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NASA NTRS1990

Discrete integration of continuous Kalman filtering equations for time invariant second-order structural systems

A general form for the first-order representation of the continuous second-order linear structural-dynamics equations is introduced to derive a corresponding form of first-order continuous Kalman filtering equations. Time integration of the resulting equations is carried out via a set of linear multistep integration formulas. It is shown that a judicious combined selection of computational paths and the undetermined matrices introduced in the general form of the first-order linear structural systems leads to a class of second-order discrete Kalman filtering equations involving only symmetric sparse N x N solution matrices.

Park, K. C.↗

DOE OSTI2021

Dynamic global vegetation models underestimate net CO 2 flux mean and inter-annual variability in dryland ecosystems

Despite their sparse vegetation, dryland regions exert a huge influence over global biogeochemical cycles because they cover more than 40% of the world surface (Schimel 2010 Science 327 418–9). It is thought that drylands dominate the inter-annual variability (IAV) and long-term trend in the global carbon (C) cycle (Poulter et al 2014 Nature 509 600–3, Ahlstrom et al 2015 Science 348 895–9, Zhang et al 2018 Glob. Change Biol. 24 3954–68). Projections of the global land C sink therefore rely on accurate representation of dryland C cycle processes; however, the dynamic global vegetation models (DGVMs) used in future projections have rarely been evaluated against dryland C flux data. Here, we carried out an evaluation of 14 DGVMs (TRENDY v7) against net ecosystem exchange (NEE) data from 12 dryland flux sites in the southwestern US encompassing a range of ecosystem types (forests, shrub- and grasslands). We find that all the models underestimate both mean annual C uptake/release as well as the magnitude of NEE IAV, suggesting that improvements in representing dryland regions may improve global C cycle projections. Across all models, the sensitivity and timing of ecosystem C uptake to plant available moisture was at fault. Spring biases in gross primary production (GPP) dominate the underestimate of mean annual NEE, whereas models' lack of GPP response to water availability in both spring and summer monsoon are responsible for inability to capture NEE IAV. Errors in GPP moisture sensitivity at high elevation forested sites were more prominent during the spring, while errors at the low elevation shrub and grass-dominated sites were more important during the monsoon. We propose a range of hypotheses for why model GPP does not respond sufficiently to changing water availability that can serve as a guide for future dryland DGVM developments. Our analysis suggests that improvements in modeling C cycle processes across more than a quarter of the Earth's land surface could be achieved by addressing the moisture sensitivity of dryland C uptake.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Modular hybrid modeling to increase efficiency, explore structural uncertainty, and allow multidimensional complexity scaling in land surface models

Land surface models (LSMs) are indispensable tools for predicting hydrologic extremes, as well as a particularly uncertain component of Earth system models that has stubbornly resisted the convergence in projections over several successive generations of model intercomparisons. This uncertainty in LSMs is poorly quantified and poorly attributed to specific processes, which has hampered efforts to focus research in reducing uncertainty. This has resulted from sparse sampling of the possible uncertainty space—which is high-dimensional and has contributions from parametric, structural, initial, and boundary condition uncertainties—as an artifact of CMIP-type ensembles of opportunity and limitations inherent in observational benchmarks. A new approach is needed to understand and reduce this uncertainty, based around individual LSMs that can represent the breadth of assumptions represented in current CMIP-type efforts, while at the same time exploring that uncertainty in a systematic way, confronting multiple types of observations, and where justified, replacing process representations with ML-driven emulators. We propose an approach of modular hybrid modeling to address these challenges.

