Results for “Gradient information” — Page 16

DOE OSTI2023

Enabling Real-time Scattering Data Analysis with Scalable Optimization [Slides]

Diffraction experiments produce datasets with rich multidimensional physics information such as microstructure, equations of state, crystal structure, elastoplastic properties, and other key inputs to LANL mission-essential multiphysics models. This information is typically extracted through a process called Rietveld refinement, which involves selecting appropriate models of the instrument, crystal structure, and microstructure, identifying suitable starting values, and then fitting often hundreds of model parameters using a sequence of empirical parameter turnon/off sequences within a non-global gradient-based optimization. Extensive user expertise is required to properly setup a refinement, identify appropriate models, and select initial parameter values close to truth, such that the refinement will yield parameter values that are optimally predictive. This is a very tedious manual process performed far after the beamline campaign has ended. As facilities have become capable of generating larger volumes of data, the limitation in throughput due to Rietveld refinement has led to a dramatic increase in unanalyzed data as opposed to an intended increase in new science. In our FY22 TED, we demonstrated an integrated toolset providing near real-time automated Rietveld analysis. If this toolset can be optimized to provide automated Rietveld analysis in real-time, this could alleviate the bottleneck in unanalyzed diffraction data, aid in decision-making during experiments, and increase efficiency of the facility.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2023

Multispectral and thermal surface imagery and surface elevation mosaics (camspec-air)

This dataset contains high resolution image products (orthomosaics) acquired from midsized uncrewed aerial systems, which have been processed for value added quality. The instrument itself, a multispectral imager, the Altum by Micasense, captures 6 spectral bands (red, green blue, NIR, red edge, and LWIR/thermal1) as radiance, which is converted to reflectance. The code used to develop these images first uses tools from the Micasense python library2 to apply dark level corrections, row gradient corrections, and radiometric corrections. Next it uses the processing API from Agisoft Metashape software to align and mosaic the processed imagery, following the processes developed by the USGS' structure from motion workflow documentation3. Captures at different altitudes (recorded in MSL) produce an orthomosaic, a tif image containing information related to the 6 spectral bands, and a digital elevation model (DEM), a tif image containing information related to the elevation of the surveyed terraine. Metadata included in every image can be used to extract lat, lon, and reflectance values. 1https://www.arm.gov/publications/tech_reports/handbooks/doe-sc-arm-tr-281.pdf 2https://micasense.github.io/imageprocessing/MicaSense%20Image%20Processing%20Setup.html 3https://pubs.usgs.gov/of/2021/1039/ofr20211039.pdf

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2023

Multispectral and thermal surface imagery and surface elevation mosaics - SGP July 2022

This data set contains high-resolution image products (orthomosaics) acquired from midsized uncrewed aerial systems that have been processed for value-added quality. The instrument itself, a multispectral imager, the Altum by Micasense, captures six spectral bands (red, green blue, NIR, red edge, and LWIR/thermal1) as radiance, which is converted to reflectance via custom code. The code used to develop these images first uses tools from the Micasense Python library2 to apply dark level corrections, row gradient corrections, and radiometric corrections. Next, it uses the processing API from Agisoft Metashape software to align and mosaic the processed imagery, following the processes developed by the USGS' structure from motion workflow documentation.3 Captures at different altitudes (recorded in MSL) produce an orthomosaic, a tif image containing information related to the six spectral bands, and a digital elevation model (DEM), a tif image containing information related to the elevation of the surveyed terraine. Metadata included in every image can be used to extract lat, lon, and reflectance values. 1 https://www.arm.gov/publications/tech_reports/handbooks/doe-sc-arm-tr-281.pdf 2 https://micasense.github.io/imageprocessing/MicaSense%20Image%20Processing%20Setup.html 3 https://pubs.usgs.gov/of/2021/1039/ofr20211039.pdf

