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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 505 records · Page 28
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

LDRD Abbreviated report: High-Order General-Discrete-Ordinates Method Enabling Efficient Deterministic Transport in Hydrodynamic Simulations

Deterministic transport simulations for national-security and energy applications often operate in high-dimensional phase-space, where accuracy and cost both become major challenges. A common numerical artifact in such problems is the “ray-effect,” which appears as unphysical streaks. Beyond misinterpretation, these artifacts can contaminate tightly coupled physics, such as fluid dynamics, radiation-hydrodynamics, and laser-plasma interactions, eroding the predictive capability of entire multiphysics workflows. Our objective was to make high-dimension studies practical on modern hardware while mitigating the ray-effect without relying on prohibitively expensive sampling approaches such as Monte Carlo methods. We developed the Generic Discretization Library (GenDiL), a Graphics Processing Unit (GPU)-first framework that uses high-order Discontinuous Galerkin (DG) methods and matrix-free algorithms to reduce memory usage and improve computational efficiency, critical for phase-space simulations. GenDiL supports phase-space adaptivity in both mesh size and polynomial order (hp-adaptivity) to place resolution only where it is needed. A central capability is Local Dimensional Refinement (LDR), which couples lower-dimension continuum models to higher-dimension kinetic models through stable and conservative interfaces, so that high-fidelity physics is applied only in regions where it is essential. Building on the GenDiL framework, we developed the General SN (GSN) family of algorithms as a true generalization of the polar SN approach (discrete ordinates, often denoted SN). Rather than tying discrete ordinates to a specific polar change of coordinates, GSN formulates transport on an arbitrary change of coordinates chosen to reduce ray-effect. We studied two complementary variants: an analytic variant, where the coordinate map is prescribed in advance by a closed-form function; and a data-driven variant, where a quantity of interest, such as the net flux, guides the coordinate system. GenDiL provides the library infrastructure for efficient GPU execution, but the GSN concept is algorithmic and independent of any one library. Across representative high-dimension tests, including non-symmetric solutions, both variants delivered strong ray-effect mitigation at practical cost, moving four- to six-dimensional analysis toward repeatable, routine studies.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Measurement techniques of thermoelectric devices and modules

Thermoelectric (TE) energy conversion devices are designed based on measured material transport properties. Although an ideal device efficiency can be calculated using the figure of merit, zT, the actual efficiency of a thermoelectric module is smaller and must be measured. TE device performance testing techniques and procedures are reviewed with a focus on energy conversion efficiency. One of the areas that attract less attention in the literature is the transition from basic thermoelectric materials research to the production of modules and devices. The effects of interface layers, diffusion barriers, thermal insulations, and heat sinks are reviewed. Finally, device performance from single couples to standard modules and long-term reliability are discussed.

Wang, Hsin↗
DOE OSTI2021

SISGR: Chemomechanics of Far-From-Equilibrium Interfaces (COFFEI)

