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All sources NASA NTRS DOE OSTI

DOE OSTI2025

Learning and discovering multiple solutions using physics-informed neural networks with random initialization and deep ensemble

In this work we explore the capability of physics-informed neural networks (PINNs) to discover multiple solutions. Many real-world phenomena governed by nonlinear differential equations (DEs), such as fluid flow, exhibit multiple solutions under the same conditions, yet capturing this solution multiplicity remains a significant challenge. A key difficulty lies in providing appropriate initial conditions or guesses, as widely used time-marching schemes and Newton’s method are highly sensitive to these choices when solving complex computational problems. While machine learning models, particularly PINNs, have shown promise in solving DEs, their ability to capture multiple solutions remains underexplored. In this work, we propose a simple and practical approach using PINNs to learn and discover multiple solutions. We first demonstrate that PINNs, when combined with random initialization and deep ensemble method—originally developed for uncertainty quantification—can effectively uncover multiple solutions to nonlinear ordinary and partial DEs. Although training large ensembles of PINNs may appear computationally demanding, this can be done efficiently using vectorization techniques supported by modern deep learning frameworks, allowing many networks to be trained simultaneously. Our approach highlights the critical role of initialization in shaping solution diversity, addressing an often-overlooked aspect of machine learning for scientific computing. Furthermore, we propose utilizing PINN-generated solutions as initial conditions or initial guesses for conventional numerical solvers to enhance accuracy and efficiency in capturing multiple solutions. Extensive numerical experiments, including the Allen–Cahn equation and cavity flow, where our approach successfully identifies both stable and unstable solutions, validate the effectiveness of our method. These findings establish a general and efficient framework for addressing solution multiplicity in nonlinear DEs.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2016

Understanding Hydraulic Fracturing: A Multi-Scale Problem

Despite the impact that hydraulic fracturing has had on the energy sector, the physical mechanisms that control its efficiency and environmental impacts remain poorly understood in part because the length scales involved range from nano-meters to kilo-meters. We characterize flow and transport in shale formations across and between these scales using integrated computational, theoretical, and experimental efforts. At the field scale, we use discrete fracture network modeling to simulate production at a well site whose fracture network is based on a site characterization of a shale formation. At the core scale, we use triaxial fracture experiments and a finite-element discrete-element fracture propagation model with a coupled fluid solver to study dynamic crack propagation in low permeability shale. We use lattice Boltzmann pore-scale simulations and microfluidic experiments in both synthetic and real micromodels to study pore-scale flow phenomenon such as multiphase flow and mixing. A mechanistic description and integration of these multiple scales is required for accurate predictions of production and the eventual optimization of hydrocarbon extraction from unconventional reservoirs.

03 NATURAL GAS↗

NASA NTRS2008

A Three-Dimensional Variational Data Assimilation Scheme for the Regional Ocean Modeling System: Implementation and Basic Experiments

A three-dimensional variational data assimilation scheme for the Regional Ocean Modeling System (ROMS), named ROMS3DVAR, has been described in the work of Li et al. (2008). In this paper, ROMS3DVAR is applied to the central California coastal region, an area characterized by inhomogeneity and anisotropy, as well as by dynamically unbalanced flows. A method for estimating the model error variances from limited observations is presented, and the construction of the inhomogeneous and anisotropic error correlations based on the Kronecker product is demonstrated. A set of single observation experiments illustrates the inhomogeneous and anisotropic error correlations and weak dynamic constraints used. Results are presented from the assimilation of data gathered during the Autonomous Ocean Sampling Network (AOSN) experiment during August 2003. The results show that ROMS3DVAR is capable of reproducing complex flows associated with upwelling and relaxation, as well as the rapid transitions between them. Some difficulties encountered during the experiment are also discussed.

