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DOE OSTI2022

Deep Learning for Simultaneous Inference of Hydraulic and Transport Properties

Abstract Identification of a heterogeneous conductivity field and reconstruction of a contaminant release history are key aspects of subsurface remediation. These two goals are achieved by combining model predictions with sparse and noisy hydraulic head and concentration measurements. Solution of this inverse problem is notoriously difficult due to, in part, high dimensionality of the parameter space and high computational cost of repeated forward solves. We use a convolutional adversarial autoencoder (CAAE) to parameterize a heterogeneous non‐Gaussian conductivity field via a low‐dimensional latent representation. A three‐dimensional dense convolutional encoder‐decoder (DenseED) network serves as a forward surrogate of the flow and transport model. The CAAE‐DenseED surrogate is fed into the ensemble smoother with multiple data assimilation (ESMDA) algorithm to sample from the Bayesian posterior distribution of the unknown parameters, forming a CAAE‐DenseED‐ESMDA inversion framework. The resulting CAAE‐DenseED‐ESMDA inversion strategy is used to identify a three‐dimensional contaminant source and conductivity field. A comparison of the inversion results from CAAE‐ESMDA with physical flow and transport simulator and from CAAE‐DenseED‐ESMDA shows that the latter yields accurate reconstruction results at the fraction of the computational cost of the former.

Zhou, Zitong↗

DOE OSTI2026

Goal-oriented real-time Bayesian inference for linear autonomous dynamical systems with application to digital twins for tsunami early warning

We present a goal-oriented framework for constructing digital twins with the following properties: (1) they employ discretizations of high-fidelity partial differential equation (PDE) models governed by autonomous dynamical systems, leading to large-scale forward problems; (2) they solve a linear inverse problem to assimilate observational data to infer uncertain model components followed by a forward prediction of the evolving dynamics; and (3) the entire end-to-end, data-to-inference-to-prediction computation is carried out without approximation and in real time through a Bayesian framework that rigorously accounts for uncertainties. Several challenges must be overcome to realize this framework, including the large scale of the forward problem, the high dimensionality of the parameter space, and for a class of problems including those we target, the slow decay of the singular values of the parameter-to-observable map. Here we introduce a methodology to overcome these challenges by exploiting the autonomous structure of the forward model to decompose the solution of the inverse problem into a one-time-only offline phase in which the PDE model is solved a limited number of times (equal to the number of sensors), and an online phase that maps well onto GPUs and computes the parameter inference and prediction of quantities of interest in real time, given observational data. Our ultimate goal is to apply this framework to construct digital twins for subduction zones, including Cascadia, to provide early warning for tsunamis generated by megathrust earthquakes. To this end, we demonstrate how our methodology can be used to employ seafloor pressure observations, along with the coupled acoustic–gravity wave equations, to infer the earthquake-induced spatiotemporal seafloor motion (discretized with $\mathscr{O}$ (10 9 ) parameters) and forward predict the tsunami propagation. We present results of an end-to-end inference, prediction, and uncertainty quantification for a representative test problem with $\mathscr{O}$ (10 8 ) inversion parameters for which goal-oriented Bayesian inference is accomplished exactly and in real time, that is, in a matter of seconds.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2013

Monte Carlo Bayesian Inference on a Statistical Model of Sub-gridcolumn Moisture Variability Using High-resolution Cloud Observations : Sensitivity Tests and Results - Part II

Part I presented a Monte Carlo Bayesian method for constraining a complex statistical model of GCM sub-gridcolumn moisture variability using high-resolution MODIS cloud data, thereby permitting large-scale model parameter estimation and cloud data assimilation. This part performs some basic testing of this new approach, verifying that it does indeed significantly reduce mean and standard deviation biases with respect to the assimilated MODIS cloud optical depth, brightness temperature and cloud top pressure, and that it also improves the simulated rotational-Ramman scattering cloud optical centroid pressure (OCP) against independent (non-assimilated) retrievals from the OMI instrument. Of particular interest, the Monte Carlo method does show skill in the especially difficult case where the background state is clear but cloudy observations exist. In traditional linearized data assimilation methods, a subsaturated background cannot produce clouds via any infinitesimal equilibrium perturbation, but the Monte Carlo approach allows finite jumps into regions of non-zero cloud probability. In the example provided, the method is able to restore marine stratocumulus near the Californian coast where the background state has a clear swath. This paper also examines a number of algorithmic and physical sensitivities of the new method and provides guidance for its cost-effective implementation. One obvious difficulty for the method, and other cloud data assimilation methods as well, is the lack of information content in the cloud observables on cloud vertical structure, beyond cloud top pressure and optical thickness, thus necessitating strong dependence on the background vertical moisture structure. It is found that a simple flow-dependent correlation modification due to Riishojgaard (1998) provides some help in this respect, by better honoring inversion structures in the background state.

