. The experiments were conducted at 1200 RPM and 12.8 ± 0.2 bar (75 % load), and λ was varied by decreasing the commanded air flow to the engine at greater than 90 % ammonia energy substitution level. A diesel injection timing sweep was conducted for both the injection strategies at fixed λ, and the timing with the lowest engine-out N2O emissions was identified. The results indicated an optimal balance between CO2,eq and thermal efficiency benefits both E-pilot and L-pilot injection strategy cases compared with CDC at a λ of 1.4. The indicated nitrogen-based emissions exhibited a strong correlation to the ratio of CA5–50 and ignition delay for L-pilot, but no apparent trend emerged for the E-pilot injection strategy at the tested boundary conditions. This dataset includes the raw experimental data and documentation of the experiment conditions and methods.

30 DIRECT ENERGY CONVERSION↗

Experimental Studies of Low-Load Limit in a Stoichiometric Micro-Pilot Diesel Natural Gas Engine

While operating at light loads, diesel pilot-ignited natural gas engines with lean premixed natural gas suffer from poor combustion efficiency and high methane emissions. This work investigates the limits of low-load operation for a micro-pilot diesel natural gas engine that uses a stoichiometric mixture to enable methane and nitrogen oxide emission control. By optimizing engine hardware, operating conditions, and injection strategies, this study focused on defining the lowest achievable load while maintaining a stoichiometric equivalence ratio and with acceptable combustion stability. A multi-cylinder diesel 6.7 L engine was converted to run natural gas premix with a maximum diesel micro-pilot contribution of 10%. With a base diesel compression ratio of 17.3:1, the intake manifold pressure limit was 80 kPa(absolute). At a reduced compression ratio of 15:1, this limit increased to 85 kPa, raising the minimum stable load. Retarding the combustion phasing, typically used in spark-ignition engines to achieve lower loads, was also tested but found to be limited by degraded diesel ignition at later timings. Reducing the pilot injection pressure improved combustion stability, as did increasing pilot quantity at the cost of lower substitution ratios. The lean operation further reduced load but increased NOx and hydrocarbon emissions. At loads below the practical dual-fuel limit, a transition to lean diesel operation will likely be required with corresponding implications for the aftertreatment system.

03 NATURAL GAS↗

Lithium-Ion Battery Diagnostics Using Electrochemical Impedance via Machine-Learning

Diagnosing battery states such as health, state-of-charge, or temperature is crucial for ensuring the safety and reliability of electrochemical energy storage systems. While some states, such as temperature, may be measured using cheap sensors, accurate diagnosis of battery health metrics usually requires time-consuming performance measurements, making them infeasible for use in real-world operation. These health metrics can be measured during lab-testing and then estimated on-line using predictive life models or via state observer algorithms such as Kalman filters, but these predictive methods should be supplemented by actual measurement of battery health whenever possible to ensure reliability. Rapid measurement of battery health may be done by various types of fast diagnostic techniques such as electrochemical impedance spectroscopy (EIS), which can be performed in only a few minutes and require only a fraction of the energy and power needed for a full charge and discharge measurement. But there is a substantial challenge for estimating battery health using EIS data, as EIS is sensitive to cell temperature, state-of-charge, current, and resting time in addition to health. Thus, utilizing EIS data to predict battery capacity requires correcting for all these additional variables, a task that is extremely difficult to handle analytically. This talk utilizes machine-learning methods to estimate the effectiveness of battery capacity prediction from EIS data, leveraging a data set of hundreds of EIS measurements recorded at varying temperature and state-of-charge throughout a 500-day aging study of 32 commercial, large-format NMC-Graphite lithium-ion batteries. Using EIS as input to machine-learning models is complicated by the nonlinear response of impedance to battery health, temperature, and state-of-charge, as well as the collinearity between the impedance response at neighboring frequencies, which can easily lead to overfit models. To train robust models, features from EIS data need to be extracted from the data or some subset of critical frequencies selected. Many approaches for extracting and selecting features from EIS data from electrochemical analysis and machine-learning fields were identified for analysis: using the entire raw spectra; selection of one, two, or many frequencies from the entire spectra; selecting interesting points from the EIS measurement using domain knowledge; fitting EIS with an equivalent-circuit model; calculating statistics on the raw impedance values; and reducing the dimensionality of the data using unsupervised linear (principal component analysis) and non-linear (uniform manifold approximation and projection) methods. These approaches were rigorously compared using a machine-learning pipeline approach, training linear, Gaussian process, and random forest regression models and quantifying performance using cross-validation as well as a held-out test set. An artificial neural network model trained on the raw spectra was also tested. Promising pipelines were fine-tuned via Bayesian hyperparameter optimization using cross-validation loss and training with class-specific weights to counter data set imbalance. The most reliable method for utilizing impedance in this work was the selection of two optimal frequencies through an exhaustive search, resulting in about 2% mean absolute error on test data for both Gaussian process and random forest model architectures. Interrogation of a variety of models reveals critical frequencies of 100 Hz and 103 Hz for this data set, though the optimal set of frequencies is not necessarily intuitive, i.e., the best performing models are not simply those that use impedance at frequencies that have the highest correlation to the relative discharge capacity. The best performing model is an ensemble model, which is able to predict battery capacity with 1.9% mean absolute error for unseen cells using impedance recorded at a variety of temperatures and states-of-charge.

