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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Position Papers for Inverse Methods for Complex Systems under Uncertainty Workshop

The ability to solve inverse problems – inferring unknown parameters, structures, or states of a system from observed data – is essential for advancing scientific discovery and innovation capabilities for the DOE mission. Basic research needs and challenges are particularly acute in emerging areas such as the interactive, data-driven, modeling and simulation of digital twins; decision support for experiments at DOE scientific user facilities; and for other complex systems and workflows. Inverse problems are at the heart of understanding and controlling complex systems due to factors such as observational data with varying modalities and fidelities, inherent uncertainties in physical measurements and numerical models, and the computational demands of rapid and high-fidelity simulations. The convergence of recent scientific computing trends – scientific machine learning, artificial intelligence, and computing advances such as exascale computing – is creating unprecedented opportunities. These advancements offer the potential to revolutionize how we approach inverse problems to extract actionable insights with the required level of accuracy and computational efficiency. This workshop and the Call for Position Papers are vital steps in bringing together experts to collectively explore and identify the new computational and mathematical directions needed in inverse methods for complex systems under uncertainty.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Use of Gas Adsorption and Inversion Methods for Shale Pore Structure Characterization

The analysis of porosity and pore structure of shale rocks has received special attention in the last decades as unconventional reservoir hydrocarbons have become a larger parcel of the oil and gas market. A variety of techniques are available to provide a satisfactory description of these porous media. Some techniques are based on saturating the porous rock with a fluid to probe the pore structure. In this sense, gases have played an important role in porosity and pore structure characterization, particularly for the analysis of pore size and shapes and storage or intake capacity. In this review, we discuss the use of various gases, with emphasis on N2 and CO2, for characterization of shale pore architecture. We describe the state of the art on the related inversion methods for processing the corresponding isotherms and the procedure to obtain surface area and pore-size distribution. The state of the art is based on the collation of publications in the last 10 years. Limitations of the gas adsorption technique and the associated inversion methods as well as the most suitable scenario for its application are presented in this review. Finally, we discuss the future of gas adsorption for shale characterization, which we believe will rely on hybridization with other techniques to overcome some of the limitations.

04 OIL SHALES AND TAR SANDS↗
NASA NTRS1986

An inverse method for subcritical flows

An exact method is presented for two-dimensional subsonic flow within the limitations of the tangent gas approximation. While Woods (1961) studied these equations and proposed iterative methods for the solution of both the iterative and inverse problems, the inverse method here presented is noniterative and exact. It is shown that the direct Euler solution over the designed airfoil is very close to the input speed distribution, and that the constraints necessitated by upstream condition and closure requirements are easily incorporated.

Daripa, P. K.↗
NASA NTRS1990

Inverse methods for assessing ship-of-opportunity networks and estimating circulation and winds from tropical expendable bathythermograph data

Inverse methods for estimating the surface ciculation of the equatorial Pacific by combining a linear reduced-gravity shallow-water model with the Tropical Ocean-Global Atmosphere ship-of-opportunity expendable bathythermograph (TOGA SOP XBT) observing program are examined. It is demonstrated that a simple linear model of the upper circulation of the equatorial Pacific can be successfully used as a weak constraint when smoothing the TOGA SOP XBT data. A circulation is sought as the weighted least squares fit to the dynamics and the data. The solution method is an expansion in representer functions, and the generalized inverse problem is thereby reduced from a functional problem to an algebraic problem for the coefficients of the representer. A specific inverse calculation using synthetic forcing and data is presented.

Bennett, Andrew F.↗
NASA NTRS1969

Towards an optimal inversion method for remote atmospheric sensing

The inference of atmospheric structure from satellite radiometric observations requires an inversion algorithm. A variety of techniques was spawned to meet these demands. One class, the nonlinear inversion methods, copes with the problem of data noise. Unlike linear techniques which require a priori data smoothing, the nonlinear method can be applied directly to raw data. The algorithm discriminates the noise input by resolving the inferences into two types of solution, associating the real roots with atmospheric structure while ascribing the imaginary roots to noise.

