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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Group Projected subspace pursuit for IDENTification of variable coefficient differential equations (GP-IDENT)

We propose an effective and robust algorithm for identifying partial differential equations (PDEs) with space-time varying coefficients from the noisy observation of a single solution trajectory. Identifying unknown differential equations from noisy data is a difficult task, and it is even more challenging with space and time varying coefficients in the PDE. The proposed algorithm, GP-IDENT, has three ingredients: (i) we use B-spline bases to express the unknown space and time varying coefficients, (ii) we propose Group Projected Subspace Pursuit (GPSP) to find a sequence of candidate PDEs with various levels of complexity, and (iii) we propose a new criterion for model selection using the Reduction in Residual (RR) to choose an optimal one among a pool of candidates. The new GPSP considers group projected subspaces which is more robust than existing methods in distinguishing correlated group features. We test GP-IDENT on a variety of PDEs and PDE systems, and compare it with the state-of-the-art parametric PDE identification algorithms under different settings to illustrate its outstanding performance. Furthermore, our experiments show that GP-IDENT is effective in identifying the correct terms from a large dictionary, and our model selection scheme is robust to noise.

Data-driven method↗
DOE OSTI2021

Clinical knowledge extraction via sparse embedding regression (KESER) with multi-center large scale electronic health record data

The increasing availability of electronic health record (EHR) systems has created enormous potential for translational research. However, it is difficult to know all the relevant codes related to a phenotype due to the large number of codes available. Traditional data mining approaches often require the use of patient-level data, which hinders the ability to share data across institutions. In this project, we demonstrate that multi-center large-scale code embeddings can be used to efficiently identify relevant features related to a disease of interest. We constructed large-scale code embeddings for a wide range of codified concepts from EHRs from two large medical centers. We developed knowledge extraction via sparse embedding regression (KESER) for feature selection and integrative network analysis. We evaluated the quality of the code embeddings and assessed the performance of KESER in feature selection for eight diseases. Besides, we developed an integrated clinical knowledge map combining embedding data from both institutions. The features selected by KESER were comprehensive compared to lists of codified data generated by domain experts. Features identified via KESER resulted in comparable performance to those built upon features selected manually or with patient-level data. The knowledge map created using an integrative analysis identified disease-disease and disease-drug pairs more accurately compared to those identified using single institution data. Analysis of code embeddings via KESER can effectively reveal clinical knowledge and infer relatedness among codified concepts. KESER bypasses the need for patient-level data in individual analyses providing a significant advance in enabling multi-center studies using EHR data.

96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗
DOE OSTI2023

Reduced Order Model to Predict Dispersion of Flammable Refrigerant into a Space

As the HVAC&R industry mobilizes to deploy more low-GWP refrigerants, relevant standards are being continually reviewed and updated. Those include the general safety standards ISO 5149 and ASHRAE 15, and the equipment standards IEC and UL. The standards systematically set the allowable maximum amount of refrigerant that should be used in different equipment types and different applications. To do so, they rely on predictions of how a leaked refrigerant mass will disperse into a space. Dispersion characteristics, such as total flammable volume and its residence time, determine the risk associated with the presence of the flammable refrigerant. The standards have included provisions for the use of flammable refrigerants for approximately two decades. They relied on limited analytical analyses and test cases in their development. Dispersion of a refrigerant into a space is complex. Computational fluid dynamics (CFD) are the most accurate in predicting a given problem. However, CFD is computationally expensive and requires specialized expertise and resources and is not suitable for use by standards development working group as prediction tool. This paper presents the development of a reduced order model (ROM) that predicts the key dispersion characteristics relevant to the dispersion of a leaked refrigerant into a space for any combination of input variables. The inputs are the refrigerant release height, the total released refrigerant mass and its release flow rate, the refrigerant molecular weight, the ventilation flow rate, the floor area and height of the space, recirculation air flow rate, and the tightness of the space. The outputs are histograms of volume fraction of the room in prescribed concentration bins and the total mass of the refrigerant in each bin normalized by the total refrigerant charge at 13 prescribed simulation time stamps between 1 and 900 seconds. The ROM is constructed from a set of CFD simulations with carefully chosen combinations of input parameters. The selection if done using a multidimensional sparse grid which is a generalization of the classical tensor approach but offers additional flexibility and thus can be more carefully tuned towards a specific model. The tuning is done to improve the accuracy, measured in the difference between the output values of the ROM and the CFD model, while minimizing the computational cost, measured in number of CFD simulations which is orders of magnitude more expensive than the processing the training data.

