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.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Efficient mapping between void shapes and stress fields using Deep Convolutional Neural Networks with sparse data
Establishing fast and accurate structure-to-property relationships is an important component in the design and discovery of advanced materials. Physics-based simulation models like the finite element method (FEM) are often used to predict deformation, stress, and strain fields as a function of material microstructure in material and structural systems. Such models may be computationally expensive and time intensive if the underlying physics of the system is complex. This limits their application to solve inverse design problems and identify structures that maximize performance. In such scenarios, surrogate models are employed to make the forward mapping computationally efficient to evaluate. However, the high dimensionality of the input microstructure and the output field of interest often renders such surrogate models inefficient, especially when dealing with sparse data. Deep convolutional neural network (CNN) based surrogate models have shown great promise in handling such high-dimensional problems. In this paper, a single ellipsoidal void structure under a uniaxial tensile load represented by a linear elastic, high-dimensional and expensive-to-query, FEM model. We consider two deep CNN architectures, a modified convolutional autoencoder framework with a fully connected bottleneck and a UNet CNN, and compare their accuracy in predicting the von Mises stress field for any given input void shape in the FEM model. Additionally, a sensitivity analysis study is performed using the two approaches, where the variation in the prediction accuracy on unseen test data is studied through numerical experiments by varying the number of training samples from 20 to 100.
Sparse measurement medical CT reconstruction using multi-fused block matching denoising priors
A major challenge for medical X-ray CT imaging is reducing the number of X-ray projections to lower radiation dosage and reduce scan times without compromising image quality. However these under-determined inverse imaging problems rely on the formulation of an expressive prior model to constrain the solution space while remaining computationally tractable. Traditional analytical reconstruction methods like Filtered Back Projection (FBP) often fail with sparse measurements, producing artifacts due to their reliance on the Shannon-Nyquist Sampling Theorem. Consensus Equilibrium, which is a generalization of Plug and Play, is a recent advancement in Model-Based Iterative Reconstruction (MBIR), has facilitated the use of multiple denoisers are prior models in an optimization free framework to capture complex, non-linear prior information. However, 3D prior modelling in a Plug and Play approach for volumetric image reconstruction requires long processing time due to high computing requirement. Instead of directly using a 3D prior, this work proposes a BM3D Multi Slice Fusion (BM3D-MSF) prior that uses multiple 2D image denoisers fused to act as a fully 3D prior model in Plug and Play reconstruction approach. Our approach does not require training and are thus able to circumvent ethical issues related with patient training data and are readily deployable in varying noise and measurement sparsity levels. In addition, reconstruction with the BM3D-MSF prior achieves similar reconstruction image quality as fully 3D image priors, but with significantly reduced computational complexity. We test our method on clinical CT data and demonstrate that our approach improves reconstructed image quality.
Multigrid Optimization for Large-Scale Ptychographic Phase Retrieval
Ptychography is a popular imaging technique that combines diffractive imaging with scanning microscopy. The technique consists of a coherent beam that is scanned across an object in a series of overlapping positions, leading to reliable and improved reconstructions. Ptychographic microscopes allow for large fields to be imaged at high resolution at the cost of additional computational expense. Herein, we propose a multigrid-based optimization framework to reduce the computational burdens of large-scale ptychographic phase retrieval. Our proposed method exploits the inherent hierarchical structures in ptychography through tailored restriction and prolongation operators for the object and data domains. Our numerical results show that our proposed scheme accelerates the convergence of its underlying solver and outperforms the ptychographical iterative engine, a workhorse in the optics community.
Large-Scale Materials Modeling at Quantum Accuracy: Ab Initio Simulations of Quasicrystals and Interacting Extended Defects in Metallic Alloys
Ab initio electronic-structure has remained dichotomous between achievable accuracy and length-scale. Quantum many-body (QMB) methods realize quantum accuracy but fail to scale. Density functional theory (DFT) scales favorably but remains far from quantum accuracy. We present a framework that breaks this dichotomy by use of three interconnected modules: (i) invDFT: a methodological advance in inverse DFT linking QMB methods to DFT; (ii) MLXC: a machine-learned density functional trained with invDFT data, commensurate with quantum accuracy; (iii) DFT-FE-MLXC: an adaptive higher-order spectral finite-element (FE) based DFT implementation that integrates MLXC with efficient solver strategies and HPC innovations in FE-specific dense linear algebra, mixed-precision algorithms, and asynchronous compute-communication. Furthermore, we demonstrate a paradigm shift in DFT that not only provides an accuracy commensurate with QMB methods in ground-state energies, but also attains an unprecedented performance of 659.7 PFLOPS (43.1% peak FP64 performance) on 619,124 electrons using 8,000 GPU nodes of Frontier supercomputer.