King, J. I. F.↗
NASA NTRS1991

A proposed through-flow inverse method for the design of mixed-flow pumps

A through-flow (hub-to-shroud) truly inverse method is proposed and described. It uses an imposition of mean swirl, i.e., radius times mean tangential velocity, given throughout the meridional section of the turbomachine as an initial design specification. In the present implementation, it is assumed that the fluid is inviscid, incompressible, and irrotational at inlet and that the blades are supposed to have zero thickness. Only blade rows that impart to the fluid a constant work along the space are considered. An application of this procedure to design the rotor of a mixed-flow pump is described in detail. The strategy used to find a suitable mean swirl distribution and the other design inputs is also described. The final blade shape and pressure distributions on the blade surface are presented, showing that it is possible to obtain feasible designs using this technique. Another advantage of this technique is the fact that it does not require large amounts of CPU time.

Borges, Joao Eduardo↗
NASA NTRS1981

The general circulation and meridional heat transport of the subtropical South Atlantic determined by inverse methods

The circulation and meridional heat transport of the subtropical South Atlantic Ocean are determined through the application of the inverse method of Wunsch (1978) to hydrographic data from the IGY and METEOR expeditions. Meridional circulation results of the two data sets agree on a northward mass transport of about 20 million metric tons/sec for waters above the North Atlantic Deep Water (NADW), and a comparable southward transport of deep waters. Additional gross features held in common are the Benguela, South Equatorial and North Brazilian Coastal currents' northward transport of the Surface Water, and the deflection of the southward-flowing NADW from the South American Coast into the mid ocean by a seamount chain near 20 deg S. Total heat transport is equatorward, with a magnitude of 0.8 X 10 to the 15th W near 30 deg S and indistinguishable from zero near 8 deg S.

Fu, L.-L.↗
NASA NTRS1994

Microbial community structure at the U.S.-Joint Global Ocean Flux Study Station ALOHA: Inverse methods for estimating biochemical indicator ratios

Modeling biogeochemical fluxes in the marine plankton requires the application of factors for extrapolation of biomass indicators measured in the field (chlorophyll a, adenosine triphosphate, bacterial counts) to biomass carbon or nitrogen. These are often inferred from culture studies and are poorly constrained for natural populations. At least squares inverse method with a simple linear model constrains the values of several common indicator ratios, giving self-consistent solutions that provide useful information about the structure of the microbial community at our North Pacific Ocean study site (Station ALOHA (A Long-term Oligotrophic Habitat Assessment)). These results indicate that the fraction of the microbial biomass that is autotrophic (pigmented) is greater in the mixed layer than at the deep chlorophyll maximum layer and that heterotrophic bacteria are a significant but not necessarily predominant component of the microbial community in the euphotic zone.

Christian, James R.↗
NASA NTRS1986

Performance comparisons on spatial lattice algorithm and direct matrix inverse method with application to adaptive arrays processing

Lattice algorithm has been employed in numerous adaptive filtering applications such as speech analysis/synthesis, noise canceling, spectral analysis, and channel equalization. In this paper the application to adaptive-array processing is discussed. The advantages are fast convergence rate as well as computational accuracy independent of the noise and interference conditions. The results produced by this technique are compared to those obtained by the direct matrix inverse method.

An, S. H.↗
NASA NTRS1990

Flare heating and ionization of the low solar chromosphere. I - Inversion methods for Mg I 4571 and 5173

Various methods of inverting solar Mg I 4571 and 5173 spectral line observations are examined to find the best method of using these lines to calculate the vertical temperature and electron density structure around the temperature minimum region. Following a perturbation analysis by Mein (1971), a Fredholm integral equation of the first kind is obtained which can be inverted to yield these temperature and density structures as a function of time. Several inversion methods are tested and compared. The methods are used to test data as well as to a subset of observations of these absorption lines taken on February 3, 1986 before and during a solar flare. A small but significant increase is found in the temperature and a relatively large increase in the electron density during this flare. The observations are inconsistent with heating and ionization by an intense beam of electrons and with ionization by UV photoionization of Si I.