battery↗

An a priori evaluation of a principal component and artificial neural network based combustion model in diesel engine conditions

A principal component analysis (PCA) and artificial neural network (ANN) based chemistry tabulation approach is presented. ANNs are used to map the thermochemical state onto a low-dimensional manifold consisting of five control variables that have been identified using PCA. Three canonical configurations are considered to train the PCA-ANN model: a series of homogeneous reactors, a nonpremixed flamelet, and a two-dimensional lifted flame. The performance of the model in predicting the thermochemical manifold of a spatially-developing turbulent jet flame in diesel engine thermochemical conditions is a priori evaluated using direct numerical simulation (DNS) data. The PCA-ANN approach is compared with a conventional tabulation approach (tabulation using ad hoc defined control variables and linear interpolation). The PCA-ANN model provides higher accuracy and requires several orders of magnitude less memory. Here, these observations indicate that the PCA-ANN model is superior for chemistry tabulation, especially for modelling complex chemistries that present multiple combustion modes as observed in diesel combustion. The performance of the PCA-ANN model is then compared to the optimal estimator, i.e. the conditional mean from the DNS. The results indicate that the PCA-ANN model gives high prediction accuracy, comparable to the optimal estimator, especially for major species and the thermophysical properties. Higher errors are observed for the minor species and reaction rate predictions when compared to the optimal estimator. It is shown that the prediction of minor species and reaction rates can be improved by using training data that exhibits a variation of parameters as observed in the turbulent flame. The output of the ANN is analysed to assess mass conservation. It is observed that the ANN incurs a mean absolute error of 0.05% in mass conservation. Furthermore, it is demonstrated that this error can be reduced by modifying the cost function of the ANN to penalise for deviation from mass conservation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Optimal Low Thrust Orbit Transfers for Space Telescope Refueling at SEL2

The James Webb Space Telescope (JWST), a ten billion-dollar infrared telescope with a 6.5m primary mirror to be launched in 2021, is designed to operate in a Halo orbit around the second Sun-Earth Lagrange point (SEL2) for five to ten years. At that point fuel for station keeping and attitude maneuvers will run out. Refueling missions to JWST, as well as to similar space telescope missions proposed for SEL2, could greatly enhance the “science-per-dollar” value and promote a more sustainable use of space assets. In this paper, we present a novel approach to designing fuel optimal trajectories that will allow the refueling spacecraft to arrive at the SEL2 Halo orbit with maximum final mass (i.e. fuel payload). The low thrust optimal control problem is formulated using an indirect optimization method, leading to a two-point boundary value problem with a bang-bang control structure. We make use of a hyperbolic tangent smoothing technique for performing continuation on the thrust magnitude to reduce the sharpness of the control switches in early iterations and, thus, promote convergence. The problem is posed and solved in the circular restricted three-body problem. In this dynamical system, invariant manifolds exist that can be utilized to reduce fuel consumption. The here presented methodology to this challenging and important problem in astrodynamics demonstrates a significant potential for low-cost refueling mission design.