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2020

Thermochemically-Informed Mass Transport Model for Zr in U-Zr Fuel

Recent improvements to the coupled Thermochimica-MOOSE/BISON code system have enabled efficient calculations of species transport based on direct evaluation of composition and temperature dependent chemical potentials of the species. This presents an alternative to the traditional approach to species transport in nuclear fuels, which has been to employ a diffusion formulation that combines concentration-gradient driven Fickian diffusion with a Soret term based on a heat of transport fit to experimental data. Here we describe the application of the coupled code system to the diffusion of Zr in U-Zr metallic fuel. New classes implemented in BISON to solve this problem are documented. The Zr concentration profile after 50 years of diffusion is found to be strongly dependent on the assumptions made pertaining how to mobility is calculated in multi-phase regions of the fuel element. Two assumptions are compared (simple averaging of mobilities and using the majority phase mobility), and good qualitative agreement with experimental measurements is obtained using the majority phase assumption.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2020

Blind Modeling Validation Exercises Using the Horizontal Dry Cask Simulator

The U.S. Department of Energy (DOE) established a need to understand the thermal-hydraulic properties of dry storage systems for commercial spent nuclear fuel (SNF) in response to a shift towards the storage of high-burnup (HBU) fuel (> 45 gigawatt days per metric ton of uranium, or GWd/MTU). This shift raises concerns regarding cladding integrity, which faces increased risk at the higher temperatures within spent fuel assemblies present within HBU fuel compared to low-burnup fuel (≤ 45 GWd/MTU). A dry cask simulator (DCS) was built at Sandia National Laboratories (SNL) in Albuquerque, New Mexico to produce validation-quality data that can be used to test the accuracy of the modeling used to predict cladding temperatures. These temperatures are critical to evaluating cladding integrity throughout the storage cycle of commercial spent nuclear fuel. A model validation exercise was previously carried out for the DCS in a vertical configuration. Lessons learned during the previous validation exercise have been applied to a new, blind study using a horizontal dry cask simulator (HDCS). Three modeling institutions – the Nuclear Regulatory Commission (NRC), Pacific Northwest National Laboratory (PNNL), and Empresa Nacional del Uranio, S.A., S.M.E. (ENUSA) – were granted access to the input parameters from the DCS Handbook, SAND2017-13058R, and results from a limited data set from the horizontal BWR dry cask simulator tests reported in the HDCS update report, SAND2019-11688R. With this information, each institution was tasked to calculate peak cladding temperatures and air mass flow rates for ten HDCS test cases. Axial as well as vertical and horizontal transverse temperature profiles were also calculated. These calculations were done using modeling codes (ANSYS/Fluent, STAR-CCM+, or COBRA-SFS), each with their own unique combination of modeling assumptions and boundary conditions. For this validation study, the ten test cases of the horizontal dry cask simulator were defined by three independent variables – fuel assembly decay heat (0.5 kW, 1 kW, 2.5 W, and 5 kW), internal backfill pressure (100 kPa and 800 kPa), and backfill gas (helium and air). The plots provided in Chapter 3 of this report show the axial, vertical, and horizontal temperature profiles obtained from the dry cask simulator experiments in the horizontal configuration and the corresponding models used to describe the thermal-hydraulic behavior of this system. The tables provided in Chapter 3 illustrate the closeness of fit of the model data to the experiment data through root mean square (RMS) calculations of the error in peak cladding temperatures (PCTs), PCT axial locations, axial temperature profiles, vertical and horizontal temperature profiles at two different axial locations, and air mass flow rates for the ten test cases, normalized by the experimental results. The model results are assigned arbitrary model numbers to retain anonymity. Due to the relatively flat axial temperature profiles, small temperature gradients resulted in large deviations of all models’ PCT axial location from the experimental PCT axial location. When the PCT axial location error is excluded in the calculation of the combined RMS of the normalized errors that considers PCT, the temperature profiles, and the air mass flow rates, the model data fits the experimental data to within 5%. When the vault information is excluded, the model data fits the experimental data to within 2.5%. An error analysis was developed further for one model, using the model and experimental uncertainties in each validation parameter to calculate validation uncertainties. The uncertainties for each parameter were used to define quantifiable validation criteria. For this analysis, the model was considered validated for a given comparison metric if the normalized error in that metric divided by the validation uncertainty was less than or equal to 1. When considering the combined RMS of the normalized errors of all metrics divided by their validation uncertainties, the model was found to have satisfied the criterion for model validation.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2021