California coastal ocean↗

DOE OSTI2017

The influence of interfacial slip on two-phase flow in rough pores

The migration and trapping of supercritical CO 2 (scCO 2 ) in geologic carbon storage is strongly dependent on the geometry and wettability of the pore network in the reservoir rock. During displacement, resident fluids may become trapped in the pits of a rough pore surface forming an immiscible two-phase fluid interface with the invading fluid, allowing apparent slip flow at this interface. We present a two-phase fluid dynamics model, including interfacial tension, to characterize the impact of mineral surface roughness on this slip flow. We show that the slip flow can be cast in more familiar terms as a contact-angle (wettability)-dependent effective permeability to the invading fluid, a nondimensional measurement which relates the interfacial slip to the pore geometry. The analysis shows the surface roughness-induced slip flow can effectively increase or decrease this effective permeability, depending on the wettability and roughness of the mineral surfaces. Configurations of the pore geometry where interfacial slip has a tangible influence on permeability have been identified. The results suggest that for large roughness features, permeability to CO 2 may be enhanced by approximately 30% during drainage, while the permeability to brine during reimbibition may be enhanced or diminished by 60%, depending on the contact angle with the mineral surfaces and degrees of roughness. For smaller roughness features, the changes in permeability through interfacial slip are small. As a result, a much larger range of effective permeabilities are suggested for general fluid pairs and contact angles, including occlusion of the pore by the trapped phase.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2017

Inducing porosity and growing carbon nanofibers in ferroin perchlorate: An example of morphological transitions in coordination complexes

Inducing porosity in solid coordination complex crystals, which are an important class of catalysts, is critical for many applications where a high surface area is required. However, unlike metal organic frameworks (MOFs), fabrication of porous coordination crystals remains a significant challenge. Here we demonstrate a simple method to produce and modulate porosity in coordination complex crystals using ferroin perchlorate, a model system that combines a common ionic complex with a very reactive counter-ion. Using thermal chemical vapor deposition (CVD), we show that by annealing ferroin perchlorate crystals at 350 °C under a flow of ethylene, hydrogen, argon, and oxygen, we induced pores in the crystal. We demonstrate that small amounts of oxygen, which may combine with hydrogen to form water, are essential for pore formation. We also demonstrate that pore size and density can be easily controlled by varying the ethylene flow. Upon raising the annealing temperature to 500 °C, we observed a second transition in which carbon nanofibers (CNFs) grew from the porous crystal. This approach represents a simple and effective method for the synthesis of porous materials with good control over pore size and density. It also enables the synthesis of complex networks of nanostructures (in our case CNFs) by simply varying process parameters such as temperature and gas flows. This represents an important advance for the fabrication of porous coordination complex crystals. - Graphical abstract: Annealing ferroin perchlorate at 350 °C induces porosity in the complex while annealing at 500 °C leads to the additional growth of carbon nanofibers Display Omitted.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

SimH 2 : an integrated techno-economic modeling framework for hydrogen pipeline infrastructure and network optimization

Large-scale hydrogen (H 2 ) pipeline transport design and network optimization have seldom been reported due to the lack of a cost model accounting for the relationship between transport cost and hydrogen mass flow rate. Here, this work introduced a system-level cost model for hydrogen pipeline transport at supercritical state and integrated it with an existing CO 2 pipeline network tool, SimCCS, for hydrogen-specific pipeline design and optimization. The Intermountain West (I-West) region of the U.S., historically dependent on fossil fuel-based economies, is chosen to demonstrate the capabilities of our H 2 pipeline cost model and transport network optimization platform called SimH 2 . Two scenarios are examined: one where the pipeline is not allowed to pass through disadvantaged communities and the other where it is permitted. The results highlight that incorporating disadvantaged-community constraints lead to longer pipeline routes and increased transport costs, reflecting the trade-offs involved in equitable infrastructure development. It is demonstrated that the newly developed SimH 2 tool not only enables the efficient design of H 2 transportation pipelines but also optimizes the network by accounting for local terrain and the presence of disadvantaged areas.