Woollands, Robyn↗

Low Greenhouse Gas (GHG) Vehicle Technologies Research, Development, Demonstration and Deployment Topic 5 Natural Gas Engine Enabling Technologies

A 10 liter natural gas engine has been developed with significant improvements in efficiency while maintaining ultra low NOx emissions and meeting all other EPA criteria emissions limits. This was accomplished through design and analysis of performance components specifically for operation with natural gas in contrast to current production engines which are a minimally modified diesel engine that retain most diesel design features including a flat deck swirl head. The architecture developed here includes a pent roof cylinder head with tumble charge motion and cooling passages specifically optimized for effective cooling around the spark plug and valve bridges. Also in contrast to current production natural gas engines, EGR was not used, in part to avoid the initial cost and warranty expense associated with EGR systems, but also for performance benefits of faster combustion, reduced risk of misfire and high open cycle efficiency due to the turbocharger’s ability to extract energy from the high temperature exhaust. The exhaust manifold uses high temperature material and thermal mechanical fatigue analysis was completed to ensure the ability to withstand high exhaust temperatures without EGR. Other features include dual overhead cam with late intake valve closing Miller cycle and 14:1 compression ratio steel pistons. Low NOx emissions are achieved with stoichiometric combustion and application of a close coupled plus underfloor three way catalysts. The program target of peak brake thermal efficiency of 42% has been demonstrated along with bsNOx of 0.02 g/hp-hr over HD-FTP and RMCSET emissions cycles.

99 GENERAL AND MISCELLANEOUS↗

Fuel-Optimal Trajectories in a Planet-Moon Environment Using Multiple Gravity Assists

For low energy spacecraft trajectories such as multi-moon orbiters for the Jupiter system, multiple gravity assists by moons could be used in conjunction with ballistic capture to drastically decrease fuel usage. In this paper, we outline a procedure to obtain a family of zero-fuel multi-moon orbiter trajectories, using a family of Keplerian maps derived by the first author previously. The maps capture well the dynamics of the full equations of motion; the phase space contains a connected chaotic zone where intersections between unstable resonant orbit manifolds provide the template for lanes of fast migration between orbits of different semimajor axes. Patched three body approach is used and the four body problem is broken down into two three-body problems, and the search space is considerably reduced by the use of properties of the Keplerian maps. We also introduce the notion of Switching Region where the perturbations due to the two perturbing moons are of comparable strength, and which separates the domains of applicability of the corresponding two Keplerian maps.

Ross, Shane D.↗

Manifold Learning-Based Polynomial Chaos Expansions for High-Dimensional Surrogate Models

In this work we introduce a manifold learning-based method for uncertainty quantification (UQ) in systems describing complex spatiotemporal processes. Our first objective is to identify the embedding of a set of high-dimensional data representing quantities of interest of the computational or analytical model. For this purpose, we employ Grassmannian diffusion maps, a two-step nonlinear dimension reduction technique which allows us to reduce the dimensionality of the data and identify meaningful geometric descriptions in a parsimonious and inexpensive manner. Polynomial chaos expansion is then used to construct a mapping between the stochastic input parameters and the diffusion coordinates of the reduced space. An adaptive clustering technique is proposed to identify an optimal number of clusters of points in the latent space. The similarity of points allows us to construct a number of geometric harmonic emulators which are finally utilized as a set of inexpensive pretrained models to perform an inverse map of realizations of latent features to the ambient space and thus perform accurate out-of-sample predictions. Thus, the proposed method acts as an encoder-decoder system which is able to automatically handle very high-dimensional data while simultaneously operating successfully in the small-data regime. The method is demonstrated on two benchmark problems and on a system of advection-diffusion-reaction equations which model a first-order chemical reaction between two species. In all test cases, the proposed method is able to achieve highly accurate approximations which ultimately lead to the significant acceleration of UQ tasks.