Evaluation and Applications of Multi-Instrument Boundary-Layer Thermodynamic Retrievals

Recent reports have highlighted the need for improved observations of the atmosphere boundary layer. In this study, we explore the combination of ground-based active and passive remote sensors deployed for thermodynamic profiling to analyze various boundary-layer observation strategies. Optimal-estimation retrievals of thermodynamic profiles from Atmospheric Emitted Radiance Interferometer (AERI) observed spectral radiance are compared with and without the addition of active sensor observations from a May–June 2017 observation period at the Atmospheric Radiation Measurement Southern Great Plains site. In all, three separate thermodynamic retrievals are considered here: retrievals including AERI data only, retrievals including AERI data and Vaisala water vapour differential-absorption lidar data, and retrievals including AERI data and Raman lidar data. First, the three retrievals are compared to each other and to reference radiosonde data over the full observation period to obtain a bulk understanding of their differences and characterize the impact of clouds on these retrieved profiles. These analyses show that the most significant differences are in the water vapour field, where the active sensors are better able to represent the moisture gradient in the entrainment zone near the boundary-layer top. Furthermore, we also explore how differences in retrievals may affect results of applied analyses including land–atmosphere coupling, convection indices, and severe storm environmental characterization. Overall, adding active sensors to the optimal-estimation retrieval shows some added information, particularly in the moisture field. Given the costs of such platforms, the value of that added information must be weighed for the application at hand.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

OASIS: Offsetting Active Reconstruction Attacks in Federated Learning

Federated Learning (FL) has garnered significant attention for its potential to protect user privacy while enhancing model training efficiency. For that reason, FL has found its use in various domains, from health care to industrial engineering, especially where data cannot be easily exchanged due to sensitive information or privacy laws. However, recent research has demonstrated that FL protocols can be easily compromised by active reconstruction attacks executed by dishonest servers. These attacks involve the malicious modification of global model parameters, allowing the server to obtain a verbatim copy of users' private data by inverting their gradient updates. Tackling this class of attack remains a crucial challenge due to the strong threat model. In this paper, we propose a defense mechanism, namely OASIS, based on image augmentation that effectively counteracts active reconstruction attacks while preserving model performance. We first uncover the core principle of gradient inversion that enables these attacks and theoretically identify the main conditions by which the defense can be robust regardless of the attack strategies. We then construct our defense with image augmentation showing that it can undermine the attack principle. Comprehensive evaluations demonstrate the efficacy of the defense mechanism highlighting its feasibility as a solution.

deep neural networks↗

DOE OSTI2022

A deep learning-enhanced framework for multiphysics joint inversion

Joint inversion has drawn considerable attention due to the availability of multiple geophysical data sets, ever-increasing computational resources, the development of advanced algorithms, and its ability to reduce inversion uncertainty. A key issue of joint inversion is to develop effective strategies to link different geophysical data in a unified mathematical framework, in which the information obtained from different models can complement each other. We have developed a deep learning-enhanced joint inversion framework to simultaneously reconstruct different physical models by fusing different types of geophysical data. Traditionally, structure similarity constraints are pursued by joint inversion algorithms using manually crafted formulations (e.g., cross gradient). The constraint is constructed by a deep neural network (DNN) during the learning process. The framework is designed to combine the DNN and a traditional independent inversion workflow and improve the joint inversion result iteratively. The network can be easily extended to incorporate multiphysics without structural changes. Numerical experiments on the joint inversion of 2D DC resistivity data and seismic traveltime are used to validate our method. In addition, this learning-based framework demonstrates excellent generalization abilities when tested on data sets using different geologic structures. It also can handle different sensing configurations and nonconforming discretization.