08 HYDROGEN↗

DOE OSTI2023

Updated Application of Frequency of Detection Methods for the INL Site Ambient Air Monitoring Network

This report presents a quantitative assessment of the current INL Site air monitoring network using frequency of detection (FD) methods. The first assessment of the INL network was performed in 2015 and made recommendations for improving the network. As a result of changes made in response to the recommendations and the addition of new source locations, the network was modified and reassessed in 2017. Since 2017, administration of the air sampling program has been consolidated under one contractor, which resulted in additional changes to the network (sampler numbers and locations) and changes in radionuclide detection levels. As a result of these changes and others, an updated assessment of the INL Site ambient air monitoring network was performed. The same two exposure scenarios used in previous assessments were used for this assessment: a resident scenario and a shepherd/rancher scenario. The resident was assumed to be continuously present at their residence/business/farm operation outside the INL Site boundary while the shepherd/rancher was assumed to be present 24-hours at the nearest INL grazing allotment boundary in each of the 22.5-degree sectors along the sector centerline from each source. Updates to both the resident and shepherd/rancher receptor locations were included. Other changes include updates to flow rates for stack sources, expansion of the list of important radionuclides based on the most recent National Emission Standards for Hazardous Pollutants (NESHAPs) analysis, and updated dose coefficients. The assessment was conducted to determine whether the current INL monitoring network is capable of detecting releases of important radionuclides from INL Site sources that have the potential to exceed a conservative dose threshold for the two exposure scenarios. The assessment revealed that for the resident scenario, the current network meets the desired performance objective (FD = 95%) for all radionuclides and sources except for Cl-36 from the TRA-770 stack (94.4%). For the shepherd/rancher scenario, the FD performance objective is met for all radionuclides and sources except tritium from MFC-774 and TAN 679 (91% for both). An investigation of reported emissions for the past three years revealed that Cl 36 is not emitted from TRA-770, and routine tritium emissions from MFC-774 and TAN-679 are very small and the sources are likely incapable of emitting enough tritium to cause a release that should be detectable by the monitoring network. This assessment is based on a conservative dose threshold. This coupled with fact that the FD for Cl 36 is only slightly less than the performance objective and Cl-36 is not emitted from TRA-770, modifying the network (i.e. adding another sampler, increasing sampler flow rate, moving samplers) to meet the 95% performance objective for this radionuclide/source/receptor scenario is not warranted. Similarly, because tritium emissions from MFC-774 and TAN-679 are very small and these two sources are likely incapable of causing a dose due to tritium release that should be detectable by the network, modifications to increase tritium detection for these sources is also unwarranted at this time. However, if it is required to meet the performance objective for tritium for all sources and receptor scenarios, additional analysis determined the FD could be raised from 91% to > 99% for both sources by adding two tritium samplers to the network.

61 RADIATION PROTECTION AND DOSIMETRY↗

DOE OSTI2022

Lifelike behavior of chemically oscillating mobile capsules

Inspired by the self-organization of unicellular species into multicellular organisms, we use theory and simulation to design a system of mobile, active microcapsules that produce chemicals according to a catalytic reaction network (CRN). In solution, the catalytic reactions generate a force that drives the flow of the surrounding fluid. The convective flow, in turn, transports the capsules to new chemical surroundings with each successive translation. Consequently, the chemical signal produced by a cluster of capsules is critically dependent on the proximity and spatial configuration of the neighboring capsules. If all of the capsules and chemical products involved in the CRN lie within sufficient proximity, then the system develops oscillatory behavior that drives the dynamic self-assembly of capsules into larger clusters that are capable of collective action. Finally, these simulations indicate potential chemo-mechanic mechanisms that enable single cellular units, such as ameba, to organize into multicellular life forms.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2018

Simulation of solute transport through heterogeneous networks: analysis using the method of moments and the statistics of local transport characteristics

We used a time domain random walk approach to simulate passive solute transport in networks. In individual pores, solute transport was modeled as a combination of Poiseuille flow and Taylor dispersion. The solute plume data were interpreted via the method of moments. Analysis of the first and second moments showed that the longitudinal dispersivity increased with increasing coefficient of variation of the pore radii CV and decreasing pore coordination number Z. The third moment was negative and its magnitude grew linearly with time, meaning that the simulated dispersion was intrinsically non-Fickian. The statistics of the Eulerian mean fluid velocities $\hat{u}_i$, the Taylor dispersion coefficients $\hat{D}_i$ and the transit times $\hat{t}_i$ were very complex and strongly affected by CV and Z. In particular, the probability of occurrence of negative velocities grew with increasing CV and decreasing Z. Hence, backward and forward transit times had to be distinguished. The high-τ branch of the transit-times probability curves had a power law form associated to non-Fickian behavior. However, the exponent was insensitive to pore connectivity, although variations of Z affected the third moment growth. Thus, we conclude that both the low- and high-τ branches played a role in generating the observed non-Fickian behavior.

