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Results for “Inverse Optimization”

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

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All sourcesNASA NTRSDOE OSTI
NASA NTRS1990

Optimal impulsive time-fixed orbital rendezvous and interception with path constraints

Minimum-fuel, impulsive, time-fixed solutions are obtained for the problem of orbital rendezvous and interception with interior path constraints. Transfers between coplanar circular orbits in an inverse-square gravitational field are considered, subject to a circular path constraint representing a minimum or maximum permissible orbital radius. Primer vector theory is extended to incorporate path constraints. The optimal number of impulses, their times and positions, and the presence of initial or final coasting arcs are determined. The existence of constraint boundary arcs and boundary points is investigated as well as the optimality of a class of singular arc solutions. To illustrate the complexities introduced by path constraints, an analysis is made of optimal rendezvous in field-free space subject to a minimum radius constraint.

Taur, D.-R.↗
DOE OSTI2017

Nonlatching positive feedback enables robust bimodality by decoupling expression noise from the mean

Fundamental to biological decision-making is the ability to generate bimodal expression patterns where two alternate expression states simultaneously exist. Here in this study, we use a combination of single-cell analysis and mathematical modeling to examine the sources of bimodality in the transcriptional program controlling HIV’s fate decision between active replication and viral latency. We find that the HIV Tat protein manipulates the intrinsic toggling of HIV’s promoter, the LTR, to generate bimodal ON-OFF expression, and that transcriptional positive feedback from Tat shifts and expands the regime of LTR bimodality. This result holds for both minimal synthetic viral circuits and full-length virus. Strikingly, computational analysis indicates that the Tat circuit’s non-cooperative ‘non-latching’ feedback architecture is optimized to slow the promoter’s toggling and generate bimodality by stochastic extinction of Tat. In contrast to the standard Poisson model, theory and experiment show that non-latching positive feedback substantially dampens the inverse noise-mean relationship to maintain stochastic bimodality despite increasing mean-expression levels. Given the rapid evolution of HIV, the presence of a circuit optimized to robustly generate bimodal expression appears consistent with the hypothesis that HIV’s decision between active replication and latency provides a viral fitness advantage. More broadly, the results suggest that positive-feedback circuits may have evolved not only for signal amplification but also for robustly generating bimodality by decoupling expression fluctuations (noise) from mean expression levels.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2024

Neural Networks to Find the Optimal Forcing for Offsetting the Anthropogenic Climate Change Effects

Abstract Of great relevance to climate engineering is the systematic relationship between the radiative forcing to the climate system and the response of the system, a relationship often represented by the linear response function (LRF) of the system. However, estimating the LRF often becomes an ill-posed inverse problem due to high-dimensionality and nonunique relationships between the forcing and response. Recent advances in machine learning make it possible to address the ill-posed inverse problem through regularization and sparse system fitting. Here, we develop a convolutional neural network (CNN) for regularized inversion. The CNN is trained using the surface temperature responses from a set of Green’s function perturbation experiments as imagery input data together with data sample densification. The resulting CNN model can infer the forcing pattern responsible for the temperature response from out-of-sample forcing scenarios. This promising proof of concept suggests a possible strategy for estimating the optimal forcing to negate certain undesirable effects of climate change. The limited success of this effort underscores the challenges of solving an inverse problem for a climate system with inherent nonlinearity. Significance Statement Predicting the climate response for a given climate forcing is a direct problem, while inferring the forcing for a given desired climate response is often an inverse, ill-posed, problem, posing a new challenge to the climate community. This study makes the first attempt to infer the radiative forcing for a given target pattern of global surface temperature response using a deep learning approach. The resulting deeply trained convolutional neural network inversion model shows promise in capturing the forcing pattern corresponding to a given surface temperature response, with a significant implication on the design of an optimal solar radiation management strategy for curbing global warming. This study also highlights the technical challenges that future research should prioritize in seeking feasible solutions to the inverse climate problem.

