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DOE OSTI2021

Direct Observation of the Depth of Active Groundwater Circulation in an Alpine Watershed

Abstract The depth of active groundwater circulation is a fundamental control on stream flows and chemistry in mountain watersheds, yet it remains challenging to characterize and is rarely well constrained. We collected hydraulic conductivity, hydraulic head, temperature, chemical, noble gas, and 3 H/ 3 He groundwater age data from discrete levels in two boreholes 46 and 81 m deep in an alpine watershed, in combination with chemical and age data from shallow groundwater discharge, to discern groundwater flow rates at different depths and directly observe active and inactive groundwater. Vertical head gradients are steep (average of 0.4) and thermal profiles are consistent with typical linear conductive continental geotherms. Groundwater deeper than ∼20 m is distinct from shallow groundwater and creek water in its chemistry, noble gas signature, and age (dominantly >65 years compared to <9 years). Together these results suggest low vertical groundwater flow velocities and a relatively shallow active circulation depth of ∼20 m. This hypothesis is tested with a simple 2‐D numerical fluid flow and heat transport model representing a hillslope transect through the two boreholes. The modeling indicates that the subhorizontally bedded sedimentary rocks underlying the basin are highly anisotropic with low vertical hydraulic conductivity, and at most ∼10% of bedrock recharge (equivalent to <2% of stream baseflow) flows below a depth of 20 m. The study demonstrates the considerable value of discrete‐depth hydrogeologic, chemical, and age data for determining active circulation depth, and illustrates an approach for maximizing the utility of individual boreholes drilled for mountain bedrock aquifer characterization.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

River Organic Carbon Fluxes Modulated by Hydrodynamic Sorting of Particulate Organic Matter

Rivers regulate the global carbon cycle by transferring particulate organic carbon (POC) from terrestrial landscapes to marine sedimentary basins, but the processes controlling the amount and composition of fluvially exported POC are poorly understood. We propose that hydrodynamic sorting processes modify POC fluxes during fluvial transit. We test this hypothesis by studying POC transported along a ~1,200 km reach of the Rio Bermejo, Argentina. Nanoscale secondary ion mass spectrometry revealed that POC was either fine, mineral-associated organic matter, or coarse discrete organic particles. Mineral-associated POC is more resistant to oxidation and has a lower particle settling velocity than discrete POC. Consequently, hydraulic sorting and downstream fining amplify the proportion of fine, mineral-associated POC from ~55% to ~78% over 1,220 km of downstream transit. This suggests that mineral-associated POC has a greater probability of export and preservation in marine basins than plant detritus, which may be oxidized to CO 2 during transit.

58 GEOSCIENCES↗

DOE OSTI2022

Physics‐Informed Machine Learning Method for Large‐Scale Data Assimilation Problems

Abstract We develop a physics‐informed machine learning approach for large‐scale data assimilation and parameter estimation and apply it for estimating transmissivity and hydraulic head in the two‐dimensional steady‐state subsurface flow model of the Hanford Site given synthetic measurements of said variables. In our approach, we extend the physics‐informed conditional Karhunen‐Loéve expansion (PICKLE) method to modeling subsurface flow with unknown flux (Neumann) and varying head (time‐dependent Dirichlet) boundary conditions. We demonstrate that the PICKLE method is comparable in accuracy with the standard maximum a posteriori (MAP) method, but is significantly faster than MAP for large‐scale problems. Both methods use a mesh to discretize the computational domain. In MAP, the parameters and states are discretized on the mesh; therefore, the size of the MAP parameter estimation problem directly depends on the mesh size. In PICKLE, the mesh is used to evaluate the residuals of the governing equation, while the parameters and states are approximated by the truncated conditional Karhunen‐Loéve expansions with the number of parameters controlled by the smoothness of the parameter and state fields, and not by the mesh size. For a considered example, we demonstrate that the computational cost of PICKLE increases near linearly (as N 1.15 ) with the number of grid nodes N , while that of MAP increases much faster (as N 3.28 ). We also show that once trained for one set of Dirichlet boundary conditions (i.e., one river stage), the PICKLE method provides accurate estimates of the hydraulic head for any value of the Dirichlet boundary conditions (i.e., for any river stage).