Machine learning materials inverse design
A Python-based workflow code applying various machine learning techniques for materials inverse design problems.
Machine Learning assisted optimization and parameter space exploration dataset of spin ice Hamiltonian
This repository contains both simulated and experimental structure factor data for the data challenge involving the inverse scattering problem. The simulated data were generated during a machine-learning-assisted optimization routine described in ref[1]. The experimental structure factor was measured on a rare-earth oxide, Dy2Ti2O7 using diffuse neutron scattering from time-of-flight techniques on the CORELLI instrument at the Spallation Neutron Source, Oak Ridge National Laboratory. A Metropolis Monte Carlo code implemented to run in a High-performance computing setting was used to calculated simulated structure factors for the spin-ice Hamiltonian at 680 mK, which is the same temperature as for the experimental data. The total size of all the files in this repository is 5.12 GB. A detailed description of the files is given below. ExperimentalData_630mK.dat – A linearized version of 3-dimensional experimental data of size 61×81×21. This data was processed to remove an estimation of non-magnetic background, including nuclear scattering signal and instrumentation background. Parameters.dat – 6700 samples were evaluated over the 4-dimensional parameter space (J_1, J_2, J_3 and J_(3^' )). There is an additional parameter, D in the spin Hamiltonian to mimic the dipolar interaction between magnetic ions. However, this parameter, D was fixed to a value determined by prior work. This file contains five columns for the parameters J_1, J_2, J_3, J_(3^' ) and D respectively. 3D_Simulation_Data.dat – The simulated structure factor, S(Q) data are included in this file. Each raw contains a linearized array of 3D volumes of S(Q) calculated for the parameter set given in the corresponding row of the file Parameters.dat. The size of the volume data was matched to the experimental data. Qx(h,-h,0).dat, Qy(k,k,-2k).dat, Qz(l,l,l).dat – These files contain the h, k, and l values along with the reciprocal vectors [h,-h,0], [k,k,-2k] and [l,l,l] respectively.
A Bayesian Calibration Framework with Embedded Model Error for Model Diagnostics
We study the utility and performance of a Bayesian model error embedding construction in the context of molecular dynamics modeling of metallic alloys, where we embed model error terms in existing interatomic potential model parameters. To alleviate the computational burden of this approach, we propose a framework combining likelihood approximation and Gaussian process surrogates. Here we leverage sparse Gaussian process techniques to construct a hierarchy of increasingly accurate but more expensive surrogate models. This hierarchy is then exploited by multilevel Markov chain Monte Carlo methods to efficiently sample from the target posterior distribution. We illustrate the utility of this approach by calibrating an interatomic potential model for a family of gold-copper alloys. In particular, this case study highlights effective means for dealing with computational challenges with Bayesian model error embedding in large-scale physical models, and the utility of embedded model error for model diagnostics.
Machine learning and LHC event generation
First-principle simulations are at the heart of the high-energy physics research program. They link the vast data output of multi-purpose detectors with fundamental theory predictions and interpretation. This review illustrates a wide range of applications of modern machine learning to event generation and simulation-based inference, including conceptional developments driven by the specific requirements of particle physics. New ideas and tools developed at the interface of particle physics and machine learning will improve the speed and precision of forward simulations, handle the complexity of collision data, and enhance inference as an inverse simulation problem.
Machine learning in the context of inverse, control, and experimental design problems.
Abstract not provided.
Quantifying Uncertainties in Limited-Angle Tomography - Applications to Dynamic Materials Science Experiments
Explore the source record for details and available documents.