Ren, Huiying↗
DOE OSTI2025

LATTE: open-source, high-performance traveltime computation, tomography and source location in acoustic and elastic media

Traveltime-based tomography and source location are fundamental approaches for imaging subsurface structures and understanding the spatiotemporal distribution of seismicity from local to global scales. We present an open-source, high-performance framework integrating eikonal equation solvers and adjoint-state theory for traveltime computation, velocity tomography, source location and joint tomography-location in 2-D/3-D acoustic and elastic media. We introduce novel regularization schemes based on total generalized p-variation, structural similarity and multitask machine learning to enhance the fidelity and interpretability of inverted models and source locations. Key features of our implementation also include the ability to leverage both absolute-difference and double-difference traveltime misfits for high-fidelity velocity tomography and source parameter estimation; support for traveltime computation and inversion in diverse 2-D/3-D scenarios with arbitrary source and receiver distributions; and a perturbation-based optimal step-size estimation method to reduce computational costs. In addition, our implementation employs shared-memory and distributed-memory parallelization to provide an efficient solution for traveltime computation, tomography, and source location. In conclusion, we validate the efficacy and accuracy of our approach through multiple synthetic data examples.

58 GEOSCIENCES↗
DOE OSTI2023

Adaptive Pore Opening to Form Tailored Adsorption Sites in a Cooperatively Flexible Framework Enables Record Inverse Propane/Propylene Separation

A proposed low-energy alternative to the separation of alkanes from alkenes by energy-intensive cryogenic distillation is separation by porous adsorbents. Unfortunately, most adsorbents preferentially take up the desired, high-value major component alkene, requiring frequent regeneration. Adsorbents with inverse selectivity for the minor component alkane would enable the direct production of purified, reagent-grade alkene, greatly reducing global energy consumption. However, such materials are exceedingly rare, especially for propane/propylene separation. Here, we report that through adaptive and spontaneous pore size and shape adaptation to optimize an ensemble of weak noncovalent interactions, the structurally responsive metal-organic framework CdIF-13 (sod-Cd(benzimidazolate) 2 ) exhibits inverse selectivity for propane over propylene with record-setting separation performance under industrially relevant temperature, pressure, and mixture conditions. Powder synchrotron X-ray diffraction measurements combined with first-principles calculations yield atomic-scale insight and reveal the induced fit mechanism of adsorbate-specific pore adaptation and ensemble interactions between ligands and adsorbates. Dynamic column breakthrough measurements confirm that CdIF-13 displays selectivity under mixed-component conditions of varying ratios, with a record measured selectivity factor of α ≈ 3 at 95:5 propylene:propane at 298 K and 1 bar. When sequenced with a low-cost rigid adsorbent, we demonstrated the direct purification of propylene under ambient conditions. In conclusion, this combined atomic-level structural characterization and performance testing firmly establishes how cooperatively flexible materials can be capable of unprecedented separation factors.

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

Machine learning-guided discovery of polymer membranes for CO 2 separation with genetic algorithm

Designing polymer membranes with high gas permeability and selectivity is a difficult multi-task constrained problem due to the trade-off between these two properties. In this work, we present a machine learning (ML) driven genetic algorithm to tackle the design problem of polymer membranes for CO 2 separation from N 2 and O 2 . Using literature data of permeability for three gases, we constructed multiple ML models with different fingerprinting featurization schemes to predict gas permeabilities. Then, we employed a genetic algorithm to design new polymers and evaluated their performance using our ML models. We were able to identify new polymer membranes that are promising for both CO 2 /N 2 and CO 2 /O 2 separations. Further, the top discovered polymers are predicted to have high glass transition temperatures. Similarly, the pyridine functionality was found in ≈20% of the predicted polymers. This framework can be used to design polymers for any application involving constrained optimization. Finally, we outlined the challenges and opportunities with using ML guided data-driven inverse design of polymers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Prediction of binary nanoparticle superlattices from soft potentials

Driven by the hypothesis that a sufficiently continuous short-ranged potential is able to account for shell flexibility and phonon modes and therefore provides a more realistic description of nanoparticle interactions than a hard sphere model, we compute the solid phase diagram of particles of different radii interacting with an inverse power law potential. From a pool of 24 candidate lattices, the free energy is optimized with respect to additional internal parameters and the p-exponent, determining the short-range properties of the potential, is varied between p = 12 and p = 6. The phase diagrams contain the phases found in ongoing self-assembly experiments, including DNA programmable self-assembly and nanoparticles with capping ligands assembled by evaporation from an organic solvent. Thus, the resulting phase diagrams can be mapped quantitatively to existing experiments as a function of only two parameters: Nanoparticle radius ratio (γ) and softness asymmetry.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2015