Metcalf, Thomas R.↗
DOE OSTI2022

A combined experimental and numerical approach that eliminates the non-uniqueness associated with the Johnson-Cook parameters obtained using inverse methods

Abstract Johnson-Cook constitutive model is a commonly used material model for machining simulations. The model includes five parameters that capture the initial yield stress, strain-hardening, strain-rate hardening, and thermal softening behavior of the material. These parameters are difficult to determine using experiments since the conditions observed during machining (such as high strain-rates of the order of $$10^5$$ 10 5 /sec - $$10^6$$ 10 6 /sec) are challenging to recreate in the laboratory. To address this problem, several researchers have recently proposed inverse approaches where a combination of experiments and analytical models are used to predict the Johnson-Cook parameters. The errors between the measured cutting forces, chip thicknesses and temperatures and those predicted by analytical models are minimized and the parameters are determined. In this work, it is shown that only two of the five Johnson-Cook parameters can be determined uniquely using inverse approaches. Two different algorithms, namely, Adaptive Memory Programming for Global Optimization (AMPGO) and Particle Swarm Optimization (PSO), are used for this purpose. The extended Oxley’s model is used as the analytical tool for optimization. For determining a parameter’s value, a large range for each parameter is provided as an input to the algorithms. The algorithms converge to several different sets of values for the five Johnson-Cook parameters when all the five parameters are considered as unknown in the optimization algorithm. All of these sets, however, yield the same chip shape and cutting forces in FEM simulations. Further analyses show that only the strain-rate and thermal softening parameters can be determined uniquely and the three parameters present in the strain-hardening term of the Johnson-Cook model cannot be determined uniquely using the inverse method. A combined experimental and numerical approach is proposed to eliminate this determine all parameters uniquely.

42 ENGINEERING↗
NASA NTRS2017

Inverse Method for Estimation of Composite Kink-Band Toughness from Open-Hole Compression Strength Data

Fiber-reinforced polymer matrix composite materials can fail by kink-band propagation mechanism when subjected to in-plane compressive loading. This mode of failure is especially prevalent in compressive loading of laminates with holes, cut-outs, or impact damage. Most of the successful models for predicting compressive strength of such laminates require “fracture” toughness associated with kink-band propagation under in-plane compression. However, this property is difficult to measure experimentally, limiting the use of such models in design practice. In this paper an inverse method is proposed to estimate the kink-band toughness of the laminate from its open-hole compression strength data, which is an easier property to measure experimentally. Furthermore, a scaling relationship is proposed to estimate kink-band toughness for other laminate configurations of the same material.

Luke Borkowski↗
NASA NTRS1991

Supercritical blade design on stream surfaces of revolution with an inverse method

A method to solve the inverse problem of supercritical blade-to-blade flow on stream surfaces of revolution with variable radius and variable stream surface thickness in a relative system is described. Some aspects of shockless design and of leading edge resolution in the numerical procedure are depicted. Some supercritical compressor cascades were designed and their complete flow field results were compared with computations of two different analysis methods.

Schmidt, E.↗
NASA NTRS1985

A direct-inverse method for transonic and separated flows about airfoils

A direct-inverse technique and computer program called TAMSEP that can be sued for the analysis of the flow about airfoils at subsonic and low transonic freestream velocities is presented. The method is based upon a direct-inverse nonconservative full potential inviscid method, a Thwaites laminar boundary layer technique, and the Barnwell turbulent momentum integral scheme; and it is formulated using Cartesian coordinates. Since the method utilizes inverse boundary conditions in regions of separated flow, it is suitable for predicing the flowfield about airfoils having trailing edge separated flow under high lift conditions. Comparisons with experimental data indicate that the method should be a useful tool for applied aerodynamic analyses.

Carlson, K. D.↗
NASA NTRS1990

A direct-inverse method for transonic and separated flows about airfoils

A direct-inverse technique and computer program called TAMSEP that can be used for the analysis of the flow about airfoils at subsonic and low transonic freestream velocities is presented. The method is based upon a direct-inverse nonconservative full potential inviscid method, a Thwaites laminar boundary layer technique, and the Barnwell turbulent momentum integral scheme; and it is formulated using Cartesian coordinates. Since the method utilizes inverse boundary conditions in regions of separated flow, it is suitable for predicting the flow field about airfoils having trailing edge separated flow under high lift conditions. Comparisons with experimental data indicate that the method should be a useful tool for applied aerodynamic analyses.

Carlson, Leland A.↗