End-to-end optimization for battery materials and molecules by combining graph neural networks and reinforcement learning
The National Renewable Energy Laboratory (NREL), together with the Colorado School of Mines (CSM) and Colorado State University (CSU), has developed a machine learning-enhanced approach to design new battery materials. Currently, such materials are designed in part via numerous expensive high-fidelity computational simulations that predict the performance of a given composition. Even with computational screening tools, the vast landscape of possible molecular or crystal structures exceeds current and future computational capacity. Improving the efficiency by which new materials can be optimized will therefore disrupt the cost, risk, and time required to bring new energy solutions to the marketplace. Predicting the properties of an organic molecule or periodic crystalline material given its structure has grown increasingly common. These approaches leverage large-scale computational and experimental databases and ML approaches such as graph neural networks. The inverse design problem of finding a material that possesses desired properties is substantially more challenging, since enumerating all valid material structures is not feasible. In this project, we leveraged recent success in reinforcement learning to efficiently navigate this high-dimensional search space. Just as algorithms can find the optimal chess moves from nearly limitless options, we train an approach to evolve a simple starting structure into a complex structure that possess the desired properties. Our solution has been demonstrated by applying it to two related design application tasks for short- and long-term energy storage, respectively: (1) the design of solid-state ion conductors and (2) the design of organic redox-active materials. The project has resulted an open-source software library for material design, documented examples of applying the library to both organic and inorganic material optimization, and peer-reviewed publications detailing the data, computational models, and resulting candidate materials.
End-to-End Optimization for Battery Materials and Molecules by Combining Graph Neural Networks and Reinforcement Learning
The National Renewable Energy Laboratory (NREL), together with the Colorado School of Mines (CSM) and Colorado State University (CSU), has developed a machine learning-enhanced approach to the design of new battery materials. Currently, such materials are designed in part via numerous expensive high-fidelity computational simulations that predict the performance of a given composition. Even with computational screening tools, the vast landscape of possible molecular or crystal structures exceeds current and future computational capacity. Improving the efficiency by which new materials can be optimized will therefore disrupt the cost, risk, and time required to bring new energy solutions to the marketplace. Predicting the properties of an organic molecule or periodic crystalline material given its structure has grown increasingly common. These approaches leverage large-scale computational and experimental databases and ML approaches such as graph neural networks. The inverse design problem of finding a material that possesses desired properties is substantially more challenging, since enumerating all valid material structures is not feasible. In this project, we leveraged recent success in reinforcement learning to efficiently navigate this high-dimensional search space. Just as algorithms can find the optimal chess moves from nearly limitless options, we train an approach to evolve a simple starting structure into a complex structure that possess the desired properties. Our solution has been demonstrated by applying it to two related design application tasks for short- and long-term energy storage, respectively: (1) the design of solid-state ion conductors and (2) the design of organic redox-active materials. The project has resulted an open-source software library for material design, documented examples of applying the library to both organic and inorganic material optimization, and peer-reviewed publications detailing the data, computational models, and resulting candidate materials.
Extended Physics-Informed Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition Based Deep Learning Framework for Nonlinear Partial Differential Equations
Here we propose a generalized space-time domain decomposition approach for the physics-informed neural networks (PINNs) to solve nonlinear partial differential equations (PDEs) on arbitrary complex-geometry domains. The proposed framework, named eXtended PINNs ( X P I N N s ), further pushes the boundaries of both PINNs as well as conservative PINNs (cPINNs), which is a recently proposed domain decomposition approach in the PINN framework tailored to conservation laws. Compared to PINN, the XPINN method has large representation and parallelization capacity due to the inherent property of deployment of multiple neural networks in the smaller subdomains. Unlike cPINN, XPINN can be extended to any type of PDEs. Moreover, the domain can be decomposed in any arbitrary way (in space and time), which is not possible in cPINN. Thus, XPINN offers both space and time parallelization, thereby reducing the training cost more effectively. In each subdomain, a separate neural network is employed with optimally selected hyperparameters, e.g., depth/width of the network, number and location of residual points, activation function, optimization method, etc. A deep network can be employed in a subdomain with complex solution, whereas a shallow neural network can be used in a subdomain with relatively simple and smooth solutions. We demonstrate the versatility of XPINN by solving both forward and inverse PDE problems, ranging from one-dimensional to three-dimensional problems, from time-dependent to time-independent problems, and from continuous to discontinuous problems, which clearly shows that the XPINN method is promising in many practical problems. The proposed XPINN method is the generalization of PINN and cPINN methods, both in terms of applicability as well as domain decomposition approach, which efficiently lends itself to parallelized computation. The XPINN code is available on h t t p s : / / g i t h u b . c o m / A m e y a J a g t a p / X P I N N s .