Edwards, Dean↗
DOE OSTI2023

Combining Sparse Approximate Factorizations with Mixed-precision Iterative Refinement

The standard LU factorization-based solution process for linear systems can be enhanced in speed or accuracy by employing mixed-precision iterative refinement. Most recent work has focused on dense systems. We investigate the potential of mixed-precision iterative refinement to enhance methods for sparse systems based on approximate sparse factorizations. In doing so, we first develop a new error analysis for LU- and GMRES-based iterative refinement under a general model of LU factorization that accounts for the approximation methods typically used by modern sparse solvers, such as low-rank approximations or relaxed pivoting strategies. We then provide a detailed performance analysis of both the execution time and memory consumption of different algorithms, based on a selected set of iterative refinement variants and approximate sparse factorizations. Our performance study uses the multifrontal solver MUMPS, which can exploit block low-rank factorization and static pivoting. We evaluate the performance of the algorithms on large, sparse problems coming from a variety of real-life and industrial applications showing that mixed-precision iterative refinement combined with approximate sparse factorization can lead to considerable reductions of both the time and memory consumption.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

A DATA EFFICIENT SPARSE MODELING FRAMEWORK FOR POWER ESTIMATION IN WATER TREATMENT SENSING OPERATIONS

With increasing freshwater scarcity, advanced process design mechanisms such as Closed-Circuit Reverse Osmosis (CCRO) and Digital/Physical Twin systems are gaining traction in water treatment and reuse operations. While digital and physical twin models enable improved system insight and control, their development is often expensive and computationally intensive, requiring large volumes of synthetic or experimental data to characterize underlying process dynamics. This work introduces a sparse surrogate modeling framework to estimate power consumption from measured flow and pressure variables, along with their nonlinear polynomial and interaction expansions. To ensure model reliability and reduce overfitting, a two-stage pipeline is proposed. First, a dynamic data filtering algorithm is employed to remove uninformative observations and transient operational states. Second, a sparse penalized regression technique is applied to select a minimal set of parsimonious features. The proposed model achieves high sparsity, retaining only 7 out of 34 candidate features (≈79.41% sparsity) while delivering a root mean square error (RMSE) of 0.072 on the test dataset.

Mukherjee, Subrata [ORNL] (ORCID:0000000309930338)↗
DOE OSTI2022

Dispersion-enhanced sequential batch sampling for adaptive contour estimation

In computer simulation and optimal design, sequential batch sampling offers an appealing way to iteratively stipulate optimal sampling points based upon existing selections and efficiently construct surrogate modeling. Nonetheless, the issue of near duplicates poses tremendous quandary for sequential learning. It refers to the situation that selected critical points cluster together in each sampling batch, which are individually but not collectively informative towards the optimal design. Near duplicates severely diminish the computational efficiency as they barely contribute extra information towards update of the surrogate. To address this issue, we impose a dispersion criterion on concurrent selection of sampling points, which essentially forces a sparse distribution of critical points in each batch, and demonstrate the effectiveness of this approach in adaptive contour estimation. Specifically, we adopt Gaussian process surrogate to emulate the simulator, acquire variance reduction of the critical region from new sampling points as a dispersion criterion, and combine it with the modified expected improvement (EI) function for critical batch selection. The critical region here is the proximity of the contour of interest. This proposed approach is vindicated in numerical examples of a two-dimensional four-branch function, a four-dimensional function with a disjoint contour of interest and a time-delay dynamic system.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Path-Based Dictionary Augmentation: A Framework for Improving $k$ -Sparse Image Processing