Portable, reliable, and deployable devices for energy storage and conversion require fundamental changes in design of solid-state composites comprising ceramics and metals. These materials comprise the electrodes and electrolytes of next-generation solid-oxide fuel cells and all solid-state batteries, forming solid-state functional composites. The advent of solid-state batteries – which replace liquid electrolytes with solid electrolytes capable of lithium ion transport for reliable energy storage in portable batteries – and the increased demand space for all solid-state fuel cells capable of oxygen reduction at intermediate temperatures remain important challenges for improved material stability and decreased system cost. However, little is understood about three fundamental facets of materials that enable such solid-state energy applications. First, how do such materials deform, fracture, or delaminate under operando conditions? Second, how does such mechanical deformation limit or facilitate electronic and ionic transport within and across such material interfaces? Third, how we can predictably design interface-rich composites to engineer both structural and electrochemical stability? This COFFEI Group comprised expertise from Materials Science & Engineering and Nuclear Science & Engineering to integrate unique in situ experiments, simulations, and fabricated interfaces that address these fundamental questions in solid-state interfaces of nanoscale composites that will guide solid-state electrochemistry, transport kinetics, and mechanical deformation for nonstoichiometric materials that enable such applications. In particular, we built on COFFEI’s understanding of chemomechanical coupling among defect concentrations, ionic transport, electron transport, and stored elastic energy that is particularly acute in the far-from-equilibrium conditions typical of energy device applications. By tailoring our focus to solid-state interfaces, we addressed these important issues by (a) developing and applying advanced in situ and ex situ characterization tools to characterize model materials and interfaces synthesized with molecular-level control, under both laboratory-controlled and extreme environments representative of energy device operation; and (b) employing computational modeling and simulation frameworks to predict transport mechanisms, reactivity and stability of these model materials and interfaces under significant chemical strains typical of energy device operation. Recent progress provided insights to additional materials systems and electrochemomechanical fatigue and fracture that were not fully envisioned when the program was initiated. Specifically, in the final three years of COFFEI we pursued two integrated thrusts, with complementary focus. Thrust I focused on failure-resistant electrochemomechanical composites, while Thrust II focused on strain-modulated conductivity and reactivity across interfaces. In contrast to our initial COFFEI focus, these thrusts concentrated wholly on solid-state material interfacial interactions and included greater integration of multiscale visualization including in situ electron microscopy of strained structures/interactions and mesoscale simulations. Successful development of functionally superior and long-lived battery and fuel cell systems and stress adaptable oxides requires a deeper, fundamental understanding of the coupling among the historically important subfields of solid-state electrochemistry, transport kinetics, and mechanical deformation for nonstoichiometric metal oxide electrodes. In this program, the understanding and the application of chemomechanical coupling of defect concentrations, ionic transport, electro-catalytic activity and stored elastic energy, particularly acute in the far-from-equilibrium conditions typical of energy device applications, are being refined and implications for device operation clarified, including for miniaturized solid-state batteries and fuel cells.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Understanding the interface interaction between U3Si2 fuel and SiC cladding

Abstract Triuranium disilicide (U 3 Si 2 ) fuel with silicon carbide (SiC) composite cladding is being considered as an advanced concept/accident tolerant fuel for light water reactors thus, understanding their chemical compatibility under operational and accident conditions is paramount. Here we provide a comprehensive view of the interaction between U 3 Si 2 and SiC by utilizing density functional theory calculations supported by diffusion couple experiments. From the calculated reaction energies, we demonstrate that triuranium pentasilicide (U 3 Si 5 ), uranium carbide (UC), U 20 Si 16 C 3 , and uranium silicide (USi) phases can form at the interface. A detailed study of U 3 Si 2 and SiC defect formation energies of the equilibrated materials yielding the interfacial phases U 20 Si 16 C 3 , U 3 Si 5 and UC reveal a thermodynamic driving force for generating defects in both fuel and cladding. The absence of either the U 3 Si 2 or SiC phase, however, causes the defect formation energies in the other phase to be positive, removing the driving force for additional interfacial reactions. The diffusion couple experiments confirm the conclusion with demonstrated restricted formation of U 3 Si 5 , UC, and U 20 Si 16 C 3 /USi phases at the interface. The resulting lack of continuous interaction between the U 3 Si 2 and SiC, reflects the diminishing driving force for defect formation, demonstrating the substantial stability of this fuel-cladding system.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2020

Surface-Mediated Interconnections of Nanoparticles in Cellulosic Fibrous Materials toward 3D Sensors

Fibrous materials serve as an intriguing class of 3D materials to meet the growing demands for flexible, foldable, biocompatible, biodegradable, dis- posable, inexpensive, and wearable sensors and the rising desires for higher sensitivity, greater miniaturization, lower cost, and better wearability. The use of such materials for the creation of a fibrous sensor substrate that interfaces with a sensing film in 3D with the transducing electronics is however difficult by conventional photolithographic methods. Here, a highly effective pathway featuring surface-mediated interconnection (SMI) of metal nanoclusters (NCs) and nanoparticles (NPs) in fibrous materials at ambient conditions is demon- strated for fabricating fibrous sensor substrates or platforms. Bimodally distrib- uted gold–copper alloy NCs and NPs are used as a model system to demonstrate the semiconductive-to-metallic conductivity transition, quantized capacitive charging, and anisotropic conductivity characteristics. Upon coupling SMI of NCs/NPs as electrically conductive microelectrodes and surface-mediated assembly (SMA) of the NCs/NPs as chemically sensitive interfaces, the resulting fibrous chemiresistors function as sensitive and selective sensors for gaseous and vaporous analytes. Finally, this new SMI–SMA strategy has significant implications for manufacturing high-performance fibrous platforms to meet the growing demands of the advanced multifunctional sensors and biosensors.