58 GEOSCIENCES↗

DOE OSTI2025

Joint state-parameter estimation for the reduced fracture model via the united filter

Here, in this paper, we introduce an effective United Filter method for jointly estimating the solution state and physical parameters in flow and transport problems within fractured porous media. Fluid flow and transport in fractured porous media are critical in subsurface hydrology, geophysics, and reservoir geomechanics. Reduced fracture models, which represent fractures as lower-dimensional interfaces, enable efficient multi-scale simulations. However, reduced fracture models also face accuracy challenges due to modeling errors and uncertainties in physical parameters such as permeability and fracture geometry. To address these challenges, we propose a United Filter method, which integrates the Ensemble Score Filter (EnSF) for state estimation with the Direct Filter for parameter estimation. EnSF, based on a score-based diffusion model framework, produces ensemble representations of the state distribution without deep learning. Meanwhile, the Direct Filter, a recursive Bayesian inference method, estimates parameters directly from state observations. The United Filter combines these methods iteratively: EnSF estimates are used to refine parameter values, which are then fed back to improve state estimation. Numerical experiments demonstrate that the United Filter method surpasses the state-of-the-art Augmented Ensemble Kalman Filter, delivering more accurate state and parameter estimation for reduced fracture models. This framework also provides a robust and efficient solution for PDE-constrained inverse problems with uncertainties and sparse observations.

Bayesian inference↗

DOE OSTI2023

Implementing and Benchmarking the Locally Competitive Algorithm on the Loihi 2 Neuromorphic Processor

Neuromorphic processors have garnered considerable interest in recent years for their potential in enabling energy-efficient and high-speed computing. The Locally Competative Algorithm (LCA) has been utilized for power efficient sparse coding on neuromophic processors, including the first Loihi processor \cite{appletospikes, loihi1}. With the Loihi 2 processor enabling custom neuron models and graded spike communication, more complex implementations of LCA are possible \cite{loihi2}. We present a new implementation of LCA designed for the Loihi 2 processor and perform an initial set of benchmarks comparing it to LCA on CPU and GPU devices. In these experiments LCA on Loihi 2 is faster and orders of magnitude more efficient, while maintaining similar reconstruction quality. We find this performance improvement increases as the LCA parameters are tuned towards greater representation sparsity. Our study highlights the potential of neuromorphic processors, particularly Loihi 2, in enabling intelligent,autonomous, real-time processing on small robots, satellite where there are strict SWaP (small, lightweighr, and low-power) requirement. By demonstrating the superior performance of LCA on Loihi 2 compared to conventional computing device, our study suggests that Loihi 2 could be a valuable tool in advancing these types of applications. Overall, our study highlights the potential of neuromorphic processors for efficient and accurate data processing on resource-constrained devices.

Parpart, Gavin G.↗

DOE OSTI2021

Satellite solar-induced chlorophyll fluorescence and near-infrared reflectance capture complementary aspects of dryland vegetation productivity dynamics

Mounting evidence indicates dryland ecosystems play an important role in driving the interannual variability and trend of the terrestrial carbon sink. Nevertheless, our understanding of the seasonal dynamics of dryland ecosystem carbon uptake through photosynthesis [gross primary productivity (GPP)] remains relatively limited due in part to the limited availability of long-term data and unique challenges associated with satellite remote sensing across dryland ecosystems. Here, we comprehensively evaluated longstanding and emerging satellite vegetation proxies in their ability to capture seasonal dryland GPP dynamics. Specifically, we evaluated: 1) reflectance-based proxies normalized difference vegetation index (NDVI), soil adjusted vegetation index (SAVI), near infrared reflectance index (NIR v ), and kernel NDVI (kNDVI) from the MODerate resolution Imaging Spectroradiometer (MODIS); and 2) newly available physiologically-based proxy solar-induced chlorophyll fluorescence (SIF) from the TROPOspheric Monitoring Instrument (TROPOMI). As a performance benchmark, we used GPP estimates from a robust network of 21 western United States eddy covariance tower sites that span representative gradients in dryland ecosystem climate and functional composition. We found that NIR v and SIF were the best performing GPP proxies and captured complementary aspects of seasonal GPP dynamics across dryland ecosystem types. NIR v offered better performance than the other proxies across relatively low-productivity, sparsely non-evergreen vegetated sites (R 2 = 0.59 ± 0.13); whereas SIF best captured seasonal dynamics across relatively high-productivity sites, including evergreen-dominated sites (R 2 = 0.74 ± 0.07). Notably, across grass-dominated sites, all reflectance-based proxies (NDVI, SAVI, NIRv and kNDVI) showed significant seasonal bias (hysteresis) that strengthened with the total fraction of woody vegetation cover, likely due to seasonal patterns in woody vegetation reflectance that are unrelated to or decoupled from GPP. In conclusion, future efforts to fully integrate the complementary strengths of NIR v and SIF could significantly improve our understanding and representation of dryland GPP dynamics in satellite-based models.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS2021