Deep learning of free boundary and Stefan problems
Free boundary problems appear naturally in numerous areas of mathematics, science and engineering. These problems present a great computational challenge because they necessitate numerical methods that can yield an accurate approximation of free boundaries and complex dynamic interfaces. In this work, we propose a multi-network model based on physics-informed neural networks to tackle a general class of forward and inverse free boundary problems called Stefan problems. Specifically, we approximate the unknown solution as well as any moving boundaries by two deep neural networks. Besides, we formulate a new type of inverse Stefan problems that aim to reconstruct the solution and free boundaries directly from sparse and noisy measurements. We demonstrate the effectiveness of our approach in a series of benchmarks spanning different types of Stefan problems, and illustrate how the proposed framework can accurately recover solutions of partial differential equations with moving boundaries and dynamic interfaces. All code and data accompanying this manuscript are publicly available at https://github.com/PredictiveIntelligenceLab/DeepStefan.
One-shot omnidirectional pressure integration through matrix inversion
In this work, we present a method to perform 2D and 3D omnidirectional pressure integration from velocity measurements with a single-iteration matrix inversion approach. This work builds upon our previous work, where the rotating parallel ray approach was extended to the limit of infinite rays by taking continuous projection integrals of the ray paths and recasting the problem as an iterative matrix inversion problem. This iterative matrix equation is now 'fast-forwarded' to the 'infinity' iteration, leading to a different matrix equation that can be solved in a single step, thereby presenting the same computational complexity as the Poisson equation. We observe computational speedups of ~10 6 when compared to brute-force omnidirectional integration methods, enabling the treatment of grids of ~10 9 points and potentially even larger in a desktop setup at the time of publication. Further examination of the boundary conditions of our one-shot method shows that omnidirectional pressure integration implements a boundary condition where the boundary points are treated as interior points to the extent that information is available. Finally, we show how the method can be extended from the regular grids typical of particle image velocimetry to the unstructured meshes characteristic of particle tracking velocimetry data.
Real-Time Bayesian Inference at Extreme Scale: A Digital Twin for Tsunami Early Warning Applied to the Cascadia Subduction Zone
We present a Bayesian inversion-based digital twin that employs acoustic pressure data from seafloor sensors, along with 3D coupled acoustic–gravity wave equations, to infer earthquake-induced spatiotemporal seafloor motion in real time and forecast tsunami propagation toward coastlines for early warning with quantified uncertainties. Our target is the Cascadia subduction zone, with one billion parameters. Computing the posterior mean alone would require 50 years on a 512 GPU machine. Instead, exploiting the shift invariance of the parameter-to-observable map and devising novel parallel algorithms, we induce a fast offline–online decomposition. The offline component requires just one adjoint wave propagation per sensor; using MFEM, we scale this part of the computation to the full El Capitan system (43,520 GPUs) with 92% weak parallel efficiency. Moreover, given real-time data, the online component exactly solves the Bayesian inverse and forecasting problems in 0.2 seconds on a modest GPU system, a ten-billion-fold speedup.
Adjoint-Based Inversion of Geodetic Data for Sources of Deformation and Strain
An adjoint-based formulation leads to a particularly efficient approach for inverting geodetic measurements for the source of the deformation. Specifically, the quantities necessary to iteratively improve the fit to the observations can be computed with just three forward calculations, one to obtain the current residuals, another to solve the adjoint problem, and a third to compute the step length. An inversion algorithm utilizing the adjoint-based gradient is applied to a set of Interferometric Synthetic Aperture Radar (InSAR) data gathered between 2016 and 2018 over the Tulare Basin in California's Central Valley. Because the measured deformation is due to groundwater withdrawal, a penalty function is included in the inversion to avoid placing aquifer volume change in locations that are far from any documented wells. The solution of the inverse problem provides estimates of aquifer compaction that provide a match to the observed range changes while honoring the well data. The solution indicates an average aquifer volume loss of 2.17 km 3 /year over the two year period from January 2016 to January 2018, encompassing one drought year (2016) and one wet year (2017). Finally, this magnitude of lost volume is compatible with the 3.1 km 3 /year decrease in water volume for the entire Central Valley, estimated from GRACE satellite gravity data.