Constraining subglacial hydrology with ice surface velocity observations by solving an inverse ice dynamics-subglacial hydrology problem.
Abstract not provided.
Bertagna, Luca↗
SEARCH · Engineering Papers
Results for “inverse problems”
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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Estimation of extreme temperatures in direct solar methane pyrolysis within a porous medium
Porous media have wide application in renewable energy conversion processes, such as solar-thermal fuels production and decarbonization. Heat transport mechanisms within porous media can be highly complex, particularly under extreme conditions encountered in concentrated solar thermal reactors in which direct measurement of temperature is challenging. Here, we implement and report an inverse heat conduction model to estimate the temperature distribution throughout a porous substrate domain in a direct solar methane pyrolysis process. By solving a two-dimensional heat transfer problem and applying an inverse optimization algorithm, we estimate the quasi-steady state spatial temperature distribution in a fibrous porous carbon substrate. The results are validated indirectly by experimentally measured graphite deposition and a simplified reaction kinetic model.
finite difference method↗
A novel conditional generative model for efficient ensemble forecasts of state variables in large-scale geological carbon storage
Integrating monitoring data to efficiently update reservoir pressure and CO 2 plume distribution forecasts presents a significant challenge in geological carbon storage (GCS) applications. Inverse modeling techniques are commonly used to fuse observational data and refine reservoir model parameters, thereby improving state variable forecasts. However, these techniques often rely on linear or Gaussian assumptions, which can limit their effectiveness in accurately predicting state variables. Moreover, simulating large-scale three-dimensional (3D) GCS problems is computationally expensive, making iterative runs in inverse problems prohibitive. To address these challenges, we propose a conditional generative model utilizing the score-based diffusion method for real-time 3D pressure and saturation field distribution predictions. Our approach involves solving the score function with a mini-batch-based Monte Carlo estimator to generate labeled data. This data is subsequently employed to train a fully connected neural network, enabling it to learn the conditional sample generator within a supervised learning framework. This method enables the rapid generation of a large ensemble of predictions, facilitating comprehensive uncertainty quantification of state variables. Here we applied our method to forecast the dynamic 3D distributions of pressure and saturation fields over a 30-year injection period. The statistical assessment with low root mean square error (RMSE) values demonstrates that our method can accurately predict the spatiotemporal distributions of both pressure and saturation fields. Moreover, the developed conditional generative model shows high computational efficiency by generating 100 ensemble forecasts of 3D state variables in less than 10 min. The consistency between ensemble averages and ground truth values further illustrates the model’s capability to capture state variable dynamics during the CO 2 plume injection process. Notably, the ground truth values fall within the ensemble forecasts, indicating that our uncertainty quantification effectively captures variability and potential noise in the observations. Thus, the developed conditional generative model proves to be a more efficient, accurate, and practical tool for GCS applications, facilitating timely risk analysis and informed decision-making.
58 GEOSCIENCES↗
Inverse design for waveguide dispersion with a differentiable mode solver
Inverse design of optical components based on adjoint sensitivity analysis has the potential to address the most challenging photonic engineering problems. However, existing inverse design tools based on finite-difference-time-domain (FDTD) models are poorly suited for optimizing waveguide modes for adiabatic transformation or perturbative coupling, which lies at the heart of many important photonic devices. Among these, dispersion engineering of optical waveguides is especially challenging in ultrafast and nonlinear optical applications involving broad optical bandwidths and frequency-dependent anisotropic dielectric material response. In this work, we develop gradient back-propagation through a general-purpose electromagnetic eigenmode solver and use it to demonstrate waveguide dispersion optimization for second harmonic generation with maximized phase-matching bandwidth. This optimization of three design parameters converges in eight steps, reducing the computational cost of optimization by ∼100x compared to exhaustive search and identifying new designs for broadband optical frequency doubling of laser sources in the 1.3–1.4 µm wavelength range. Furthermore, we demonstrate that the computational cost of gradient back-propagation is independent of the number of parameters, as required for optimization of complex geometries. This technique enables practical inverse design for a broad range of previously intractable photonic devices.