Assimilation of DAWN Doppler Wind Lidar Data During the 2017 Convective Processes Experiment (CPEX): Impact on Precipitation and Flow Structure

An improved representation of 3-D air motion and precipitation structure through forecast models and assimilation of observations is vital for improvements in weather forecasting capabilities. However, there are few independent data to properly validate a model forecast of precipitation structure when the underlying dynamics are evolving on short convective timescales. Using data from the JPL Ku/Ka-band Airborne Precipitation Radar (APR-2) and the 2 μmDoppler Aerosol Wind (DAWN) lidar collected during the2017 Convective Processes Experiment (CPEX), the NASA Unified Weather Research and Forecasting (WRF) Ensemble Data Assimilation System (EDAS) modeling system was used to quantify the impact of high-resolution sparsely sampled DAWN measurements on the analyzed variables and on the forecast when the DAWN winds were assimilated. Over-all, the assimilation of the DAWN wind profiles had a discernible impact on the wind field as well as the evolution and timing of the 3-D precipitation structure. Analysis of individual variables revealed that the assimilation of the DAWN winds resulted in important and coherent modifications of the environment. It led to an increase in the near-surface convergence, temperature, and water vapor, creating more favorable conditions for the development of convection exactly where it was observed (but not present in the control run). Comparison to APR-2 and observations by the Global Precipitation Measurement (GPM) satellite shows a much-improved forecast after the assimilation of the DAWN winds – development of precipitation where there was none, more organized precipitation where there was some, and a much more intense and organized cold pool, similar to the analysis of the dropsonde data. The onset of the vertical evolution of the precipitation showed similar radar-derived cloud-top heights, but delayed in time. While this investigation was limited to a single CPEX flight date, the investigation design is appropriate for further investigation of the impact of airborne Doppler wind lidar observations upon short-term convective precipitation forecasts

DAWN↗

DOE OSTI2020

Modeling the smoky troposphere of the southeast Atlantic: a comparison to ORACLES airborne observations from September of 2016

The southeast Atlantic is home to well-defined smoke outflow from Africa coinciding vertically with extensive marine boundary-layer cloud decks, both reaching their climatological maxima in spatial extent around September. A framework is put forth for evaluating the performance of a range of global and regional aerosol models against observations made during the NASA ORACLES (ObseRvations of Aerosols above CLouds and their intEractionS) airborne mission in September 2016. The sparse airborne observations are first aggregated into 2o grid boxes and into three vertical layers: the cloud-topped marine boundary layer (MBL), the layer from cloud top to 3 km, and the 3-6 km layer. Aerosol extensive properties simulated for the entire study region for all September suggest that the 2016 ORACLES observations are reasonably representative of the regional monthly average, with systematic deviations of 30% or less. All six models typically place the bottom of the smoke layer at lower altitudes than do the airborne lidar observations by 300-1400 m, whereas model aerosol top heights are within 0-500 m of the observations. All but one of the models that report carbonaceous aerosol masses underestimate the ratio of particulate extinction to the masses, a proxy for mass extinction efficiency, in 3-6 km. Notable findings on individual models include that WRF-CAM5 predicts the mass of black carbon and organic aerosols with minor (~10% or less) biases. GEOS-5 overestimates the carbonaceous particle masses in the MBL by a factor of 3-6. Extinction coefficients in the free troposphere (FT) and above-cloud aerosol optical depth (ACAOD) are 10-30% lower in WRF-CAM5, 30-50% lower in GEOS-5, 10-40% higher in GEOS-Chem, 10-20% higher in EAM-E3SM except for the practically unbiased 3-6 km extinction, and 20-70% lower in the Unified Model, than the airborne in situ, lidar and sunphotometer measurements. ALADIN-Climate also underestimates the ACAOD, by 30%. GEOS-5 and GEOS-Chem predict carbon monoxide in the MBL with small (10% or less) negative biases, despite their overestimates of carbonaceous aerosol masses. Overall, this study highlights a new approach to utilizing airborne aerosol measurements for model diagnosis.