Monte Carlo Bayesian inference↗

DOE OSTI2022

Development of an open-source regional data assimilation system in PEcAn v. 1.7.2: application to carbon cycle reanalysis across the contiguous US using SIPNET

Abstract. The ability to monitor, understand, and predict the dynamics of the terrestrial carbon cycle requires the capacity to robustly and coherently synthesize multiple streams of information that each provide partial information about different pools and fluxes. In this study, we introduce a new terrestrial carbon cycle data assimilation system, built on the PEcAn model–data eco-informatics system, and its application for the development of a proof-of-concept carbon “reanalysis” product that harmonizes carbon pools (leaf, wood, soil) and fluxes (GPP, Ra, Rh, NEE) across the contiguous United States from 1986–2019. We first calibrated this system against plant trait and flux tower net ecosystem exchange (NEE) using a novel emulated hierarchical Bayesian approach. Next, we extended the Tobit–Wishart ensemble filter (TWEnF) state data assimilation (SDA) framework, a generalization of the common ensemble Kalman filter which accounts for censored data and provides a fully Bayesian estimate of model process error, to a regional-scale system with a calibrated localization. Combined with additional workflows for propagating parameter, initial condition, and driver uncertainty, this represents the most complete and robust uncertainty accounting available for terrestrial carbon models. Our initial reanalysis was run on an irregular grid of ∼ 500 points selected using a stratified sampling method to efficiently capture environmental heterogeneity. Remotely sensed observations of aboveground biomass (Landsat LandTrendr) and leaf area index (LAI) (MODIS MOD15) were sequentially assimilated into the SIPNET model. Reanalysis soil carbon, which was indirectly constrained based on modeled covariances, showed general agreement with SoilGrids, an independent soil carbon data product. Reanalysis NEE, which was constrained based on posterior ensemble weights, also showed good agreement with eddy flux tower NEE and reduced root mean square error (RMSE) compared to the calibrated forecast. Ultimately, PEcAn's new open-source regional data assimilation framework provides a scalable workflow for harmonizing multiple data constraints and providing a uniform synthetic platform for carbon monitoring, reporting, and verification (MRV) as well as accelerating terrestrial carbon cycle research.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2023

Extending Parsimonious Bayesian Inference

Parsimonious Bayesian inference is a theoretical framework for efficient data assimilation that seeks to balance increased consistency between predictions and training data against corresponding increases in model complexity. Within this framework, over-training is understood as optimization that encodes excessive information within model parameters while only achieving small improvements between predictions and training data. This project aims to develop practical methods of limiting excess model information during optimization. One key observation is that practical heuristics for parsimonious learning in high-dimensions must balance expressivity, i.e. the ability of the model to capture diverse predictions with only a few non-zero parameters, against discoverability, i.e. the ability to train the model with gradient-based optimization and drive parameters to low information states. As such, we developed logical activation functions that are able to adaptively approximate arbitrary truth tables that define Boolean logic operations within a probabilistic framework. These functions have demonstrated the ability to learn exclusive disjunction (XOR) and conditioned disjunction (if [condition] then [result_if_true] else [result_if_false]) within a single layer of a neural network. To efficiently exploit these activation functions to drive parsimonious learning required several other advances within the domain of variational inference. The most efficient form of complexity suppression is structured sparsification, driving most model parameters to zero while achieving the structural coherence among nonzeros needed for bandwidth reduction. Such models are not only far more efficient at suppressing information-theoretic complexity, they also reduce the other forms of complexity (computations, communication, storage, and the number of dependencies needed to evaluate predictions). Aiming to support enhanced sparsification, this project examined new approaches to high-dimensional variational inference that allow us to calibrate and control parameter uncertainty during optimization. By identifying which parameters can sustain sparsifying perturbations with little impact on prediction quality, we can develop better pruning strategies by framing them as approximate Bayesian inference. These advances also open paths to mitigate concerns with deploying advanced learning methods in resource-constrained environments, such as running models on power-limited or communication-limited devices.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