36 MATERIALS SCIENCE↗
DOE OSTI2023

SA508 low alloy steel to 316L stainless steel dissimilar metal joint made by powder metallurgy hot isostatic pressing

Joining ferritic SA508 low alloy steel (LAS) and austenitic 316 L stainless steel (SS) via powder metallurgy hot isostatic pressing (PM-HIP) was evaluated as an alternative method to welding. This study investigated the mechanical and microstructural evolutions of the bimetallic interface under different joint designs and heat treatments. Here, the direct joining of dissimilar metal alloys by PM-HIP method resulted in two designs: 1) powder SA508 to solid bar 316 L (P508–B316L) and 2) powder 316 L solid bar SA508 (P316L-B508). In both cases, P508–B316L and P316L-demonstrated satisfactory tensile strength, however, high hardness and severe depreciation in toughness were located on the bimetallic interface. The mechanisms responsible for the detrimental mechanical properties were verified. Large oxides were observed in P508–B316L due to the prior powder boundary (PPB) oxides present in SA508 powder. The intense sensitization occurred from the formation of M 23 C 6 carbides, consequently from the slow cooling after PM-HIP in P316L-B508. Post-HIP heat treatments were explored to reduce the distance of carbide formation; however, the heat treatment could not eliminate the carbides. The experimental results were compared to the diffusion couple simulation as a function of carbide formation with distance. The analysis also showed the high hardness at the bimetallic interface was primarily contributed by solid solution strengthening. In conclusion, the direct joining of P316L-B508 and P508–B316L via PM-HIP was deemed to be unfeasible, and a transitional material is necessary to impede the diffusion of carbon.

316L stainless Steel↗
DOE OSTI2021

Mechanical coupling in the nitrogenase complex

The enzyme nitrogenase reduces dinitrogen to ammonia utilizing electrons, protons, and energy obtained from the hydrolysis of ATP. Mo-dependent nitrogenase is a symmetric dimer, with each half comprising an ATP-dependent reductase, termed the Fe Protein, and a catalytic protein, known as the MoFe protein, which hosts the electron transfer P-cluster and the active-site metal cofactor (FeMo-co). A series of synchronized events for the electron transfer have been characterized experimentally, in which electron delivery is coupled to nucleotide hydrolysis and regulated by an intricate allosteric network. We report a graph theory analysis of the mechanical coupling in the nitrogenase complex as a key step to understanding the dynamics of allosteric regulation of nitrogen reduction. This analysis shows that regions near the active sites undergo large-scale, large-amplitude correlated motions that enable communications within each half and between the two halves of the complex. Computational predictions of mechanically regions were validated against an analysis of the solution phase dynamics of the nitrogenase complex via hydrogen-deuterium exchange. These regions include the P-loops and the switch regions in the Fe proteins, the loop containing the residue β-188Ser adjacent to the P-cluster in the MoFe protein, and the residues near the protein-protein interface. In particular, it is found that: (i) within each Fe protein, the switch regions I and II are coupled to the [4Fe-4S] cluster; (ii) within each half of the complex, the switch regions I and II are coupled to the loop containing β-188Ser; (iii) between the two halves of the complex, the regions near the nucleotide binding pockets of the two Fe proteins (in particular the P-loops, located over 130 Å apart) are also mechanically coupled. Notably, we found that residues next to the P-cluster (in particular the loop containing β-188Ser) are important for communication between the two halves.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2026

Coupling Noah-Multiparameterization land-surface Model with Energy Research and Forecasting Model