SU-E-T-531: Large--Scale DVH Quality Study: Correlated Aims Lead Relaxations

Purpose: Intensity modulated radiation therapy plans are designed to optimally target a tumor while sparing surrounding tissue. Desired dose distributions are iteratively approached via inverse planning. This leads to tradeoffs between clinical objectives for the planning target volume (PTV), organs at risk, and normal tissues. Dose volume histogram (DVHs) related aims are followed that are either institutional or internationally recommended. We analyze common goals and identify potential reasons that often lead to tradeoffs. Methods: 524 IMRT plans for various tumor sites were analyzed based on the main institutional DVH goal for PTV (D95) and the recommendations by ICRU-83 (D2, D50, and D98). Robust statistical tools are developed and applied to ensure that the results are immune to data uncertainties. The probability of violation was measured for each of the DVH goals based on the frequency of not meeting recommended doses. Conditional probabilities for satisfying and/or violating DVH aims were computed to test the hypothesized pair-wise relations between DVH aims. For example, for plans that satisfied D50, the probability of violating D98 was computed via P(D98 < 95% | 98% ≤ D50 ≤ 102%). The equality constraint D50 = 100% was relaxed to encompass the range [98,102]%. Results: A large majority of cases (88%) satisfied the institutional goal for PTV of D95 ≤ 95%. Similar consensus existed for D98. 51% of cases satisfied D2 ≥ 107%. However, only 18% of cases satisfied D50. The conditional probability showed correlations amongst the studied DVH goals. In fact, a negative correlation was revealed between D50 and D95 (and D98), suggesting that these competing goals cannot be satisfied concurrently. Conclusion: The majority of plans followed the institutional guidelines. The reason for their deviation from international recommendations seems to be that the latter goals are competing and cannot be satisfied concurrently in clinical practice.

60 APPLIED LIFE SCIENCES↗
NASA NTRS1971

Users manual for the Variable dimension Automatic Synthesis Program (VASP)

A dictionary and some problems for the Variable Automatic Synthesis Program VASP are submitted. The dictionary contains a description of each subroutine and instructions on its use. The example problems give the user a better perspective on the use of VASP for solving problems in modern control theory. These example problems include dynamic response, optimal control gain, solution of the sampled data matrix Ricatti equation, matrix decomposition, and pseudo inverse of a matrix. Listings of all subroutines are also included. The VASP program has been adapted to run in the conversational mode on the Ames 360/67 computer.

White, J. S.↗
NASA NTRS1980

Inventory estimation on the massively parallel processor

This paper describes algorithms for efficiently computing inventory estimates from satellite based images. The algorithms incorporate a one dimensional feature extraction which optimizes the pairwise sum of Fisher distances. Biases are eliminated with a premultiplication by the inverse of the analytically derived error matrix. The technique is demonstrated with a numerical example using statistics obtained from an actual Landsat scene. Attention was given to implementation of the Massively Parallel processor (MPP). A timing analysis demonstrates that the inventory estimation can be performed an order of magnitude faster on the MPP than on a conventional serial machine.