Geochemistry & Geophysics↗

DOE OSTI2023

Deep Neural Network Informed Markov Chain Monte Carlo Methods

In subsurface flow modeling, quantifying the uncertainty of model parameters and the corresponding uncertainly on output quantities is a crucial task for groundwater management. Markov chain Monte Carlo (MCMC) methods can take advantage of observed data to estimate parameters in a Bayesian setting. However, MCMC can be slow to converge and produce highly correlated samples when the dimensions of the parameters is high. Using gradients for the posterior distribution can help samplers explore the parameter space more efficiently, but obtaining gradients can be computationally challenging.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2022

Kinetics and Reactor Modeling of VFA Ketonization for Sustainable Aviation Fuel Production

Ketonization of volatile fatty acids (VFAs) produced via arrested methanogenesis of wet waste represents the only unit operation of wet waste upgrading to sustainable (net-zero or negative life cycle CO2 emissions) aviation fuel not currently in industrial practice. Ketone product yields of close to 100% have been obtained during gas-phase reactions of VFAs over oxide catalysts at the laboratory scale, but design of an industrial ketonization reactor requires understanding of the impacts of reactant and product partial pressures, deactivation, and heat and mass transport phenomena on observed ketonization rates. Our work leverages rigorous kinetic analysis of ketonization processes to inform reactor scale-up efforts through packed-bed reactor modeling. We first present results of a kinetic study of ketonization of a model VFA, hexanoic acid, over an industrial ZrO2 catalyst performed in a packed-bed microreactor in conditions free of significant heat or mass transfer gradients. Major findings of the analysis include: (i) hexanoic acid saturates all catalyst active sites at relatively low partial pressure (~10 kPa) and (ii) ketonization products 6-undecanone, water, and CO2 inhibit reaction rates. Kinetic data are used to fit a rate expression quantifying the functional dependence of ketonization rate on partial pressures of VFA reactants and ketone, water, and CO2 products. A packed-bed reactor model describing vapor-phase hexanoic acid ketonization over ZrO2 extrudate catalysts is developed based on the kinetic model. The effects of (i) bed- and pellet-scale mass- and heat-transfer limitations and (ii) axial pressure drop guide our development of recommendations for optimal sizing, temperature, and influent flow composition of an industrial-scale ketonization reactor. The quantitative understanding of VFA ketonization developed in this study represents an advance toward derisking the VFA ketonization step of wet waste upgrading to sustainable aviation fuel.

biojet↗

DOE OSTI2026

Determining Optimal Magnetometer Configuration on MAGIS-100

Long-baseline atom interferometers such as the Matter-wave Atomic Gradiometer Interferometric Sensor (MAGIS-100) require stringent control and continuous characterization of background magnetic fields and spatial gradients to prevent systemic phase shifts that mimic ultralight dark matter or gravitational wave signatures. Because direct sensor placement within the ultra-high vacuum beam pipe is infeasible, in-situ magnetic field monitoring relies on external sensor arrays situated in the surrounding annular region. This work demonstrates a field reconstruction framework for a 5.3-meter MAGIS-100 modular section using finite-element Opera simulations. Transverse magnetic fields are expanded using a cylindrical multipole framework as informed by Fermilab’s Muon g-2 experiment, with magnetometer array configurations optimized via Fisher information matrix D-optimality. Inverting external sensor readings through a Gauss-Newton scheme recovers interior tube fields across distinct axial positions. In the discontinuity-averse uniform region (slice pair P4), the model achieves sub-noise-floor performance with a cross-validated root-mean-square error (RMSE) of $6.7227 \times 10^{-4}\text{ A/m}$ ($0.845\times$ sensor noise floor) and an interior field coefficient of variation of $1.71\%$. An elbow criterion in the Fisher bounds establishes $n_{\text{max}} = 2$ as the optimal multipole truncation order to prevent noise amplification from over-parameterization, with $n_{\text{max}} = 3$ (sextupole) order chosen for analysis to demonstrate further complexity and cross-pair comparison. Furthermore, analytical differentiation of the fitted multipole coefficients yields dense spatial maps of the transverse Jacobian gradient matrix $\nabla \mathbf{H}$ along with propagated $1\sigma$ uncertainty bounds across the beam region ($r \le 2.75\text{ in}$). This operational framework confirms that external magnetometer arrays can reliably monitor magnetic field uniformity and spatial gradients along the 100-meter flight path given appropriate sampling for any complexity order.