Shinozuka, Yohei↗

NASA NTRS1990

Recognition of simple visual images using a sparse distributed memory: Some implementations and experiments

Previously, a method was described of representing a class of simple visual images so that they could be used with a Sparse Distributed Memory (SDM). Herein, two possible implementations are described of a SDM, for which these images, suitably encoded, will serve both as addresses to the memory and as data to be stored in the memory. A key feature of both implementations is that a pattern that is represented as an unordered set with a variable number of members can be used as an address to the memory. In the 1st model, an image is encoded as a 9072 bit string to be used as a read or write address; the bit string may also be used as data to be stored in the memory. Another representation, in which an image is encoded as a 256 bit string, may be used with either model as data to be stored in the memory, but not as an address. In the 2nd model, an image is not represented as a vector of fixed length to be used as an address. Instead, a rule is given for determining which memory locations are to be activated in response to an encoded image. This activation rule treats the pieces of an image as an unordered set. With this model, the memory can be simulated, based on a method of computing the approximate result of a read operation.

Jaeckel, Louis A.↗

DOE OSTI2019

Solving equilibrium problems using extended mathematical programming

We introduce an extended mathematical programming framework for specifying equilibrium problems and their variational representations, such as generalized Nash equilibrium, multiple optimization problems with equilibrium constraints, and (quasi-) variational inequalities, and computing solutions of them from modeling languages. We define a new set of constructs with which users annotate variables and equations of the model to describe equilibrium and variational problems. Our constructs enable a natural translation of the model from one formulation to another more computationally tractable form without requiring the modeler to supply derivatives. In the context of many independent agents in the equilibrium, we facilitate expression of sophisticated structures such as shared constraints and additional constraints on their solutions. We define shared variables and demonstrate their uses for sparse reformulation, economic equilibrium problems sharing economic states, mixed pricing behavior of agents, and so on. We give some equilibrium and variational examples from the literature and describe how to formulate them using our framework. Experimental results comparing performance of various complementarity formulations for shared variables are provided. Our framework has been implemented and is available within GAMS/EMP.

Equilibrium programming↗

DOE OSTI2018

Compressed sparse tensor based quadrature for vibrational quantum mechanics integrals

A new method for fast evaluation of high dimensional integrals arising in quantum mechanics is proposed. Here, the method is based on sparse approximation of a high dimensional function followed by a low-rank compression. In the first step, we interpret the high dimensional integrand as a tensor in a suitable tensor product space and determine its entries by a compressed sensing based algorithm using only a few function evaluations. Secondly, we implement a rank reduction strategy to compress this tensor in a suitable low-rank tensor format using standard tensor compression tools. This allows representing a high dimensional integrand function as a small sum of products of low dimensional functions. Finally, a low dimensional Gauss–Hermite quadrature rule is used to integrate this low-rank representation, thus alleviating the curse of dimensionality. Finally, numerical tests on synthetic functions, as well as on energy correction integrals for water and formaldehyde molecules demonstrate the efficiency of this method using very few function evaluations as compared to other integration strategies.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

AIVT: Inference of turbulent thermal convection from measured 3D velocity data by physics-informed Kolmogorov-Arnold networks

We propose the artificial intelligence velocimetry-thermometry (AIVT) method to reconstruct a continuous and differentiable representation of the temperature and velocity in turbulent convection from measured three-dimensional (3D) velocity data. AIVT is based on physics-informed Kolmogorov-Arnold networks and trained by optimizing a loss function that minimizes residuals of the velocity data, boundary conditions, and governing equations. We apply AIVT to a set of simultaneously measured 3D temperature and velocity data of Rayleigh-Bénard convection, obtained by combining particle image thermometry and Lagrangian particle tracking. This enables us to directly compare machine learning results to true volumetric, simultaneous temperature and velocity measurements. We demonstrate that AIVT can reconstruct and infer continuous, instantaneous velocity and temperature fields and their gradients from sparse experimental data at a high resolution, providing an additional approach for understanding thermal turbulence.