In this study, we have previously shown that augmenting orthogonal matching pursuit (OMP) with an additional step in the identification stage of each pursuit iteration yields improved $k$ -sparse reconstruction and denoising performance relative to baseline OMP. At each iteration a “path” or geodesic, is generated between the two dictionary atoms that are most correlated with the residual and from this path a new atom that has a greater correlation to the residual than either of the two bracketing atoms is selected. Here, we provide new computational results illustrating improvements in sparse coding and denoising on canonical datasets using both learned and structured dictionaries. The two methods of constructing a path are investigated for each dictionary type: the Euclidean geodesic formed by a linear combination of the two atoms and the 2-Wasserstein geodesic corresponding to the optimal transport map between the atoms. We prove here the existence of a higher-correlation atom in the Euclidean case under assumptions on the two bracketing atoms and introduce algorithmic modifications to improve the likelihood that the bracketing atoms meet those conditions. Although, we demonstrate our augmentation on OMP alone, in general it may be applied to any reconstruction algorithm that relies on the selection and sorting of high-similarity atoms during an analysis or identification phase.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

A Computational Information Criterion for Particle-Tracking with Sparse or Noisy Data

Traditional probabilistic methods for the simulation of advection-diffusion equations (ADEs) often overlook the entropic contribution of the discretization, e.g., the number of particles, within associated numerical methods. Many times, the gain in accuracy of a highly discretized numerical model is outweighed by its associated computational costs or the noise within the data. Herein, we address the question of how many particles are needed in a simulation to best approximate and estimate parameters in one-dimensional advective-diffusive transport. To do so, we use the well-known Akaike Information Criterion (AIC) and a recently-developed correction called the Computational Information Criterion (COMIC) to guide the model selection process. Random-walk and mass-transfer particle tracking methods are employed to solve the model equations at various levels of discretization. Numerical results demonstrate that the COMIC provides an optimal number of particles that can describe a more efficient model in terms of parameter estimation and model prediction compared to the model selected by the AIC even when the data is sparse or noisy, the sampling volume is not uniform throughout the physical domain, or the error distribution of the data is non-IID Gaussian.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Comprehensive compartmental model and calibration algorithm for the study of clinical implications of the population-level spread of COVID-19: a study protocol

The complex dynamics of the coronavirus disease 2019 (COVID-19) pandemic has made obtaining reliable long-term forecasts of the disease progression difficult. Simple mechanistic models with deterministic parameters are useful for short-term predictions but have ultimately been unsuccessful in extrapolating the trajectory of the pandemic because of unmodelled dynamics and the unrealistic level of certainty that is assumed in the predictions. We propose a 22-compartment epidemiological model that includes compartments not previously considered concurrently, to account for the effects of vaccination, asymptomatic individuals, inadequate access to hospital care, post-acute COVID-19 and recovery with long-term health complications. Additionally, new connections between compartments introduce new dynamics to the system and provide a framework to study the sensitivity of model outputs to several concurrent effects, including temporary immunity, vaccination rate and vaccine effectiveness. Subject to data availability for a given region, we discuss a means by which population demographics (age, comorbidity, socioeconomic status, sex and geographical location) and clinically relevant information (different variants, different vaccines) can be incorporated within the 22-compartment framework. Considering a probabilistic interpretation of the parameters allows the model's predictions to reflect the current state of uncertainty about the model parameters and model states. We propose the use of a sparse Bayesian learning algorithm for parameter calibration and model selection. This methodology considers a combination of prescribed parameter prior distributions for parameters that are known to be essential to the modelled dynamics and automatic relevance determination priors for parameters whose relevance is questionable. This is useful as it helps prevent overfitting the available epidemiological data when calibrating the parameters of the proposed model. Population-level administrative health data will serve as partial observations of the model states.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2023

WeakIdent: Weak formulation for identifying differential equation using narrow-fit and trimming