The Energy Research and Forecasting (ERF) model is a high-performance atmospheric model built on the AMReX adaptive mesh refinement (AMR) framework, enabling efficient simulations on heterogeneous computing platforms that combine multicore processors with hardware accelerators. To support land–atmosphere interactions within ERF’s AMR-based environment, a land-surface model must be capable of operating directly on hierarchically refined meshes. In this work, we present a methodology for coupling the Fortran-based Noah-Multiparameterization (Noah-MP) land-surface model with ERF’s C++ codebase. Rather than rewriting Noah-MP, we construct a Fortran–C interoperability layer using CodeScribe, a tool that leverages large language models (LLMs) to automate the generation of interface code. CodeScribe applies structured prompting techniques to generate bindings that support efficient data exchange and function calls between ERF and Noah-MP. The coupling framework also incorporates AMR-aware data handling strategies, allowing NoahMP to operate seamlessly within ERF’s hierarchical mesh structure. This work provides a structured approach for integrating legacy Fortran models into modern C++-based modeling systems using LLM-assisted code generation.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Phonon‐Dominated Energy Transport in Purely Metallic Heterostructures

Abstract Ultrafast X‐ray diffraction is used to quantify the transport of energy in laser‐excited nanoscale gold–nickel (Au–Ni) bilayers. Electron transport and efficient electron–phonon coupling in Ni convert the laser‐deposited energy in the conduction electrons within a few picoseconds into a strong non‐equilibrium between hot Ni and cold Au phonons at the bilayer interface. Modeling of the subsequent equilibration dynamics within various two‐temperature models confirms that for ultrathin Au films, the thermal transport is dominated by phonons instead of conduction electrons because of the weak electron–phonon coupling in Au.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Ionic Modulation at the LaAlO 3 /KTaO 3 Interface for Extreme High-Mobility Two-Dimensional Electron Gas

Due to the coexistence of many emergent phenomena, including 2D superconductivity and a large Rashba spin-orbit coupling, 5d transition metal oxides-based two-dimensional electron systems (2DESs) have been prospected as one of the potential intrants for modern electronics. However, despite the lighter electron mass, the mobility of carriers, a key requisite for high-performance devices, in 5d-oxides devices remains far behind their 3d-oxides analogs. The carriers’ mobility in these oxides is significantly hampered by the inevitable presence of defects. Here, in this study, very high mobility (≈22 650 cm 2 V –1 s –1 ) of 5d-2DES confined at the LaAlO 3 /KTaO 3 interface is reported. The high mobility, which is beyond the values observed in SrTiO 3 2DESs in the same carrier-density range, is achieved using the ionic-liquid gating at room temperature. The authors postulate that the ionic-liquid gating affects the oxygen vacancies and efficiently reduces any disorder at the interface. Investigating density and mobility in a broad range of back-gate voltage, the authors reveal that the mobility follows the power-law µ ∝ n 1.2 , indicating the very high quality of ionic-liquid-gated LaAlO 3 /KTaO 3 devices, consistent with the postulate. Furthermore, the analysis of the quantum oscillations confirms that the high-mobility electrons occupy the electronic sub-bands emerging from the Ta:5d orbitals of KTaO 3 .

36 MATERIALS SCIENCE↗
DOE OSTI2025

Can Charge Transfer Across C─H⋅⋅⋅O Hydrogen Bonds Stabilize Oil Droplets in Water?

Oil-water emulsions resist aggregation due to the presence of negative charges at their surface that leads to mutual repulsion between droplets, but the molecular origin of oil charge is currently under debate. Although much evidence has suggested that ionic species must accumulate at the interface, an alternative perspective attributes the negative charge on the oil droplet to charge transfer of electron density from water to oil molecules. Although the charge transfer mechanism is consistent with the correct sign of oil charge, it is just as important to provide good estimates of the charge magnitude to explain emulsion stability and electrophoresis experiments. Here, we show using energy decomposition analysis that the amount of net flow of charge from water to oil is negligibly small due to nearly equal forward and backward charge transfer through weak oil-water interactions, such that oil droplets would be unstable and coalesce, contrary to experiment. The lack of charge transfer also explains why vibrational sum frequency scattering reports a blue shift in the oil C-H frequency when forming emulsions with water, which arises from Pauli repulsion due to localized confinement at the interface. Finally, unlike ions, neither charge transfer nor dynamic polarization can produce a finite conductivity needed to couple to electric fields that would explain electrophoretic mobility.