Appleby, Darwin [William Rainey Harper Coll.] (ORC↗

DOE OSTI2026

Determining Optimal Magnetometer Configuration on MAGIS-100

Long-baseline atom interferometers such as the Matter-wave Atomic Gradiometer Interferometric Sensor (MAGIS-100) require stringent control and continuous characterization of background magnetic fields and spatial gradients to prevent systemic phase shifts that mimic ultralight dark matter or gravitational wave signatures. Because direct sensor placement within the ultra-high vacuum beam pipe is infeasible, in-situ magnetic field monitoring relies on external sensor arrays situated in the surrounding annular region. This work demonstrates a field reconstruction framework for a 5.3-meter MAGIS-100 modular section using finite-element Opera simulations. Transverse magnetic fields are expanded using a cylindrical multipole framework as informed by Fermilab’s Muon g-2 experiment, with magnetometer array configurations optimized via Fisher information matrix D-optimality. Inverting external sensor readings through a Gauss-Newton scheme recovers interior tube fields across distinct axial positions. In the discontinuity-averse uniform region (slice pair P4), the model achieves sub-noise-floor performance with a cross-validated root-mean-square error (RMSE) of $6.7227 \times 10^{-4}\text{ A/m}$ ($0.845\times$ sensor noise floor) and an interior field coefficient of variation of $1.71\%$. An elbow criterion in the Fisher bounds establishes $n_{\text{max}} = 2$ as the optimal multipole truncation order to prevent noise amplification from over-parameterization, with $n_{\text{max}} = 3$ (sextupole) order chosen for analysis to demonstrate further complexity and cross-pair comparison. Furthermore, analytical differentiation of the fitted multipole coefficients yields dense spatial maps of the transverse Jacobian gradient matrix $\nabla \mathbf{H}$ along with propagated $1\sigma$ uncertainty bounds across the beam region ($r \le 2.75\text{ in}$). This operational framework confirms that external magnetometer arrays can reliably monitor magnetic field uniformity and spatial gradients along the 100-meter flight path given appropriate sampling for any complexity order.

Appleby, Darwin [William Rainey Harper Coll.] (ORC↗

DOE OSTI2026

In-Situ Magnetic Field Reconstruction in the MAGIS-100 Experiment

Long-baseline atom interferometers such as the Matter-wave Atomic Gradiometer Interferometric Sensor (MAGIS-100) require stringent control and continuous characterization of background magnetic fields and spatial gradients to prevent systemic phase shifts that mimic ultralight dark matter or gravitational wave signatures. Because direct sensor placement within the ultra-high vacuum beam pipe is infeasible, in-situ magnetic field monitoring relies on external sensor arrays situated in the surrounding annular region. This work demonstrates a field reconstruction framework for a 5.3-meter MAGIS-100 modular section using finite-element Opera simulations. Transverse magnetic fields are expanded using a cylindrical multipole framework as informed by Fermilab’s Muon g-2 experiment, with magnetometer array configurations optimized via Fisher information matrix D-optimality. Inverting external sensor readings through a Gauss-Newton scheme recovers interior tube fields across distinct axial positions. In the discontinuity-averse uniform region (slice pair P4), the model achieves sub-noise-floor performance with a cross-validated root-mean-square error (RMSE) of $6.7227 \times 10^{-4}\text{ A/m}$ ($0.845\times$ sensor noise floor) and an interior field coefficient of variation of $1.71\%$. An elbow criterion in the Fisher bounds establishes $n_{\text{max}} = 2$ as the optimal multipole truncation order to prevent noise amplification from over-parameterization, with $n_{\text{max}} = 3$ (sextupole) order chosen for analysis to demonstrate further complexity and cross-pair comparison. Furthermore, analytical differentiation of the fitted multipole coefficients yields dense spatial maps of the transverse Jacobian gradient matrix $\nabla \mathbf{H}$ along with propagated $1\sigma$ uncertainty bounds across the beam region ($r \le 2.75\text{ in}$). This operational framework confirms that external magnetometer arrays can reliably monitor magnetic field uniformity and spatial gradients along the 100-meter flight path given appropriate sampling for any complexity order.