Science & Technology - Other Topics↗

DOE OSTI2025

FM4NPP: A Scaling Foundation Model for Nuclear and Particle Physics

Large language models have revolutionized artificial intelligence by enabling large, generalizable models trained through self-supervision. This paradigm has inspired the development of scientific foundation models (FMs). However, applying this capability to experimental particle physics is challenging due to the sparse, spatially distributed nature of detector data, which differs dramatically from natural language. This work addresses if an FM for particle physics can scale and generalize across diverse tasks. We introduce a new dataset with more than 11 million particle collision events and a suite of downstream tasks and labeled data for evaluation. We propose a novel self-supervised training method for detector data and demonstrate its neural scalability with models that feature up to 188 million parameters. With frozen weights and task-specific adapters, this FM consistently outperforms baseline models across all downstream tasks. The performance also exhibits robust data-efficient adaptation. Further analysis reveals that the representations extracted by the FM are task-agnostic but can be specialized via a single linear mapping for different downstream tasks.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2018

Compact video content representation for video coding using low multi-linear tensor rank approximation with dynamic core tensor order

Tensor is a multi-way representation of an entity that is widely used in many applications of mathematics and physics. The wide range of tensor algebra operations attract the researchers of graphical and vision field to identify unique methods for various applications such as segmentation, compression, indexing and so on. In this paper, low multi-linear rank approximation of a tensor is used for decomposition so as to perform compression on a video that is represented as a 4D tensor. Thus, the encoder has blocks for (1) multilinear rank approximation method so as to aid decomposition, (2) sparsity removal of residual data to reduce the required memory storage to a small level, (3) quantization on the sparse less residual data and (4) LZ77 dictionary coding for the video. The decoder uses a tensor reconstruction block along with residual error correction block that reduces loss/error in the reconstructed video. The size of core tensor is an important factor in rank approximation. It is identified at run time depending on the video contents. This size is determined adaptively using Tikhonov’s regularization method. The best value of core tensor size is identified with the corner of L-curve which preserves the video contents from heavy loss/error. Experimental results of the proposed work on comparison with H.264/AVC compression method indicate that the proposed method achieves up to 10% improvement in compression ratio with the least amount of loss and a maximum signal to noise ratio of 0.14. The proposed system gives better compression ratio than H.265 for videos with more number of frames without compromising quality.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1998

Data Mining and Optimization Tools for Developing Engine Parameters Tools

This project was awarded for understanding the problem and developing a plan for Data Mining tools for use in designing and implementing an Engine Condition Monitoring System. From the total budget of $5,000, Tricia and I studied the problem domain for developing ail Engine Condition Monitoring system using the sparse and non-standardized datasets to be available through a consortium at NASA Lewis Research Center. We visited NASA three times to discuss additional issues related to dataset which was not made available to us. We discussed and developed a general framework of data mining and optimization tools to extract useful information from sparse and non-standard datasets. These discussions lead to the training of Tricia Erhardt to develop Genetic Algorithm based search programs which were written in C++ and used to demonstrate the capability of GA algorithm in searching an optimal solution in noisy datasets. From the study and discussion with NASA LERC personnel, we then prepared a proposal, which is being submitted to NASA for future work for the development of data mining algorithms for engine conditional monitoring. The proposed set of algorithm uses wavelet processing for creating multi-resolution pyramid of the data for GA based multi-resolution optimal search. Wavelet processing is proposed to create a coarse resolution representation of data providing two advantages in GA based search: 1. We will have less data to begin with to make search sub-spaces. 2. It will have robustness against the noise because at every level of wavelet based decomposition, we will be decomposing the signal into low pass and high pass filters.