Li, Min↗

DOE OSTI2025

Integrated Framework of Multisource Data Fusion for Outage Location in Looped Distribution Systems

Accurate outage location is essential for expediting post-outage power restoration, minimizing outage duration, and enhancing the resilience of distribution networks. With the advent of advanced metering infrastructure, data-driven outage location methods have significantly advanced beyond traditional approaches that rely on manual inspections. However, existing methods still face critical challenges, like reliance on single-source data, limited ability to handle partially observable systems or difficulties with loop networks. To the best of our knowledge, no single approach has comprehensively addressed all of these challenges at once. To this end, this paper proposes a comprehensive multisource data fusion framework for outage locations via probabilistic graph networks. The framework consists of three key phases. First, a novel method for reconstituting distribution networks with loops is developed, transforming looped networks into multiple radial subnetworks that retain all outage causalities of the original network. Second, Bayesian network (BN) models are established for each subnetwork, integrating multiple data sources and network structures. Finally, a joint Gibbs sampling mechanism, featuring forward and backward information flow, is designed to merge data from separate BN models and maximize the utilization of limited evidence, ensuring accurate outage location identification. In conclusion, the framework was validated on two modified public test systems, and comparative studies confirmed its effectiveness.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2024

Symbolic diagnostics to interpret and analyze neural network models

Embedded machine-learned models (EMLMs) have the promise to improve the predictive accuracy of engineering simulators in environments of national interest. EMLMs often comprise complex input-output maps (e.g., neural networks), which make them unamenable to rigorous analysis and generally difficult to interpret. In the face of decades of theory, this lack of interpretability is a significant barrier to building confidence in these models. This work outlines an approach to interpret EMLMs using sparse polynomial regression for comparison with theoretical understanding. To do so, we build on the concept of Locally Interpretable Model-agnostic Explanations (LIME) using physics-informed clustering, prototype selection, and library construction. While general, we demonstrate our method on tensor-basis neural networks used in Reynolds-Averaged Navier-Stokes simulations of hypersonic fluid flows. Results are presented for a simulated toy model and for direct numerical simulations (DNS) of turbulent flows over a flat plate.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Los Alamos National Laboratory LiDAR Processing and Hydro-Enforcement Report

This report describes a project conducted by Los Alamos National Laboratory (LANL) and 3AE Green to process and hydro-enforce LiDAR data over approximately 170 square miles. A variety of Government Furnished Information (GFI) including LiDAR (2021), 3-inch pixel resolution natural-color imagery (2018), stormwater infrastructure, culvert, bridge, and building features were analyzed to develop a hydro-enforced digital elevation model (DEM). Where overland flow was obstructed by elevation surface feature, representational cutline features were placed and integrated into the LiDAR-based elevation surface to allow for more appropriate flow across roadbeds and other impediments to natural flow. This hydro-enforced DEM was utilized to model and develop more than 6.5 million three-dimensional (3D) vector flow line features (prior to line joining / merging) representing the derived digital drainage network deliverable.