42 ENGINEERING↗

“Freedom of design” in chemical compound space: towards rational in silico design of molecules with targeted quantum-mechanical properties

The rational design of molecules with targeted quantum-mechanical (QM) properties requires an advanced understanding of the structure–property/property–property relationships (SPR/PPR) that exist across chemical compound space (CCS). In this work, we analyze these fundamental relationships in the sector of CCS spanned by small (primarily organic) molecules using the recently developed QM7-X dataset, a systematic, extensive, and tightly converged collection of 42 QM properties corresponding to ≈4.2M equilibrium and non-equilibrium molecular structures containing up to seven heavy/non-hydrogen atoms (including C, N, O, S, and Cl). By characterizing and enumerating progressively more complex manifolds of molecular property space—the corresponding high-dimensional space defined by the properties of each molecule in this sector of CCS—our analysis reveals that one has a substantial degree of flexibility or “freedom of design” when searching for a single molecule with a desired pair of properties or a set of distinct molecules sharing an array of properties. To explore how this intrinsic flexibility manifests in the molecular design process, we used multi-objective optimization to search for molecules with simultaneously large polarizabilities and HOMO–LUMO gaps; analysis of the resulting Pareto fronts identified non-trivial paths through CCS consisting of sequential structural and/or compositional changes that yield molecules with optimal combinations of these properties.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Projection pursuit adaptation on polynomial chaos expansions

Here, the present work addresses the issue of accurate stochastic approximations in high-dimensional parametric space using tools from uncertainty quantification (UQ). The basis adaptation method and its accelerated algorithm in polynomial chaos expansions (PCE) were recently proposed to construct low-dimensional approximations adapted to specific quantities of interest (QoI). The present paper addresses one difficulty with these adaptations, namely their reliance on quadrature point sampling, which limits the reusability of potentially expensive samples. Projection pursuit (PP) is a statistical tool to find the “interesting” projections in high-dimensional data and thus bypass the curse-of-dimensionality. In the present work, we combine the fundamental ideas of basis adaptation and projection pursuit regression (PPR) to propose a novel method to simultaneously learn the optimal low-dimensional spaces and PCE representation from given data. While this projection pursuit adaptation (PPA) can be entirely data-driven, the constructed approximation exhibits mean-square convergence to the solution of an underlying governing equation and thus captures the supports and probability distributions associated with the physics constraints. The proposed approach is demonstrated on a borehole problem and a structural dynamics problem, demonstrating the versatility of the method and its ability to discover low-dimensional manifolds with high accuracy with limited data. In addition, the method can learn surrogate models for different quantities of interest while reusing the same data set.

97 MATHEMATICS AND COMPUTING↗

Control of High-Temperature Static and Transient Thermomechanical Behavior of SiMo Ductile Iron by Al Alloying

Abstract Silicon and molybdenum ( SiMo ) ductile iron is commonly used for exhaust manifolds because these components experience thermal cycling in oxidizing environment, which requires resistance to fatigue during transient thermomechanical loads. Previous studies have demonstrated that alloying elements, such as Al , to SiMo ductile iron reduces the amount of surface degradation during static high-temperature exposure. However, deterioration of sphericity of the graphite nodules and a decrease in ductility could affect the tendency of cracking during thermal cycling. In this article, the effect of Al alloying on static and transient thermomechanical behavior of SiMo ductile iron was investigated to optimize the amount of Al alloying. A thermodynamic approach was used to confirm the effect of the Al alloying on the phase transformations in two SiMo cast irons, alloyed by 1.8% Al and 3% Al . These two alloys were cast in a laboratory along with the baseline SiMo ductile iron. Several experimental methods were used to evaluate the dimensional stability, physical properties, static oxidation, and failure resistance during constrained thermal cycling testing to compare their high-temperature capability. Experimental results verified that Al alloying increases the temperature range and decreases volume change during eutectoid transformation, which together with enhancement of oxidation protection improved the dimensional stability. Thermocycling tests showed that the number of cycles to failure depends on the amount of Al alloying and the applied high-temperature exposure during each cycle. SEM/EDX, high-resolution TEM and µCT analysis were used to verify the mechanism resulting from the Al alloying protection. It was shown that an optimal level of Al alloying for balancing oxidation and thermal cracking resistance depends on thermomechanical conditions of application.