Gray, Dodd (ORCID:000000030469599X)↗
Exact and Model Exchange-Correlation Potentials for Open-Shell Systems
The conventional approaches to the inverse density functional theory problem typically assume nondegeneracy of the Kohn–Sham (KS) eigenvalues, greatly hindering their use in open-shell systems. Here, we present a generalization of the inverse density functional theory problem that can seamlessly admit degenerate KS eigenvalues. Additionally, we allow for fractional occupancy of the Kohn–Sham orbitals to also handle noninteracting ensemble-v-representable densities, as opposed to just noninteracting pure-v-representable densities. We present the exact exchange-correlation (XC) potentials for six open-shell systems–four atoms (Li, C, N, and O) and two molecules (CN and CH 2 )–using accurate ground-state densities from configuration interaction calculations. We compare these exact XC potentials with model XC potentials obtained using nonlocal (B3LYP, SCAN0) and local/semilocal (SCAN, PBE, PW92) XC functionals. Although the relative errors in the densities obtained from these DFT functionals are of $O$(10 –3 to 10 –2 ), the relative errors in the model XC potentials remain substantially large–$O$(10 –1 to 10 0 ).
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Information theory optimization of signals from small-angle scattering measurements
Small-angle X-ray scattering (SAXS) of particles in solution informs on the conformational states and assemblies of biological macromolecules (bioSAXS) outside of cryo- and solid-state conditions. In bioSAXS, the SAXS measurement under dilute conditions is resolution limited, and through an inverse Fourier transform, the measured SAXS intensities directly relate to the physical space occupied by the particles via the P (r)-distribution. Yet, this inverse transform of SAXS data has been historically cast as an ill-posed, ill-conditioned problem requiring an indirect approach. Here, we show that through the applications of matrix and information theories, the inverse transform of SAXS intensity data is a well-conditioned problem. The so-called ill-conditioning of the inverse problem is directly related to the Shannon number. By exploiting the oversampling enabled by modern detectors, a direct inverse Fourier transform of the SAXS data is possible, provided the recovered information does not exceed the Shannon number. The Shannon limit corresponds to the maximum number of significant singular values that can be recovered in a SAXS experiment, suggesting this relationship is a fundamental property of band-limited inverse integral transform problems. This correspondence reduces the complexity of the inverse problem to the Shannon limit and maximum dimension. We propose a hybrid scoring function using an information theory framework that assesses both the quality of the model-data fit as well as the quality of the recovered P (r)-distribution. The hybrid score utilizes the Akaike information criteria and Durbin-Watson statistic that considers parameter-model complexity, i.e., degrees of freedom, and the randomness of the model-data residuals. The described tests and findings extend the boundaries for bioSAXS by completing the information theory formalism initiated by Peter B. Moore to enable a quantitative measure of resolution in SAXS, robustly determine maximum dimension, and more precisely define the best parameter model appropriately representing the observed scattering data.
Rambo, Robert P. [Science and Technology Facilitie↗
Inversion of dynamical Bragg intensities to complex structure factors by iterated projections. For Ultramic. 2020. ("Pico" Festschrift, May 2021)
We discuss a method for recovering complex structure factors from many simultaneously excited Bragg beam intensities is described. The method is applied to simulated transmission electron diffraction data over a wide range of crystal thickness and beam energies. The method is based on iterated projections between structure and scattering matrices, which are related by a matrix unitary transformation, exponential, which we invert. The algorithm removes multiple-scattering perturbations from diffraction data and might be extended to other fields, including X-ray and neutron diffraction and cryo-electron microscopy. Because coherent multiple scattering involves interference between Bragg beams, the method also solves the phase problem. Unlike dynamical inversion from electron microscope images or ptychography data, the method, which starts with Bragg beam intensities, provides complex structure factors unaffected by focusing errors or resolution limitations imposed by lenses. We provide inversions from simulated data with 441 simultaneously excited Bragg beams over a range of thickness and beam energy. We discuss the retrieval of chirality information from enantiomorphs, the efficient incorporation of symmetry information using the irreducible representation of the group of structure matrices, and the effect of HOLZ lines to provide three-dimensional information.
97 MATHEMATICS AND COMPUTING↗
Two-layer transient heat transfer using impulse response methods
Solutions to the inverse heat conduction problem (IHCP) are methods that can be used to quantify surface heat flux in multi-layer materials for components in which there are limited subsurface (internal) temperature measurements, such as coated components. A critical consideration is to capture high frequency fluctuations using a practical heat flux sensor. To that end, this paper highlights key parameters for calculating accurate surface heat transfer. Specifically, this research extends the available solutions to the IHCP for multi-substrate structures through an impulse response methodology. The sensitivity of the impulse method was quantified with respect to practical measurements. Further, when compared to the inverse case, the impulse method resulted in lower errors when calculating surface heat flux over a range of conditions. Overall, this work provides a foundation for deducing heat flux from a subsurface heat flux sensor while maintaining a high-frequency response.