Argentiero, P. D.↗
NASA NTRS2009

2-Micron Laser Transmitter for Coherent CO2 DIAL Measurement

Carbon dioxide (CO2) has been recognized as one of the most important greenhouse gases. It is essential for the study of global warming to accurately measure the CO2 concentration in the atmosphere and continuously record its variation. A high repetition rate, highly efficient, Q-switched 2-micron laser system as the transmitter of a coherent differential absorption lidar for CO2 measurement has been developed in NASA Langley Research Center. This laser system is capable of making a vertical profiling of CO2 from ground and column measurement of CO2 from air and space-borne platform. The transmitter is a master-slave laser system. The master laser operates in a single frequency, either on-line or off-line of a selected CO2 absorption line. The slave laser is a Q-switched ring-cavity Ho:YLF laser which is pumped by a Tm:fiber laser. The repetition rate can be adjusted from a few hundred Hz to 10 kHz. The injection seeding success rate is from 99.4% to 99.95%. For 1 kHz operation, the output pulse energy is 5.5mJ with the pulse length of ~50 ns. The optical-to-optical efficiency is 39% when the pump power is 14.5W. A Ho:YLF laser operating in the range of 2.05 micrometers can be tuned over several characteristic lines of CO2 absorption. Experimentally, a diode pumped Ho:Tm:YLF laser has been successfully used as the transmitter of coherent differential absorption lidar for the measurement of CO2 with a repetition rate of 5 Hz and pulse energy of 75 mJ. For coherent detection, high repetition rate is required for speckle averaging to obtain highly precise measurements. However, a diode pumped Ho:Tm:YLF laser can not operate in high repetition rate due to the large heat loading and up-conversion. A Tm:fiber laser pumped Ho:YLF laser with low heat loading can operate in high repetition rate. A theoretical model has been established to simulate the performance of Tm:fiber laser pumped Ho:YLF lasers. For continuous wave (CW) operation, high pump intensity with small beam size is suitable for high efficiency. For Q-switched operation, the optimal energy extraction relies on the pump intensity, pump volume, and pump duration which is inversely proportion to the repetition rate. CW and Q-switched Ho:YLF lasers with different linear cavity configurations have been designed and demonstrated for a 30 W Tm:fiber pump laser. The CW Ho laser slope efficiency and optical-to-optical efficiencies reach 65% and 55%, respectively. The pulsed laser efficiency depends on the repetition rate. For 1 kHz operation, the optical-to-optical efficiency is 39% when the pump power is 14.5W. Currently, the injection seeding success rate is between 99.4% and 99.95%. After a ten thousand pulses, the standard deviation of the laser frequency jitter is about 3 MHz. It meets the requirements of highly precise CO2 concentration measurement. In conclusion, an injection seeded, high repetition rate, Q-switched Ho:YLF laser has been developed for a coherent CO2 differential absorption lidar. This master-slave laser system has high optical-to-optical efficiency and seeding success rate. It can potentially meet the requirements of the coherent detection of CO2 concentration by a differential absorption lidar technique.

Singh, Upendra N.↗
DOE OSTI2018

Applying a predictive modeling methodology to a radiation transport inverse problem - 25588

In this paper, the predictive modeling of coupled multiphysics systems (PM-CMPS) procedure, developed by Cacuci and embodied in the software package MULTIPRED, has been applied to determine unknown parameters of a radioactive system from its gamma-ray and neutron signature. PM-CMPS has been integrated in two different ways with the inverse transport code INVERSE to determine the parameters. The first uses PM-CMPS in the inverse mode to directly estimate the parameters while the second mode uses a traditional nonlinear optimization routine and has PMCMPS complete a final iteration to estimate the uncertainty in the parameter best estimates. A test problem has been created and used to test both methods for varying numbers and types of responses and parameters. The first method was capable of accurately determining parameters but had a number of drawbacks. The second method functioned well at determining the correct parameter values in cases with limited numbers of parameters. (authors)

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2016

A refined methodology for stress inversions of earthquake focal mechanisms: Refined Stress Inversion Methodology

We develop an improved methodology for reliable high-resolution inversions of focal mechanisms to background stress field orientation and stress ratio R in two or three dimensions. The earthquake catalog is declustered to remove events likely affected strongly by local stress interactions rather than reflecting the large-scale background stress field. The declustered data are discretized with the k-means algorithm into groups containing a number of focal mechanisms between a minimum number N min and 2N min . Synthetic tests indicate that N min ≈ 30 provides stable inversion results under different stress regimes and noise conditions when R ≈ 0.5, while N min ≈ 45 is needed for R near 0 or 1. Additional synthetic tests compare the performance of selecting the fault plane of each focal mechanism using (a) the plane with lowest misfit angle between the slip vector from the focal mechanism and shear traction from the stress tensor and (b) the plane with highest instability coefficient representing proximity to the optimally oriented fault for given stress field and friction coefficient. The instability criterion is found to provide more accurate inversion results under all tested stress regimes, stress ratios, and noise conditions. The refined inversion methodology combines selecting fault planes using the instability criterion iteratively with a damped simultaneous inversion of different focal mechanism groups. Results characterizing neighborhoods of discretized domains merged during the damped inversion provide high-resolution information independent of the discretization. Some aspects of the methodology are illustrated with focal mechanism data from the San Jacinto Fault Zone in Southern California.