Data-driven identification of differential equations is an interesting but challenging problem, especially when the given data are corrupted by noise. When the governing differential equation is a linear combination of various differential terms, the identification problem can be formulated as solving a linear system, with the feature matrix consisting of linear and nonlinear terms multiplied by a coefficient vector. This product is equal to the time derivative term, and thus generates dynamical behaviors. The goal is to identify the correct terms that form the equation to capture the dynamics of the given data. We propose a general and robust framework to recover differential equations using a weak formulation with two new mechanisms, narrow-fit and trimming, for both ordinary and partial differential equations (ODEs and PDEs). The weak formulation facilitates an efficient and robust way to handle noise, and two new mechanisms, narrow-fit and trimming, improve the coefficient support and value recoveries respectively. For each sparsity level, Subspace Pursuit is utilized to find an initial set of support from the large dictionary. Then, we focus on highly dynamic regions (rows of the feature matrix), and error normalize the feature matrix in the narrow-fit step. The support is further updated via trimming the terms that contribute the least. Finally, the support set of features with the smallest Cross-Validation error is chosen as the result. A comprehensive set of numerical experiments are presented for both systems of ODEs and PDEs with various noise levels. The proposed method gives a robust recovery of the coefficients, and a significant denoising effect which can handle up to 100% noise-to-signal ratio for some equations. We compare the proposed method with several state-of-the-art algorithms for the recovery of differential equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Fast Sparse-Vector Cosine Similarity in Go

This software provides a fast way to perform efficient sparse matrix multiplication followed by top-n multiplication result selection. Functionality for performing matrix multiplication / cosine similarity separately is included in this package as well. This package is a pure Go port of a Python package developed by ING Bank (https://github.com/ing-bank/sparse_dot_topn) which uses Cython to execute the matrix multiplication in C++. Instructions for compiling bindings which can be called from Python are included with this package as well.

Shivers, Ryan [Oak Ridge National Lab. (ORNL), Oak↗
DOE OSTI2022

Sparsifying priors for Bayesian uncertainty quantification in model discovery

We propose a probabilistic model discovery method for identifying ordinary differential equations governing the dynamics of observed multivariate data. Our method is based on the sparse identification of nonlinear dynamics (SINDy) framework, where models are expressed as sparse linear combinations of pre-specified candidate functions. Promoting parsimony through sparsity leads to interpretable models that generalize to unknown data. Instead of targeting point estimates of the SINDy coefficients, we estimate these coefficients via sparse Bayesian inference. The resulting method, uncertainty quantification SINDy (UQ-SINDy), quantifies not only the uncertainty in the values of the SINDy coefficients due to observation errors and limited data, but also the probability of inclusion of each candidate function in the linear combination. UQ-SINDy promotes robustness against observation noise and limited data, interpretability (in terms of model selection and inclusion probabilities) and generalization capacity for out-of-sample forecast. Sparse inference for UQ-SINDy employs Markov chain Monte Carlo, and we explore two sparsifying priors: the spike and slab prior, and the regularized horseshoe prior. UQ-SINDy is shown to discover accurate models in the presence of noise and with orders-of-magnitude less data than current model discovery methods, thus providing a transformative method for real-world applications which have limited data.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Learning and meta-learning of stochastic advection–diffusion–reaction systems from sparse measurements