Dhawan, Atam P.↗

DOE OSTI2022

Design of Digital Twin Sensing Strategies Via Predictive Modeling and Interpretable Machine Learning

This work develops a methodology for sensor placement and dynamic sensor scheduling decisions for digital twins. The digital twin data assimilation is posed as a classification problem, and predictive models are used to train optimal classification trees that represent the map from observed data to estimated digital twin states. In addition to providing a rapid digital twin updating capability, the resulting classification trees yield an interpretable mathematical representation that can be queried to inform sensor placement and sensor scheduling decisions. The proposed approach is demonstrated for a structural digital twin of a 12 ft wingspan unmanned aerial vehicle. Offline, training data are generated by simulating scenarios using predictive reduced-order models of the vehicle in a range of structural states. Furthermore, these training data can be further augmented using experimental or other historical data. In operation, the trained classifier is applied to observational data from the physical vehicle, enabling rapid adaptation of the digital twin in response to changes in structural health. Within this context, we study the performance of the optimal tree classifiers and demonstrate how they enable explainable structural assessments from sparse sensor measurements and also inform optimal sensor placement.

47 OTHER INSTRUMENTATION↗

DOE OSTI2021

Global field reconstruction from sparse sensors with Veronoi tessellation-assisted deep learning

Achieving accurate and robust global situational awareness of a complex time-evolving field from a limited number of sensors has been a longstanding challenge. This reconstruction problem is especially difficult when sensors are sparsely positioned in a seemingly random or unorganized manner, which is often encountered in a range of scientific and engineering problems. Moreover, these sensors can be in motion and can become online or offline over time. The key leverage in addressing this scientific issue is the wealth of data accumulated from the sensors. As a solution to this problem, we propose a data-driven spatial field recovery technique founded on a structured grid-based deep-learning approach for arbitrary positioned sensors of any numbers. It should be noted that the naïve use of machine learning becomes prohibitively expensive for global field reconstruction and is furthermore not adaptable to an arbitrary number of sensors. In the present work, we consider the use of Voronoi tessellation to obtain a structured-grid representation from sensor locations enabling the computationally tractable use of convolutional neural networks. One of the central features of the present method is its compatibility with deep-learning based super-resolution reconstruction techniques for structured sensor data that are established for image processing. The proposed reconstruction technique is demonstrated for unsteady wake flow, geophysical data, and three-dimensional turbulence. The current framework is able to handle an arbitrary number of moving sensors, and thereby overcomes a major limitation with existing reconstruction methods. The presented technique opens a new pathway towards the practical use of neural networks for real-time global field estimation.

Fukami, Kai↗

DOE OSTI2024

Leveraging Multitime Hamilton–Jacobi PDEs for Certain Scientific Machine Learning Problems

Hamilton-Jacobi partial differential equations (HJ PDEs) have deep connections with a wide range of fields, including optimal control, differential games, and imaging sciences. By considering the time variable to be a higher dimensional quantity, HJ PDEs can be extended to the multi-time case. In this paper, we establish a novel theoretical connection between specific optimization problems arising in machine learning and the multi-time Hopf formula, which corresponds to a representation of the solution to certain multi-time HJ PDEs. Through this connection, we increase the interpretability of the training process of certain machine learning applications by showing that when we solve these learning problems, we also solve a multi-time HJ PDE and, by extension, its corresponding optimal control problem. As a first exploration of this connection, we develop the relation between the regularized linear regression problem and the Linear Quadratic Regulator (LQR). We then leverage our theoretical connection to adapt standard LQR solvers (namely, those based on the Riccati ordinary differential equations) to design new training approaches for machine learning. Lastly, we provide some numerical examples that demonstrate the versatility and possible computational advantages of our Riccati-based approach in the context of continual learning, post-training calibration, transfer learning, and sparse dynamics identification.

97 MATHEMATICS AND COMPUTING↗