58 GEOSCIENCES↗
DOE OSTI2025

Closed-Form Approximation of the Total Variation Proximal Operator

Total variation (TV) is a widely used function for regularizing imaging inverse problems that is particularly appropriate for images whose underlying structure is piecewise constant. TV regularized optimization problems are typically solved using proximal methods, but the way in which they are applied is constrained by the absence of a closed-form expression for the proximal operator of the TV function. A closed-form approximation of the TV proximal operator has previously been proposed, but its accuracy was not theoretically explored in detail. Here, we address this gap by making several new theoretical contributions, proving that the approximation leads to a proximal operator of some convex function, it is equivalent to a gradient descent step on a smoothed version of TV, and that its error can be fully characterized and controlled with its scaling parameter. We experimentally validate our theoretical results on image denoising and sparse-view computed tomography (CT) image reconstruction.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Variational design principles for nonequilibrium colloidal assembly

Using large deviation theory and principles of stochastic optimal control, we show that rare molecular dynamics trajectories conditioned on assembling a specific target structure encode a set of interactions and external forces that lead to enhanced stability of that structure. Such a relationship can be formulated into a variational principle, for which we have developed an associated optimization algorithm and have used it to determine optimal forces for targeted self-assembly within nonequilibrium steady-states. We illustrate this perspective on inverse design in a model of colloidal cluster assembly within linear shear flow. We find that colloidal clusters can be assembled with high yield using specific short-range interactions of tunable complexity. Shear decreases the yields of rigid clusters, while small values of shear increase the yields of nonrigid clusters. The enhancement or suppression of the yield due to shear is rationalized with a generalized linear response theory. Furthermore, by studying 21 unique clusters made of six, seven, or eight particles, we uncover basic design principles for targeted assembly out of equilibrium.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Inverse point source location with the Helmholtz equation on a bounded domain

The problem of recovering acoustic sources, more specifically monopoles, from point-wise measurements of the corresponding acoustic pressure at a limited number of frequencies is addressed. To this purpose, a family of sparse optimization problems in measure space in combination with the Helmholtz equation on a bounded domain is considered in this study. A weighted norm with unbounded weight near the observation points is incorporated into the formulation. Optimality conditions and conditions for recovery in the small noise case are discussed, which motivates concrete choices of the weight. The numerical realization is based on an accelerated conditional gradient method in measure space and a finite element discretization.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1989

A complete analytical solution for the inverse instantaneous kinematics of a spherical-revolute-spherical (7R) redundant manipulator

Using a method based upon resolving joint velocities using reciprocal screw quantities, compact analytical expressions are generated for the inverse solution of the joint rates of a seven revolute (spherical-revolute-spherical) manipulator. The method uses a sequential decomposition of screw coordinates to identify reciprocal screw quantities used in the resolution of a particular joint rate solution, and also to identify a Jacobian null-space basis used for the direct solution of optimal joint rates. The results of the screw decomposition are used to study special configurations of the manipulator, generating expressions for the inverse velocity solution for all non-singular configurations of the manipulator, and identifying singular configurations and their characteristics. Two functions are therefore served: a new general method for the solution of the inverse velocity problem is presented; and complete analytical expressions are derived for the resolution of the joint rates of a seven degree of freedom manipulator useful for telerobotic and industrial robotic application.

Podhorodeski, R. P.↗
DOE OSTI2018

A genetic meta-algorithm-assisted inversion approach: hydrogeological study for the determination of volumetric rock properties and matrix and fluid parameters in unsaturated formations

An evolutionary inversion approach is suggested for the interpretation of nuclear and resistivity logs measured by direct-push tools in shallow unsaturated sediments. The efficiency of formation evaluation is improved by estimating simultaneously (1) the petrophysical properties that vary rapidly along a drill hole with depth and (2) the zone parameters that can be treated as constant, in one inversion procedure. In the workflow, the fractional volumes of water, air, matrix and clay are estimated in adjacent depths by linearized inversion, whereas the clay and matrix properties are updated using a float-encoded genetic meta-algorithm. The proposed inversion method provides an objective estimate of the zone parameters that appear in the tool response equations applied to solve the forward problem, which can significantly increase the reliability of the petrophysical model as opposed to setting these parameters arbitrarily. The global optimization meta-algorithm not only assures the best fit between the measured and calculated data but also gives a reliable solution, practically independent of the initial model, as laboratory data are unnecessary in the inversion procedure. The feasibility test uses engineering geophysical sounding logs observed in an unsaturated loessy-sandy formation in Hungary. The multi-borehole extension of the inversion technique is developed to determine the petrophysical properties and their estimation errors along a profile of drill holes. The genetic meta-algorithmic inversion method is recommended for hydrogeophysical logging applications of various kinds to automatically extract the volumetric ratios of rock and fluid constituents as well as the most important zone parameters in a reliable inversion procedure.

58 GEOSCIENCES↗