How data science methods can improve the quality and efficiency of ICF and HEDP research

Data Science methods (many that are Bayesian based) are widely used in the physical sciences to estimate model parameters from experimental data, synthesize heterogeneous data, calibrate models, design experiments, and determine statistical significance of data. These methods provide a wealth of advantages over traditional analysis techniques because: 1) uncertainties are rigorously defined and propagated naturally through complex systems including covariance, 2) prior information is captured within the analysis framework (including rad-MHD and rad-hydro simulations), 3) competing models can be selected and/or ruled out using quantitative criteria, and 4) complex, heterogeneous data can be incorporated simultaneously. While these methods have been widely adopted as the gold standard in fields such as particle physics, astronomy, and biology, they have been slow to catch on in Inertial Confinement Fusion (ICF) and High Energy Density Physics (HEDP) research. Recently, several teams at LLNL, SNL, LANL, and the LLE have been exploring the use of these tools in their research and have found success. Here we propose that a concerted effort to consolidate these independent research efforts by developing and deploying common tools for use across the complex can revolutionize the way we approach data analysis, assimilation of theory and experiment, and decision making. The Bayesian formalism provides a means to accomplish this, but we are lacking certain infrastructure to make it happen on a large scale. Furthermore, once adopted, these techniques can be used to develop standards by which discoveries can be judged, similar to the so-called 5σ rule in high energy particle physics. Such standards may be used in the future to address the issue of unknown reproducibility in ICF and HED experiments caused by low shot rate and high cost per experiment. Our goals as a group are to advance the state of the art in HED measurement science by enabling: 1) better inferences from data with well-defined uncertainties, 2) better use of the data we have and continue to collect, 3) intelligent synthesis of data, 4) evaluation of the statistical significance of our data, and 5) informed decision making regarding the design of new experiments and instruments.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2020

"Sintering" Models and In-Situ Experiments: Data Assimilation for Microstructure Prediction in SLS Additive Manufacturing of Nylon Components

Selective laser sintering methods are workhorses for additively manufacturing polymer-based components. The ease of rapid prototyping also means it is easy to produce illicit components. It is necessary to have a data-calibrated in-situ physical model of the build process in order to predict expected and defective microstructure characteristics that inform component provenance. Toward this end, sintering models are calibrated and characteristics such as component defects are explored. This is accomplished by assimilating multiple data streams, imaging analysis, and computational model predictions in an adaptive Bayesian parameter estimation algorithm. From these data sources, along with a phase-field model, bulk porosity distributions are inferred. Model parameters are constrained to physically-relevant search directions by sensitivity analysis, and then matched to predictions using adaptive sampling. Using this feedback loop, data-constrained estimates of sintering model parameters along with uncertainty bounds are obtained.

3D printing, Additive Manufacturing, polymer, sint↗

DOE OSTI2025

Combining Observations and Models: A Review of the CARDAMOM Framework for Data‐Constrained Terrestrial Ecosystem Modeling