Appleby, Darwin [William Rainey Harper Coll.; Ferm↗

DOE OSTI2024

A Performance and Energy Study of GPU-Resident Preconditioners for Conjugate Gradient Solvers: In the Context of Existing and Novel Approaches

Optimizing a particular subprogram out of the set of Basic (sparse) Linear Algebra Subprograms (BLAS) for a given architecture is a common topic of research. In applications, however, these BLAS functions rarely appear in isolation; usually, many of them are used together, in various combinations and with varying inputs. As the need to solve a large, sparse linear system is ubiquitous throughout HPC applications, linear solvers constitute a realistic, sufficiently complex and well-defined representative use case for composite BLAS routines. To this end, based on a representative set of matrices drawn from a diverse set of fields, we present a framework to study, from the performance and energy perspective, the efficacy of GPU- resident parallel Conjugate Gradient (CG) linear solver with different preconditioner options, including Gauss-Seidel, Jacobi, and incomplete Cholesky. We also propose a novel GPU-based preconditioner, in which the triangular solves are approximated by an iterative process. The development of this preconditioner was motivated by solving large graph Laplacian linear systems, for which the existing preconditioners either perform slow on GPU-based platforms or are not applicable. We compare the performance of these preconditioners on different hardware accelerator architectures, i.e., AMD MI250X, MI100, Nvidia A100, V100, and Jetson. Our experiments reveal performance trade-offs and provide information on how to select the best strategy for the given linear system, dictated by its properties, and the platform of interest. We demonstrate the application of our novel preconditioner for solving CG and graph Laplacian systems. Overall, the framework can be utilized as a benchmark to guide informed decisions in choosing a specific preconditioner, i.e., whether it is better to rely on the performance of a triangular solver or on the performance of sparse matrix-vector product. Finally, by considering power consumption to solve the linear systems, we report the energy footprint for the solvers.

Preconditioned Conjugate Gradient, GPUs, iterative↗

DOE OSTI2020

Dynamic phase transformations in additively manufactured Ti-6Al-4V during thermo-mechanical gyrations

A complex interaction of process parameters, geometry and scan strategies in Additive Manufacturing (AM), can bring about spatial and temporal transients, i.e., Σ T ( x, y, z, time ), within a part. Published literature focusses on fluctuating thermal cycles on the microstructure evolution. However, the microstructural variations have not been correlated to dynamic flow behavior due to the macro- and micro-scale phenomena, i.e., accumulated plastic strains brought about by large thermal gradients, transformational strains and crystallographic misfit strains. Therefore, here we studied the mechanical response of Ti6Al4V alloys produced by AM under externally imposed controlled thermo-mechanical reversals in a Gleeble® thermo-mechanical simulator. The stress-strain behaviors were correlated to phase fractions, lattice strains, and also limited information on crystallographic texture using neutron diffraction techniques at the VULCAN Beamline at SNS, ORNL and also metallographic studies. The results are discussed and rationalized based on theories of static and dynamic phase transformations.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Autonomous sensor suite for evaluating fish-turbine interactions and environmental impacts in marine renewable energy and hydropower

Marine renewable energy (MRE) harnesses ocean-based resources such as waves, tides, currents, and thermal or salinity gradients for sustainable power generation. It has the potential to complement existing renewable resources, support remote communities, and contribute to decarbonization efforts. However, understanding the hydrodynamic forces created by MRE devices and their impacts on marine life is critical for responsible deployment. Here, to address these concerns, advanced sensor devices, including the Marine Sensor Fish (MSF), Sensor Fish Mini (SF Mini), and Flexible Sensor Fish (FSF), were developed to measure interactions between aquatic organisms and MRE systems. This paper details the design, manufacturing, calibration, and field deployment of these sensor suites, highlighting their ability to capture key physical stressors such as shear forces, pressure changes, and collision impacts. The MSF successfully evaluated turbine interactions at a tidal turbine in the Salish Sea, capturing data on turbulence, collision impact, and pressure gradients. The SF Mini validated hydrodynamic conditions in scaled hydraulic models, supporting computational fluid dynamics simulations. The FSF, with its flexible silicone body, measured species-specific impacts in turbulent environments. This research demonstrates the potential of Sensor Fish technology to advance sustainable marine energy systems by reducing biological impacts and informing environmentally sustainable designs.