42 ENGINEERING↗
A non-commutative Bayes' theorem
Using a diagrammatic reformulation of Bayes' theorem, we provide a necessary and sufficient condition for the existence of Bayesian inference in the setting of finite-dimensional C* -algebras. In other words, we prove an analogue of Bayes' theorem in the joint classical and quantum context. Our analogue is justified by recent advances in categorical probability theory, which have provided an abstract formulation of the classical Bayes' theorem. In the process, we further develop non-commutative almost everywhere equivalence and illustrate its important role in non-commutative Bayesian inversion. The construction of such Bayesian inverses, when they exist, involves solving a positive semidefinite matrix completion problem for the Choi matrix. This gives a solution to the open problem of constructing Bayesian inversion for completely positive unital maps acting on density matrices that do not have full support. In conclusion, we illustrate how the procedure works for several examples relevant to quantum information theory.
97 MATHEMATICS AND COMPUTING↗
Bayesian inference of heterogeneous epidemic models: Application to COVID-19 spread accounting for long-term care facilities
Here we propose a high dimensional Bayesian inference framework for learning heterogeneous dynamics of a COVID-19 model, with a specific application to the dynamics and severity of COVID-19 inside and outside long-term care (LTC) facilities. We develop a heterogeneous compartmental model that accounts for the heterogeneity of the time-varying spread and severity of COVID-19 inside and outside LTC facilities, which is characterized by time-dependent stochastic processes and time-independent parameters in ~ 1500 dimensions after discretization. To infer these parameters, we use reported data on the number of confirmed, hospitalized, and deceased cases with suitable post-processing in both a deterministic inversion approach with appropriate regularization as a first step, followed by Bayesian inversion with proper prior distributions. To address the curse of dimensionality and the ill-posedness of the high-dimensional inference problem, we propose use of a dimension-independent projected Stein variational gradient descent method, and demonstrate the intrinsic low-dimensionality of the inverse problem. We present inference results with quantified uncertainties for both New Jersey and Texas, which experienced different epidemic phases and patterns. Moreover, we also present forecasting and validation results based on the empirical posterior samples of our inference for the future trajectory of COVID-19.
42 ENGINEERING↗
S -matrix positivity without Lorentz invariance: a case study
We investigate the analytic structure of scattering amplitudes in theories in which Lorentz invariance is spontaneously broken. We do so by computing and studying the S-matrix for a simple example: a superfluid described by a complex scalar with quartic interactions. The computation is confined to tree-level, for there are no absolutely stable single-particle states, though the lifetime can be made long by lowering the chemical potential. For the 2 → 2 amplitude in center-of-mass configurations, not only is crossing symmetry violated, there appears a tree level branch cut for unphysical kinematics. Its appearance is a consequence of non-analyticity in the dispersion relation. The branch point defines a new scale in the problem, which scales inversely with the chemical potential. In this example, even derivatives of the forward amplitude are positive while odd derivatives are negative. This pattern can be understood in a general way in the limit of a small chemical potential, or weak Lorentz breaking.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Invertible neural networks for real-time control of extrusion additive manufacturing
Material extrusion additive manufacturing (AM) has enabled an elegant fabrication pathway for a vast material library. Nonetheless, each material requires optimization of printing parameters generally determined through significant trial-and-error testing. To eliminate arduous, iteration-based optimization approaches, many researchers have used machine learning (ML) algorithms which provide opportunities for automated process optimization. Here, in this work, we demonstrate the use of an ML-driven approach for real-time material extrusion print-parameter optimization through in-situ monitoring of printed line geometry. To do this, we use deep invertible neural networks (INNs) which can solve both forward and inverse, or optimization, problems using a single network. By combining in-situ computer vision and deep INNs, the printing parameters can be autonomously optimized to print a target line width in 1.2 s. Furthermore, defects that occur during printing can be rapidly identified and corrected autonomously. The methods developed and presented in this work eliminate user-intensive, time-consuming, and iterative parameter discovery approaches that currently limit accelerated implementation of extrusion-based AM processes. Furthermore, the presented approach can be generalized to provide real-time monitoring and optimization pathways for increasingly complex AM environments.