The rapid increase in the volume and variety of terrestrial biosphere observations (i.e., remote sensing data and in situ measurements) offers a unique opportunity to derive ecological insights, refine process‐based models, and improve forecasting for decision support. However, despite their potential, ecological observations have primarily been used to benchmark process‐based models, as many past and current models lack the capability to directly integrate observations and their associated uncertainties for parameterization. In contrast, data assimilation frameworks such as the CARbon DAta MOdel fraMework (CARDAMOM) and its suite of process‐based models, known as the Data Assimilation Linked Ecosystem Carbon Model (DALEC), are specifically designed for model‐data fusion. This review, motivated by a recent CARDAMOM community workshop, examines the development and applications of CARDAMOM, with an emphasis on its role in advancing ecosystem process understanding. CARDAMOM employs a Bayesian approach, using a Markov Chain Monte Carlo algorithm to enable data‐driven calibration of DALEC parameters and initial states (i.e., carbon pool sizes) through observation operators. CARDAMOM's unique ability to retrieve localized model process parameters from diverse datasets—ranging from in situ measurements to global satellite observations—makes it a highly flexible tool for analyzing spatially variable ecosystem responses to environmental change. However, assimilating these data also presents challenges, including data quality issues that propagate into model skill, as well as trade‐offs between model complexity, parameter equifinality, and predictive performance. We discuss potential solutions to these challenges, such as reducing parameter equifinality by incorporating new observations. This review also offers community recommendations for incorporating emerging datasets, integrating machine learning techniques, strengthening collaboration with remote sensing, field, and modeling communities, and expanding CARDAMOM's relevance for localized ecosystem monitoring and decision‐making. CARDAMOM enables a deep, mechanistic understanding of terrestrial ecosystem dynamics that cannot be achieved through empirical analyses of observational datasets or weakly constrained models alone.

Bayesian inference↗

NASA NTRS2010

Utilization of Hydrologic Remote Sensing Data in Land Surface Modeling and Data Assimilation: Current Status and Challenges

Recent advances in remote sensing technologies have enabled the monitoring and measurement of the Earth's land surface at an unprecedented scale and frequency. The myriad of these land surface observations must be integrated with the state-of-the-art land surface model forecasts using data assimilation to generate spatially and temporally coherent estimates of environmental conditions. These analyses are of critical importance to real-world applications such as agricultural production, water resources management and flood, drought, weather and climate prediction. This need motivated the development of NASA Land Information System (LIS), which is an expert system encapsulating a suite of modeling, computational and data assimilation tools required to address challenging hydrological problems. LIS integrates the use of several community land surface models, use of ground and satellite based observations, data assimilation and uncertainty estimation techniques and high performance computing and data management tools to enable the assessment and prediction of hydrologic conditions at various spatial and temporal scales of interest. This presentation will focus on describing the results, challenges and lessons learned from the use of remote sensing data for improving land surface modeling, within LIS. More specifically, studies related to the improved estimation of soil moisture, snow and land surface temperature conditions through data assimilation will be discussed. The presentation will also address the characterization of uncertainty in the modeling process through Bayesian remote sensing and computational methods.

Kumar, Sujay V.↗

NASA NTRS2020

Assimilation of satellite microwave observations over the rainbands of tropical cyclones

A novel Bayesian Monte Carlo integration (BMCI) technique was developed to retrieve geophysical variables from satellite microwave radiometer data in the presence of tropical cyclones. The BMCI technique includes three steps: generating a stochastic database, simulating satellite brightness temperatures using a radiative transfer model, and retrieving geophysical variables such as profiles of temperature, relative humidity, and cloud liquid and ice water content from real observations. The technique also provides uncertainty estimates for each retrieval and can output the error covariance matrix of selected parameters. The measurements from the Advanced Technology Microwave Sounder (ATMS) on board Suomi National Polar-Orbiting Partnership (Suomi NPP) and the Global Precipitation Measurement (GPM) Microwave Imager (GMI) were used as input. A new technique was developed to correct the ATMS and GMI observations for the beam-filling effect, which is due to small-scale variability of precipitation and clouds when compared with the instrument footprint and also the nonlinear relation between the brightness temperature and precipitation. In addition, the assimilation of the BMCI retrievals into the NASA GEOS model is discussed for Hurricane Maria. The results show that assimilating the BMCI retrievals can influence the dynamical features of the cyclone, including a stronger warm core, a symmetric eye, and vertically aligned wind columns. Two possible factors that may limit the impact of the BMCI retrievals include 1) the resolution of the model (about 25 km), which was too coarse to show the potential of the BMCI data in improving the representation of tropical storms in the model forecast, and 2) the data assimilation system not being able to consider vertically correlated observation errors.