Ecological impacts↗

DOE OSTI2023

Multispectral and thermal surface imagery and surface elevation mosaics - Pendleton Feb 2023

This data set contains high-resolution image products (orthomosaics) acquired from midsized uncrewed aerial systems that have been processed for value-added quality. The instrument Altum multispectral imager by Micasense, captures in six bands (blue - 475nm, green - 560nm, red - 668nm, red edge - 717nm, near-infrared - 840 and LWIR/thermal - 11000nm. The optical bands are converted to reflectance via custom code using the instantaneous band horizontal irradiance ratio to the radiance of the pixel. The code used to develop these images first uses tools from the Micasense Python library to apply dark level corrections, row gradient corrections, and radiometric corrections. Next, it uses the processing API from Agisoft Metashape software to align and mosaic the processed imagery, following the processes developed by the USGS' structure from motion workflow documentation. Captures from different altitudes are used to produce an orthomosaic at each height. A tif image containing information related to the six spectral bands, and a digital elevation model (DEM), a tif image containing information related to the elevation of the surveyed terrain. 1 https://www.arm.gov/publications/tech_reports/handbooks/doe-sc-arm-tr-281.pdf 2 https://micasense.github.io/imageprocessing/MicaSense%20Image%20Processing%20Setup.html 3 https://pubs.usgs.gov/of/2021/1039/ofr20211039.pdf

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2025

Bias-Variance Trade-Off in Physics-Informed Neural Networks with Randomized Smoothing for High-Dimensional PDEs

Physics-Informed Neural Networks (PINNs) have triggered a paradigm shift in scientific computing, leveraging mesh-free properties and robust approximation capabilities. While proving effective for low-dimensional partial differential equations (PDEs), the computational cost of PINNs remains a hurdle in high-dimensional scenarios. This is particularly pronounced when computing high-order and high-dimensional derivatives in the physics-informed loss. Randomized Smoothing PINN (RS-PINN) introduces Gaussian noise for stochastic smoothing of the original neural net model, enabling the use of Monte Carlo methods for derivative approximation, which eliminates the need for costly automatic differentiation. Despite its computational efficiency, especially in the approximation of high-dimensional derivatives, RS-PINN introduces biases in both loss and gradients, negatively impacting convergence, especially when coupled with stochastic gradient descent (SGD) algorithms. We present a comprehensive analysis of biases in RS-PINN, attributing them to the nonlinearity of the Mean Squared Error (MSE) loss as well as the intrinsic nonlinearity of the PDE itself. We propose tailored bias correction techniques, delineating their application based on the order of PDE nonlinearity. The derivation of an unbiased RS-PINN allows for a detailed examination of its advantages and disadvantages compared to the biased version. Specifically, the biased version has a lower variance and runs faster than the unbiased version, but it is less accurate due to the bias. To optimize the bias-variance trade-off, we combine the two approaches in a hybrid method that balances the rapid convergence of the biased version with the high accuracy of the unbiased version. In addition to methodological contributions, we present an enhanced implementation of RS-PINN. Extensive experiments on diverse high-dimensional PDEs, including Fokker-Planck, Hamilton-Jacobi-Bellman (HJB), viscous Burgers’, Allen-Cahn, and Sine-Gordon equations, illustrate the bias-variance trade-off and highlight the effectiveness of the hybrid RS-PINN. Empirical guidelines are provided for selecting biased, unbiased, or hybrid versions, depending on the dimensionality and nonlinearity of the specific PDE problem.

97 MATHEMATICS AND COMPUTING↗