36 MATERIALS SCIENCE↗
Grand Unification of Quantum Algorithms
Quantum algorithms offer significant speed-ups over their classical counterparts for a variety of problems. The strongest arguments for this advantage are borne by algorithms for quantum search, quantum phase estimation, and Hamiltonian simulation, which appear as subroutines for large families of composite quantum algorithms. A number of these quantum algorithms have recently been tied together by a novel technique known as the quantum singular value transformation (QSVT), which enables one to perform a polynomial transformation of the singular values of a linear operator embedded in a unitary matrix. In the seminal GSLW’19 paper on the QSVT [Gilyén et al., ACM STOC 2019], many algorithms are encompassed, including amplitude amplification, methods for the quantum linear systems problem, and quantum simulation. Here, we provide a pedagogical tutorial through these developments, first illustrating how quantum signal processing may be generalized to the quantum eigenvalue transform, from which the QSVT naturally emerges. Paralleling GSLW’19, we then employ the QSVT to construct intuitive quantum algorithms for search, phase estimation, and Hamiltonian simulation, and also showcase algorithms for the eigenvalue threshold problem and matrix inversion. This overview illustrates how the QSVT is a single framework comprising the three major quantum algorithms, suggesting a grand unification of quantum algorithms.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Project DarkStar: Vision for LLNL in 2030
DarkStar was a Strategic Initiative (FY2021-FY2024) to investigate applications of Artificial Intelligence (AI) and Machine Learning (ML) to scientific problems of complex hydrodynamics, shockwave physics and energetic materials. The research focused on physics and engineering design as a process that can be tremendously accelerated through merging AI with advanced physics simulation on exascale-class platforms, and to experimentally validate this revolutionary new approach through dynamic materials campaigns. A central thread of scientific inquiry was in the application of AI to enable human understanding of how to control hydrodynamic instability (which has impacts to areas such as inertial confinement fusion) via engineering features and time-dependent sources. Motivated by an unfinished line of research started by Dr. Johnny von Neumann, AI-enabled simulation approaches were developed that allowed DarkStar researchers to uncover several ground-breaking discoveries regarding hydrodynamic instability, including how to completely suppress Richtmyer-Meshkov instability (RMI). These S&T discoveries, along with other advances, have shown the way for an entirely new approach to time-dependent problems known as inverse design – the idea that complex systems can be developed directly from a final state that is to be achieved and resolve the initial design via satisfying several constraints simultaneously via AI/ML. Through experimental campaigns conducted across a wide range of facilities in the NNSA complex (the High Explosive Application Facility at LLNL, the Dynamic Compression Sector/Advanced Photon Source at Argonne National Lab, and Special Technologies Laboratory at MSTS) the radical new AI/ML approach to engineering complex material dynamics was verified, establishing a new field of study within the realm of shock physics. As advanced manufacturing capabilities continue to develop, the great importance of inverse design as a means to apply that technology effectively for NNSA missions will feature prominently over this decade. DarkStar has positioned NNSA as a world-leader in this newly emerging cross-disciplinary area of AI methods for advanced physics simulation and pioneered multiple novel approaches that have enabled the broader scientific community. By allowing us to see past the horizon, to 2030 and beyond, DarkStar has illuminated the vast potential of AI/ML to impact a wide range of new national security missions and, consequently, multiple areas of further research have already emerged across the NNSA and DOD complex.