Zhao, Ruoqi↗
DOE OSTI2021

A non‐intrusive domain‐decomposition model reduction method for linear steady‐state partial differential equations with random coefficients

Abstract Domain decomposition methods have been proved to be an effective strategy to reduce the dimension of parametric partial differential equations (PDEs). However, existing domain decomposition methods for parametric PDEs are usually intrusive, which means domain decomposition based solvers need to be implemented from scratch for each target parametric PDE. To address this issue, we develop a new non‐intrusive domain‐decomposition model reduction method for linear steady‐state PDEs with random‐field coefficients. As a variant of our previous work by Mu and Zhang, the new method only needs access to the final linear system, that is, the global stiffness matrix and the right hand side, of a deterministic PDE solver, in order to build a domain‐decomposition‐based reduced model without intrusive implementation from scratch. The key idea is to remove the interface condition between sub‐domains and rely on the correlation between columns of the linear system to couple the sub‐domains. The non‐intrusive feature enables the applicability of the proposed method to a broader class of uncertainty quantification problems, where many legacy codes/solvers can be fully reused by our method. Two numerical examples including diffusion equations with random diffusivity and convection‐dominated transport with random velocity, are provided to demonstrate the effectiveness and efficiency of our method.

Zhang, Guannan↗
DOE OSTI2025

The structure and migration of twin boundaries in tetragonal β -Sn: An application of machine learning based interatomic potentials

Although atomistic simulations have contributed significantly to our understanding of twin boundary structure and migration in metals and alloys with hexagonal close packed (HCP) crystal structures, few direct atomistic studies of twinning have been conducted for other types of low symmetry materials, in large part due to a lack of reliable interatomic potentials. In this work, we examine twin boundary structure and migration in a tetragonal material, β-Sn, comparing high resolution Transmission Electron Microscopy (TEM) images of deformation twins in β-Sn to the results of direct atomistic simulations using multiple interatomic potentials. ML-based potentials developed in this work are found to give results consistent with our experimental data, revealing faceted twin boundary structures formed by the nucleation and motion of twinning disconnections. We use bicrystallographic methods in combination with atomistic simulations to analyze the structure, energy and shear coupled migration of observed twin facets in β-Sn. In analogy to Prismatic-Basal (PB/BP) interfaces in HCP metals, we discover low energy asymmetric Prismatic-A-plane (PA/AP) interfaces important to twin growth in β-Sn. Finally, a Moment Tensor Potential (MTP) and Rapid Artificial Neural Network (RANN) interatomic potential suitable for studying twinning and phase transformations in Sn are made publicly available as part of this work.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Functional group activation and coupling agent migration induced by plasma treatment in adhesive for enhanced toughness of metal-composite joints

Commercial adhesive paste was additionally activated using low-power oxygen plasma with different plasma exposure durations to investigate its interfacial bonding contribution in adhesively-bonded Aural-5/CFRP-PA6 double cantilever beam (DCB) joints with plasma-treated adherends. The plasma-treated adhesive showed enhanced functional peak intensities in Fourier transfer infrared spectroscopy (FTIR) as plasma exposure time was increased, and some degree of oxidation was also detected via X-ray photoelectron spectroscopy (XPS). A small molecule, dicyandiamde (coupling agent) in adhesive was migrated to adhesive layer, where double concentration of coupling agent was detected after 10 minutes of plasma treatment. As a result, characterization of the adhesive/CFRP-PA6 interface after DCB fracture showed additional chemical bonds formed through amine-initiated epoxy ring opening polymerization, as well as amide bonds and ester bonds. In conclusion, these additional bonds at the adhesive/CFRP-PA6 interfaces led to significantly increased failure extensions and fracture energies of the joints as the plasma exposure time on the adhesive increased, compared to the joints with plasma-treated adherends but non-plasma-treated adhesive as commonly seen in the literature.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Structure of the G protein chaperone and guanine nucleotide exchange factor Ric-8A bound to Gαi1

Abstract Ric-8A is a cytosolic Guanine Nucleotide exchange Factor (GEF) that activates heterotrimeric G protein alpha subunits (Gα) and serves as an essential Gα chaperone. Mechanisms by which Ric-8A catalyzes these activities, which are stimulated by Casein Kinase II phosphorylation, are unknown. We report the structure of the nanobody-stabilized complex of nucleotide-free Gα bound to phosphorylated Ric-8A at near atomic resolution by cryo-electron microscopy and X-ray crystallography. The mechanism of Ric-8A GEF activity differs considerably from that employed by G protein-coupled receptors at the plasma membrane. Ric-8A engages a specific conformation of Gα at multiple interfaces to form a complex that is stabilized by phosphorylation within a Ric-8A segment that connects two Gα binding sites. The C-terminus of Gα is ejected from its beta sheet core, thereby dismantling the GDP binding site. Ric-8A binds to the exposed Gα beta sheet and switch II to stabilize the nucleotide-free state of Gα.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2023