Physics-informed neural networks (PINNs) were recently proposed in [18] as an alternative way to solve partial differential equations (PDEs). A neural network (NN) represents the solution, while a PDE-induced NN is coupled to the solution NN, and all differential operators are treated using automatic differentiation. Here, we first employ the standard PINN and a stochastic version, sPINN, to solve forward and inverse problems governed by a non-linear advection–diffusion–reaction (ADR) equation, assuming we have some sparse measurements of the concentration field at random or pre-selected locations. Subsequently, we attempt to optimise the hyper-parameters of sPINN by using the Bayesian optimisation method (meta-learning) and compare the results with the empirically selected hyper-parameters of sPINN. In particular, for the first part in solving the inverse deterministic ADR, we assume that we only have a few high-fidelity measurements, whereas the rest of the data is of lower fidelity. Hence, the PINN is trained using a composite multi-fidelity network, first introduced in [12], that learns the correlations between the multi-fidelity data and predicts the unknown values of diffusivity, transport velocity and two reaction constants as well as the concentration field. For the stochastic ADR, we employ a Karhunen–Loève (KL) expansion to represent the stochastic diffusivity, and arbitrary polynomial chaos (aPC) to represent the stochastic solution. Correspondingly, we design multiple NNs to represent the mean of the solution and learn each aPC mode separately, whereas we employ a separate NN to represent the mean of diffusivity and another NN to learn all modes of the KL expansion. For the inverse problem, in addition to stochastic diffusivity and concentration fields, we also aim to obtain the (unknown) deterministic values of transport velocity and reaction constants. The available data correspond to 7spatial points for the diffusivity and 20 space–time points for the solution, both sampled 2000 times. We obtain good accuracy for the deterministic parameters of the order of 1–2% and excellent accuracy for the mean and variance of the stochastic fields, better than three digits of accuracy. In the second part, we consider the previous stochastic inverse problem, and we use Bayesian optimisation to find five hyper-parameters of sPINN, namely the width, depth and learning rate of two NNs for learning the modes. Here, we obtain much deeper and wider optimal NNs compared to the manual tuning, leading to even better accuracy, i.e., errors less than 1% for the deterministic values, and about an order of magnitude less for the stochastic fields.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Applying Waveform Correlation to Mining Blasts Using a Global Sparse Network

Agencies that monitor for underground nuclear tests are interested in techniques that automatically characterize mining blasts to reduce the human analyst effort required to produce high-quality event bulletins. Waveform correlation is effective in finding similar waveforms from repeating seismic events, including mining blasts. We report the results of an experiment that uses waveform templates recorded by multiple International Monitoring System stations of the Comprehensive Nuclear-Test-Ban Treaty for up to 10 years prior to detect and identify mining blasts that occur during single weeks of study. We discuss approaches for template selection, threshold setting, and event detection that are specialized for mining blasts and a sparse, global network. We apply the approaches to two different weeks of study for each of two geographic regions, Wyoming and Scandinavia, to evaluate the potential for establishing a set of standards for waveform correlation processing of mining blasts that can be effective for operational monitoring systems with a sparse network. We compare candidate events detected with our processing methods to the Reviewed Event Bulletin of the International Data Centre to develop an intuition about potential reduction in analyst workload.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗
DOE OSTI2020

Applying Waveform Correlation to Mining Blasts Using a Global Sparse Network

Agencies that monitor for underground nuclear tests are interested in techniques that automatically characterize mining blasts to reduce the human analyst effort required to produce high-quality event bulletins. Waveform correlation is effective in finding similar waveforms from repeating seismic events, including mining blasts. We report the results of an experiment that uses waveform templates recorded by multiple International Monitoring System stations of the Preparatory Commission for the Comprehensive Nuclear-Test-Ban Treaty Organization for up to 10 years prior to the time period of interest to detect and identify mining blasts that occur during single weeks of study. We discuss approaches for template selection, threshold setting, and event detection that are specialized for mining blasts and a sparse, global network. We apply the approaches to two different weeks of study for each of two geographic regions, Wyoming and Scandinavia, to evaluate the potential for establishing a set of standards for waveform correlation processing of mining blasts that can be effective for operational monitoring systems with a sparse network. We compare candidate events detected with our processing methods to the Reviewed Event Bulletin of the International Data Centre to develop an intuition about potential reduction in analyst workload.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗
DOE OSTI2026

Optimizing resource allocation in Miscanthus breeding via sparse testing designs for genomic prediction