42 ENGINEERING↗
SQMS Quantum R&D in Machine Learning, Optimization and Sensing beyond Fundamental Physics Applications
This newly formed team at SQMS under the Ecosystem Thrust is looking to develop capabilities impacting societal advances outside the core domain of HEP and condensed matter physics. We explicitly leverage the experimental and algorithmic innovations developed across all groups as well as connect to broad-scope external projects of the diverse team of PIs. As the inaugural set of projects, we are studying numerically quantum machine learning models inspired by efficiently trainable echo-state and orthogonal neural networks and developing designs for related experiments to be performed on quantum processors based on SQMS SRF cQED technology and Rigetti s transmon arrays. Investigated models exploit ideas and lessons learned from multiple prior work by SQMS team members in a variety of internal and external activities [R1]. Target initial applications include noisy signal processing, potentially captured by quantum sensors or noisy QPUs, as well as simulation and classification of healthcare data. For instance, image reconstruction of the brain s electrical properties by solving the inverse Maxwell equation problem with uncertainty [R2] through a hybrid quantum-classical physics-informed architecture for time-dependent processes [R3]. The group is also investigating the application and development of novel quantum sensors based on magnetic levitation of a superconducting sphere coupled to a superconducting qubit. This coupling enables high-precision measurements of the position of the sphere, which can be used for sensitive detection of forces, enabling practical applications such as gravimetry for geophysics analysis, or accelerometry for GPS-denied navigation [R4] [R1] Rieffel, Eleanor G., Ata Akbari Asanjan, M. Sohaib Alam, Namit Anand, David E. Bernal Neira, Sophie Block, Lucas T. Brady et al. "Assessing and advancing the potential of quantum computing: A NASA case study." Future Generation Computer Systems (2024). [R2] Yu, X., Serrall s, J.E., Giannakopoulos, I.I., Liu, Z., Daniel, L., Lattanzi, R. and Zhang, Z., 2023. Pifon-ept: Mr-based electrical property tomography using physics-informed fourier networks. IEEE Journal on Multiscale and Multiphysics Computational Techniques. [R3] Wudarski, Filip, Daniel OConnor, Shaun Geaney, Ata Akbari Asanjan, Max Wilson, Elena Strbac, P. Aaron Lott, and Davide Venturelli. "Hybrid quantum-classical reservoir computing for simulating chaotic systems." arXiv preprint arXiv:2311.14105 (2023). [R4] Higgins, Gerard, Saarik Kalia, and Zhen Liu. "Maglev for dark matter: Dark-photon and axion dark matter sensing with levitated superconductors." Physical Review D 109.5 (2024): 055024.
Venturelli, Davide↗
Predictive Inverse Model for Advective Heat Transfer in a Short–Circuited Fracture: Dimensional Analysis, Machine Learning, and Field Demonstration
Identifying fluid flow maldistribution in planar geometries is a well–established problem in subsurface science/engineering. Of particular importance to the thermal performance of enhanced (or “engineered”) geothermal systems is identifying the existence of nonuniform (i.e., heterogeneous) permeability and subsequently predicting advective heat transfer. Here, machine learning via a genetic algorithm (GA) identifies the spatial distribution of an unknown permeability field in a two–dimensional Hele–Shaw geometry (i.e., parallel plates). The inverse problem is solved by minimizing the L2 norm between simulated residence time distribution (RTD) and measurements of an inert tracer breakthrough curve (BTC) (C–Dot nanoparticle). Principal component analysis (PCA) of spatially correlated permeability fields enabled reduction of the parameter space by more than a factor of 10 and restricted the inverse search to reservoir–scale permeability variations. Thermal experiments and tracer tests conducted at the mesoscale Altona Field Laboratory (AFL) demonstrate that the method accurately predicts the effects of extreme flow channeling on heat transfer in a single bedding–plane rock fracture. However, this is only true when the permeability distributions provide adequate matches to both tracer RTD and frictional pressure loss. Without good agreement to frictional pressure loss, it is still possible to match a simulated RTD to measurements, but subsequent predictions of heat transfer are grossly inaccurate. Here, the results of this study suggest that it is possible to anticipate the thermal effects of flow maldistribution, but only if both simulated RTDs and frictional pressure loss between fluid inlets and outlets are in good agreement with measurements.
42 ENGINEERING↗
Multi-frequency progressive refinement for learned inverse scattering
Interpreting scattered acoustic and electromagnetic wave patterns is a computational task that enables remote imaging in a number of important applications, including medical imaging, geophysical exploration, sonar and radar detection, and nondestructive testing of materials. However, accurately and stably recovering an inhomogeneous medium from far-field scattered wave measurements is a computationally difficult problem, due to the nonlinear and non-local nature of the forward scattering process. We design a neural network, called Multi-Frequency Inverse Scattering Network (MFISNet), and a training method to approximate the inverse map from far-field scattered wave measurements at multiple frequencies. We consider three variants of MFISNet, with the strongest performing variant inspired by the recursive linearization method — a commonly used technique for stably inverting scattered wavefield data — that progressively refines the estimate with higher frequency content. MFISNet outperforms past methods in regimes with high-contrast, heterogeneous large objects, and inhomogeneous unknown backgrounds.
97 MATHEMATICS AND COMPUTING↗
An Approximate Direct Inverse as a Preconditioner For Ill-Conditioned Problems.
Abstract not provided.
Lee, Chung Hyun↗