36 MATERIALS SCIENCE↗

MULTI-LEADER: MULTI-source LEarning-Accelerated Design of high-Efficiency multi-stage compRessor (Final Technical Report)

The objective of MULTI-LEADER is to cut design costs by 80% while generating more energy-efficient designs of multi-stage compressors by developing and implementing novel machine learning (ML) techniques, which enable faster and fewer design iterations, improved solver performance, and concurrent multi-disciplinary design. Current industrial practices for the design of multi-stage compressors involve simulation-based design optimization with successive levels of model fidelity, iteratively evaluated between distinct disciplines, one stage at a time to tackle the high dimensional design variations. This project addresses these key design challenges: (1) concurrent optimization of multiple stages under many non-linear constraints; (2) multitude of evaluation of high-fidelity and expensive solvers and their gradients during optimization convergence in high-dimensional design; (3) multi-disciplinary design to maximize aerodynamic performance while guaranteeing structural integrity and additive manufacturability; (4) utilization of multiple fidelity of solvers with disparate parameterization and modeling assumptions. MULTI-LEADER achieved more than 5x speed up in detailed design of more energy-efficient compressors via these machine learning (ML) innovations: (i) rapid design surrogates by multi-source learning from diverse fidelities across multiple disciplines, (ii) physics-constrained data-augmented modeling for improved empiricism, (iii) generative manifold embedding for high dimensional concurrent design without gradient information; (iv) budget-constrained fidelity-adaptive sampling towards fewer design iterations.

33 ADVANCED PROPULSION SYSTEMS↗

SHAPER: can you hear the shape of a jet?

The identification of interesting substructures within jets is an important tool for searching for new physics and probing the Standard Model at colliders. Many of these substructure tools have previously been shown to take the form of optimal transport problems, in particular the Energy Mover’s Distance (EMD). In this work, we show that the EMD is in fact the natural structure for comparing collider events, which accounts for its recent success in understanding event and jet substructure. We then present a Shape Hunting Algorithm using Parameterized Energy Reconstruction (SHAPER), which is a general framework for defining and computing shape-based observables. SHAPER generalizes N-jettiness from point clusters to any extended, parametrizable shape. This is accomplished by efficiently minimizing the EMD between events and parameterized manifolds of energy flows representing idealized shapes, implemented using the dual-potential Sinkhorn approximation of the Wasserstein metric. We show how the geometric language of observables as manifolds can be used to define novel observables with built-in infrared-and-collinear safety. We demonstrate the efficacy of the SHAPER framework by performing empirical jet substructure studies using several examples of new shape-based observables.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Approximating the linear response of physical chaos

Abstract Parametric derivatives of statistics are highly desired quantities in prediction, design optimization and uncertainty quantification. In the presence of chaos, the rigorous computation of these quantities is certainly possible, but mathematically complicated and computationally expensive. Based on Ruelle’s formalism, this paper shows that the sophisticated linear response algorithm can be dramatically simplified in higher-dimensional systems featuring statistical homogeneity in the physical space. We argue that the contribution of the SRB (Sinai–Ruelle–Bowen) measure gradient, which is an integral yet the most cumbersome part of the full algorithm, is negligible if the objective function is appropriately aligned with unstable manifolds. This abstract condition could potentially be satisfied by a vast family of real-world chaotic systems, regardless of the physical meaning and mathematical form of the objective function and perturbed parameter. We demonstrate several numerical examples that support these conclusions and that present the use and performance of a simplified linear response algorithm. In the numerical experiments, we consider physical models described by differential equations, including Lorenz 96 and Kuramoto–Sivashinsky.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