Phenotyping high-biomass perennial crops is laborious and the rate of genetic gain in conventional perennial crop breeding programs is typically low. So, it is especially important to identify methods that produce efficiency gains in the breeding process. Miscanthus is a C4 perennial grass with favorable characteristics for producing biomass as a feedstock for biofuels and diverse bio-based products. Increasing biomass yield will increase profitability and environmental benefits, so it is a key target for Miscanthus breeding. In addition, the identification of well-adapted genotypes across a wide range of environmental conditions requires the establishment of multi-environment trials (METs). Sparse testing is a genomic prediction-based strategy that reduces the phenotyping costs in METs by selecting a subset of genotypes to evaluate in a subset of environments and then predicts the performance of the unobserved genotype-environment combinations. A Miscanthus sacchariflorus (MSA) population comprising 336 genotypes observed across three environments was analyzed implementing sparse testing designs. Three prediction models considering main effects (environments, genotypes, genomic) and interaction effects (genotype-by-environment; G×E interaction) were implemented for forecasting dry biomass yield (YDY), total culm (TCM), average internode length (AIL), and culm node number (CNN). Multiple calibration sets based on different compositions and sizes were considered to evaluate performance in terms of the predictive ability (PA) and the mean square error (MSE) for a fixed testing set size. The training set size ranged from 52 to 112 to predict a fixed set of 224 unobserved genotypes across all three environments. The results showed that the model accounting for G×E interaction consistently presented the highest PA and the lowest MSE: for CNN (PA: ~0.77, MSE: ~0.5) and YDY (PA: ~0.70, MSE: ~1.3) while for TCM and AIL these ranged from ~0.28 to 0.41 and ~1.3 to 4.3, respectively. Overall, varying training sets and allocation strategies did not affect PA and MSE, with 52 non-overlapping and 0 overlapping genotypes per environment as the optimal cost-effective allocation framework. This suggests that implementing sparse testing designs could significantly reduce phenotyping costs by fivefold, without compromising PA in breeding programs for perennial crops such as Miscanthus.

Miscanthus sacchariflorus (MSA)↗
DOE OSTI2021

Solving the $k$-Sparse Eigenvalue Problem with Reinforcement Learning

We examine the possibility of using a reinforcement learning (RL) algorithm to solve large-scale eigenvalue problems in which the desired the eigenvector can be approximated by a sparse vector with at most k nonzero elements, where k is relatively small compare to the dimension of the matrix to be partially diagonalized. Here, this type of problem arises in applications in which the desired eigenvector exhibits localization properties and in large-scale eigenvalue computations in which the amount of computational resource is limited. When the positions of these nonzero elements can be determined, we can obtain the k-sparse approximation to the original problem by computing eigenvalues of a k × k submatrix extracted from k rows and columns of the original matrix. We review a previously developed greedy algorithm for incrementally probing the positions of the nonzero elements in a k-sparse approximate eigenvector and show that the greedy algorithm can be improved by using an RL method to refine the selection of k rows and columns of the original matrix. We describe how to represent states, actions, rewards and policies in an RL algorithm designed to solve the k-sparse eigenvalue problem and demonstrate the effectiveness of the RL algorithm on two examples originating from quantum many-body physics.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Applying Waveform Correlation to Reduce Seismic Analyst Workload Due to Repeating Mining Blasts

Agencies that monitor for underground nuclear tests are interested in techniques that automatically characterize mining blasts to reduce the human analyst effort required to produce high–quality event bulletins. Waveform correlation is effective in finding similar waveforms from repeating seismic events, including mining blasts. We report the results of an experiment to detect and identify mining blasts for two regions, Wyoming (U.S.A.) and Scandinavia, using waveform templates recorded by multiple International Monitoring System stations of the Preparatory Commission for the Comprehensive Nuclear–Test–Ban Treaty Organization (CTBTO PrepCom) for up to 10 yr prior to the time of interest. We discuss approaches for template selection, threshold setting, and event detection that are specialized for characterizing mining blasts using a sparse, global network. We apply the approaches to one week of data for each of the two regions to evaluate the potential for establishing a set of standards for waveform correlation processing of mining blasts that can be generally applied to operational monitoring systems with a sparse network. Here, we compare candidate events detected with our processing methods to the Reviewed Event Bulletin of the International Data Centre to assess potential reduction in analyst workload.

58 GEOSCIENCES↗