42 ENGINEERING↗

DOE OSTI2019

Geochemical exports to river from the intrameander hyporheic zone under transient hydrologic conditions, Water Resources Research: Dataset

To understand how redox processes influence carbon, nitrogen, and iron cycling within the intrameander hyporheic zone, we developed a biotic and abiotic reaction network and incorporated it into the reactive transport simulator PFLOTRAN. Two dimensional reactive flow and transport simulations were performed (1) to evaluate how transient hydrological conditions control the lateral redox zonation within an intrameander region of the East River in Colorado and (2) to quantify the impact of a single meander on subsurface exports of carbon and other geochemical species to the river. This data package includes simulated hydrologic and geochemical data from 23 Oct 2015 to 22 Oct 2016.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2020

Analyzing Impact of Distributed PV Generation on Integrated Transmission & Distribution System Voltage Stability—A Graph Trace Analysis Based Approach

The use of a Graph Trace Analysis (GTA)-based power flow for analyzing the voltage stability of integrated Transmission and Distribution (T&D) networks is discussed in the context of distributed Photovoltaic (PV) generation. The voltage stability of lines and the load carrying capability of buses is analyzed at various PV penetration levels. It is shown that as the PV generation levels increase, an increase in the steady state voltage stability of the system is observed. Moreover, within certain regions of stability margin changes, changes in voltage stability margins of transmission lines are shown to be linearly related to changes in the loading of the lines. Two case studies are presented, where one case study involves a model with eight voltage levels and 784,000 nodes. In one case study, a voltage-stability heat map is used to demonstrate the identification of weak lines and buses.

14 SOLAR ENERGY↗

DOE OSTI2025

Transfer learning of neural surrogates on multifidelity groundwater simulations

Multifidelity data used in the paper published in Advances in Water Resources 206 (2025) 105140, https://doi.org/10.1016/j.advwatres.2025.105140 The code used to process the data is openly available on GitHub at https://github.com/Model-Reduction-and-UQ-Group/Transfer_Learning_K_reconstruction Computationally inexpensive surrogates of process-based models, such as deep neural networks, enable ensemble-based computations used in risk assessment, data assimilation, etc. However, generation of large datasets required to train a neural network can be as expensive as the ensemble simulations themselves. We ameliorate this challenge by using data from multifidelity (MF) groundwater simulations and transfer learning (TL) to reduce data generation costs while maintaining model accuracy. As a computational example, we train a deep convolutional neural network (CNN) to reconstruct permeability fields from saturation maps derived from a multiphase flow model. Starting with very low- and low-fidelity data generated on increasingly coarse meshes, we pretrain the CNN, followed by output-layer training and fine-tuning using only a limited number of high-fidelity samples. We demonstrate the surrogate’s robustness when interpreting low-quality inputs—such as interpolated maps or data affected by noise—which has strong implications for the applicability in practical hydrogeological scenarios. This multilevel MF-TL strategy achieves a favorable trade-off between computational efficiency and predictive accuracy, significantly outperforming high-fidelity-only approaches under the same computational budget.

Chiofalo, Alessia [University of Bologna] (ORCID:0↗

NASA NTRS1970

Manned Space Flight Network Telemetry System

Manned space flight network telemetry system modification for Skylab, ERTS and Apollo J missions, giving data flow diagrams and equipment electrical characteristics

Underwood, T. C., Jr.↗

NASA NTRS1986

Reverse osmosis water purification system

A reverse osmosis water purification system, which uses a programmable controller (PC) as the control system, was designed and built to maintain the cleanliness and level of water for various systems of a 64-m antenna. The installation operates with other equipment of the antenna at the Goldstone Deep Space Communication Complex. The reverse osmosis system was designed to be fully automatic; with the PC, many complex sequential and timed logic networks were easily implemented and are modified. The PC monitors water levels, pressures, flows, control panel requests, and set points on analog meters; with this information various processes are initiated, monitored, modified, halted, or eliminated as required by the equipment being supplied pure water.

Ahlstrom, H. G.↗

NASA NTRS1991

Role of groundwater in formation of Martian channels

A global 3-D model of groundwater flow has been used to study possible behavior of groundwater on Mars and its role in creating fluvial features. Conclusions drawn from an earlier 2-D groundwater model are supplemented and expanded. Topical headings are discussed as follows: timescales of groundwater flow; wet areas on Mars and location of outflow channels; implications for valley networks; the enigma of Hellas; absence of fluvial or periglacial features on Syrtis Major; development of chaotic terrain and associated outflow channels; and structurally controlled valley networks.

Howard, Alan D.↗