Isaac Moradi↗

DOE OSTI2022

Kernel learning backward SDE filter for data assimilation

In this paper, we develop a kernel learning backward SDE filter method to estimate the state of a stochastic dynamical system based on its partial noisy observations. A system of forward backward stochastic differential equations is used to propagate the state of the target dynamical model, and Bayesian inference is applied to incorporate the observational information. Further, to characterize the dynamical model in the entire state space, we introduce a kernel learning method to learn a continuous global approximation for the conditional probability density function of the target state by using discrete approximated density values as training data. Numerical experiments demonstrate that the kernel learning backward SDE is highly effective.

97 MATHEMATICS AND COMPUTING↗

NASA NTRSDate not supplied

Assimilation of microwave satellite observations over the rainbands of tropical cyclones

The potential of microwave observations in improving the weather forecasts is limited by the accuracy of all-sky radiative transfer calculations. We introduce a novel Bayesian MonteCarlo technique to improve the assimilation of microwave observations over the rainbands of tropical cyclones. The BMCI technique eliminates the need for a forward model in the data assimilation system. The technique includes three steps, (i) generating a comprehensive dataset using in-situ cloud measurements and atmospheric profiles, (ii) generating synthetic ATMS observations from the training dataset, and (iii) using real observations to estimate the geophysical variables over the rainbands of tropical cyclones. The retrieved profiles of temperature, relative humidity, and cloud water content as well assurface information such as SST were then assimilated into the model. The results show that assimilating the BMCI retrievals can influence the dynamical features of the cyclone, including a stronger warm core, a symmetric eye, and vertically aligned wind columns.

Monte Carlo↗

DOE OSTI2022

Efficient high-dimensional variational data assimilation with machine-learned reduced-order models

Abstract. Data assimilation (DA) in geophysical sciences remains the cornerstone of robust forecasts from numerical models. Indeed, DA plays a crucial role in the quality of numerical weather prediction and is a crucial building block that has allowed dramatic improvements in weather forecasting over the past few decades. DA is commonly framed in a variational setting, where one solves an optimization problem within a Bayesian formulation using raw model forecasts as a prior and observations as likelihood. This leads to a DA objective function that needs to be minimized, where the decision variables are the initial conditions specified to the model. In traditional DA, the forward model is numerically and computationally expensive. Here we replace the forward model with a low-dimensional, data-driven, and differentiable emulator. Consequently, gradients of our DA objective function with respect to the decision variables are obtained rapidly via automatic differentiation. We demonstrate our approach by performing an emulator-assisted DA forecast of geopotential height. Our results indicate that emulator-assisted DA is faster than traditional equation-based DA forecasts by 4 orders of magnitude, allowing computations to be performed on a workstation rather than a dedicated high-performance computer. In addition, we describe accuracy benefits of emulator-assisted DA when compared to simply using the emulator for forecasting (i.e., without DA). Our overall formulation is denoted AIEADA (Artificial Intelligence Emulator-Assisted Data Assimilation).

58 GEOSCIENCES↗

NASA NTRS1998

A Conceptual Approach to Assimilating Remote Sensing Data to Improve Soil Moisture Profile Estimates in a Surface Flux/Hydrology Model: Disaggregation - 3

This is a followup on the preceding presentation by Crosson and Schamschula. The grid size for remote microwave measurements is much coarser than the hydrological model computational grids. To validate the hydrological models with measurements we propose mechanisms to disaggregate the microwave measurements to allow comparison with outputs from the hydrological models. Weighted interpolation and Bayesian methods are proposed to facilitate the comparison. While remote measurements occur at a large scale, they reflect underlying small-scale features. We can give continuing estimates of the small scale features by correcting the simple 0th-order, starting with each small-scale model with each large-scale measurement using a straightforward method based on Kalman filtering.

Caulfield, John↗

DOE OSTI2019

Application and Evaluation of Surrogate Models for Radiation Source Search

Surrogate models are increasingly required for applications in which first-principles simulation models are prohibitively expensive to employ for uncertainty analysis, design, or control. They can also be used to approximate models whose discontinuous derivatives preclude the use of gradient-based optimization or data assimilation algorithms. We consider the problem of inferring the 2D location and intensity of a radiation source in an urban environment using a ray-tracing model based on Boltzmann transport theory. Whereas the code implementing this model is relatively efficient, extension to 3D Monte Carlo transport simulations precludes subsequent Bayesian inference to infer source locations, which typically requires thousands to millions of simulations. Additionally, the resulting likelihood exhibits discontinuous derivatives due to the presence of buildings. To address these issues, we discuss the construction of surrogate models for optimization, Bayesian inference, and uncertainty propagation. Specifically, we consider surrogate models based on Legendre polynomials, multivariate adaptive regression splines, radial basis functions, Gaussian processes, and neural networks. We detail strategies for computing training points and discuss the merits and deficits of each method.