Ferroelectricity in hafnia controlled via surface electrochemical state

Ferroelectricity in binary oxides including hafnia and zirconia has riveted the attention of the scientific community due to the highly unconventional physical mechanisms and the potential for the integration of these materials into semiconductor workflows. Over the last decade, it has been argued that behaviours such as wake-up phenomena and an extreme sensitivity to electrode and processing conditions suggest that ferroelectricity in these materials is strongly influenced by other factors, including electrochemical boundary conditions and strain. Here we argue that the properties of these materials emerge due to the interplay between the bulk competition between ferroelectric and structural instabilities, similar to that in classical antiferroelectrics, coupled with non-local screening mediated by the finite density of states at surfaces and internal interfaces. Via the decoupling of electrochemical and electrostatic controls, realized via environmental and ultra-high vacuum piezoresponse force microscopy, we show that these materials demonstrate a rich spectrum of ferroic behaviours including partial-pressure-induced and temperature-induced transitions between ferroelectric and antiferroelectric behaviours. In conclusion, these behaviours are consistent with an antiferroionic model and suggest strategies for hafnia-based device optimization.

36 MATERIALS SCIENCE↗
DOE OSTI2021

The mechanism driving a solid–solid phase transition in a biomacromolecular crystal

A solid-solid phase transition (SSPT) occurs between distinguishable crystalline forms. Because of its importance in application and theory in material science and condensed matter physics, SSPT has been studied most extensively in metallic alloys, inorganic salt or small organic molecular crystals, but much less so in biomacromolecular crystals. In general, the mechanism of SSPT at atomic and molecular levels is not well understood. Here, we describe the ordered molecular rearrangements in biomacromolecular crystals of the adenine riboswitch (riboA) aptamer using real-time serial crystallography and solution atomic force microscopy (AFM). The large, ligand-induced conformational changes drive the initial phase transition from the apo unit cell (AUC) to the trans unit cell 1 (TUC1). During this transition, coaxial stacking of P1 duplexes becomes the dominant packing interface, whereas P2-P2 interactions are almost completely disrupted, resulting in “floating” layers of molecules. The coupling points in TUC1 and their local conformational flexibility allow the molecules to reorganize to achieve the more densely packed and energetically favorable bound unit cell (BUC). Our study thus reveals the interplay between the conformational changes and the crystal phases—the underlying mechanism that drives the phase transition. Using polarized video microscopy (PVM) to monitor the SSPT in small crystals at high ligand concentration, we have identified the time window during which the major conformational changes take place, and simulated the in crystallo kinetics. Together, these results provide the spatiotemporal information necessary for informing time-resolved crystallography (TRX) experiments. Moreover, this study illustrates a practical approach to characterize SSPT in transparent crystals.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Discovery of Probabilistic Dirichlet-to-Neumann Maps on Graphs

Dirichlet-to-Neumann maps enable the coupling of multiphysics simulations across computational subdomains by ensuring continuity of state variables and fluxes at artificial interfaces. We present a novel method for learning Dirichlet-to-Neumann maps on graphs using Gaussian processes, specifically for problems where the data obey a conservation law arising from an underlying partial differential equation. Our approach combines discrete exterior calculus and nonlinear optimal recovery to infer relationships between vertex and edge values. This framework yields data-driven predictions with uncertainty quantification across the entire graph, even when observations are limited to a subset of vertices and edges. By minimizing the reproducing kernel Hilbert space norm while penalizing kernel complexity through maximum likelihood estimation, our method ensures that the resulting surrogate strictly enforces conservation laws without overfitting. We demonstrate our method on two representative applications: subsurface flow in fracture networks and arterial blood flow. Finally, the results demonstrate that the method maintains high accuracy and well-calibrated uncertainty estimates even under severe data scarcity, highlighting its potential for scientific applications where limited data and reliable uncertainty quantification are critical.

Dirichlet-to-Neumann map↗