Cook, Jared A.↗

NASA NTRS2019

Assimilating microwave cloudy observations into NASA GEOS model using a novel Bayesian Monte Carlo technique

Despite the importance of clouds and their influence on atmospheric water and energy balance, Numerical Weather Prediction (NWP) centers systematically exclude cloud information from the assimilation process and only assimilate clear-sky radiances (Janiskov´a et al. 2012). In order to ensure that only clear sky radiances are assimilated, strict cloud detection thresholds are applied before radiances are fed into data assimilation (DA) systems. This process not only excludes a large portion of satellite radiances, but causes loss of information in the regions that are of high interest to meteorologists and are most challenging for weather forecasts (Errico et al. 2007; Haddad et al. 2015). Although, in recent years there has been great advances in the operational weather forecasting, the prediction of tropical cyclones (TC), especially the intensity of TCs, remains challenging. According to Aksoy et al. (2013), in addition to the model deficiencies, another important factor that contributes to this challenge includes lack of observations in the peripheral environment (rain- bands) of TCs mainly because of the selective assimilation of existing observations. Satellite observations provide more than 90 % of the input data for the initialization of NWP models but more than 75 % of satellite observations are discarded due to the cloud contamination as well as land, snow, and ice emissivity issues (Bauer et al. 2010).

Rainband↗

NASA NTRS2017

A Method for Snow Reanalysis: The Sierra Nevada (USA) Example

This work presents a state-of-the art methodology for constructing snow water equivalent (SWE) reanalysis. The method is comprised of two main components: (1) a coupled land surface model and snow depletion curve model, which is used to generate an ensemble of predictions of SWE and snow cover area for a given set of (uncertain) inputs, and (2) a reanalysis step, which updates estimation variables to be consistent with the satellite observed depletion of the fractional snow cover time series. This method was applied over the Sierra Nevada (USA) based on the assimilation of remotely sensed fractional snow covered area data from the Landsat 5-8 record (1985-2016). The verified dataset (based on a comparison with over 9000 station years of in situ data) exhibited mean and root-mean-square errors less than 3 and 13 cm, respectively, and correlation greater than 0.95 compared with in situ SWE observations. The method (fully Bayesian), resolution (daily, 90-meter), temporal extent (31 years), and accuracy provide a unique dataset for investigating snow processes. This presentation illustrates how the reanalysis dataset was used to provide a basic accounting of the stored snowpack water in the Sierra Nevada over the last 31 years and ultimately improve real-time streamflow predictions.

Bayesian↗

NASA NTRS2018

Estimation of Seasonal Snow Water Equivalent Using Landsat Observations

This work presents a methodology for estimating seasonal snow water equivalent (SWE) from the use of remotely sensed Visible and Near Infrared observations from the Landsat mission. The method is comprised of two main components: (1) a coupled land surface model and snow depletion curve model, which is used to generate an ensemble of predictions of SWE and snow cover area for a given set of (uncertain) inputs, and (2) a reanalysis step, which updates estimation variables to be consistent with the satellite observed depletion of the fractional snow cover time series. This method was applied over the Sierra Nevada (USA) based on the assimilation of remotely sensed fractional snow covered area data over the Landsat 5-8 record (1985-2016). The verified dataset (based on a comparison with over 9000 station years of in situ data) exhibited mean and root-mean-square errors less than 3 and 13 cm, respectively, and correlations with in situ SWE observations of greater than 0.95. The method (fully Bayesian), resolution (daily, 90-meter), temporal extent (32 years), and accuracy provide a unique dataset for investigating snow processes. In particular, this presentation illustrates how the reanalysis dataset was used to provide climatology of the seasonal snowfall accumulation rates, distributions, and variability over the last three decades.

SWE↗