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Learning in continuous action space for developing high dimensional potential energy models

Reinforcement learning (RL) approaches that combine a tree search with deep learning have found remarkable success in searching exorbitantly large, albeit discrete action spaces, as in chess, Shogi and Go. Many real-world materials discovery and design applications, however, involve multi-dimensional search problems and learning domains that have continuous action spaces. Exploring high-dimensional potential energy models of materials is an example. Traditionally, these searches are time consuming (often several years for a single bulk system) and driven by human intuition and/or expertise and more recently by global/local optimization searches that have issues with convergence and/or do not scale well with the search dimensionality. Here, in a departure from discrete action and other gradient-based approaches, we introduce a RL strategy based on decision trees that incorporates modified rewards for improved exploration, efficient sampling during playouts and a “window scaling scheme" for enhanced exploitation, to enable efficient and scalable search for continuous action space problems. Using high-dimensional artificial landscapes and control RL problems, we successfully benchmark our approach against popular global optimization schemes and state of the art policy gradient methods, respectively. We demonstrate its efficacy to parameterize potential models (physics based and high-dimensional neural networks) for 54 different elemental systems across the periodic table as well as alloys. We analyze error trends across different elements in the latent space and trace their origin to elemental structural diversity and the smoothness of the element energy surface. Broadly, our RL strategy will be applicable to many other physical science problems involving search over continuous action spaces.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Neuromorphic intermediate representation: A unified instruction set for interoperable brain-inspired computing

Abstract Spiking neural networks and neuromorphic hardware platforms that simulate neuronal dynamics are getting wide attention and are being applied to many relevant problems using Machine Learning. Despite a well-established mathematical foundation for neural dynamics, there exists numerous software and hardware solutions and stacks whose variability makes it difficult to reproduce findings. Here, we establish a common reference frame for computations in digital neuromorphic systems, titled Neuromorphic Intermediate Representation (NIR). NIR defines a set of computational and composable model primitives as hybrid systems combining continuous-time dynamics and discrete events. By abstracting away assumptions around discretization and hardware constraints, NIR faithfully captures the computational model, while bridging differences between the evaluated implementation and the underlying mathematical formalism. NIR supports an unprecedented number of neuromorphic systems, which we demonstrate by reproducing three spiking neural network models of different complexity across 7 neuromorphic simulators and 4 digital hardware platforms. NIR decouples the development of neuromorphic hardware and software, enabling interoperability between platforms and improving accessibility to multiple neuromorphic technologies. We believe that NIR is a key next step in brain-inspired hardware-software co-evolution, enabling research towards the implementation of energy efficient computational principles of nervous systems. NIR is available atneuroir.org

Science & Technology - Other Topics↗

DOE OSTI2026

FunDiff: diffusion models over function spaces for physics-informed generative modeling

Recent advances in generative modeling-particularly diffusion models and flow matching-have been widely used for synthesizing discrete data such as images and videos. However, adapting these models to physical applications remains challenging, as the quantities of interest are continuous functions governed by complex physical laws. To address this, we introduce FunDiff, an efficient and robust framework for generative modeling in function spaces. FunDiff combines a latent diffusion process with a function autoencoder architecture to handle input functions with varying discretizations, generates continuous functions that can be evaluated at arbitrary locations, and seamlessly incorporate physical priors. These priors are enforced through architectural constraints or physics-informed loss functions, ensuring that generated samples satisfy fundamental physical laws. We theoretically establish minimax optimality guarantees for density estimation in function spaces, demonstrating that diffusion-based estimators achieve optimal convergence rates under suitable regularity conditions. We further demonstrate the practical effectiveness of FunDiff across diverse applications in fluid dynamics and solid mechanics. Empirical results indicate that our method can generate physically consistent samples with high fidelity to the target distribution, and exhibit robustness to noisy and low-resolution data.

Wang, Sifan [Yale University, New Haven, CT (Unite↗

DOE OSTI2020

Intra- and Intermolecular Self-Assembly of a 20-nm-Wide Supramolecular Hexagonal Grid.

For the past three decades, the coordination-driven self-assembly of three-dimensional structures has undergone rapid progress; however, parallel efforts to create large discrete two-dimensional architectures-as opposed to polymers-have met with limited success. The synthesis of metallo-supramolecular systems with well-defined shapes and sizes in the range of 10-100 nm remains challenging. Here we report the construction of a series of giant supramolecular hexagonal grids, with diameters on the order of 20 nm and molecular weights greater than 65 kDa, through a combination of intra- and intermolecular metal-mediated self-assembly steps. The hexagonal intermediates and the resulting self-assembled grid architectures were imaged at submolecular resolution by scanning tunnelling microscopy. Characterization (including by scanning tunnelling spectroscopy) enabled the unambiguous atomic-scale determination of fourteen hexagonal grid isomers.

Zhang, Zhe↗

DOE OSTI2020

Preparation of cyclohexene isotopologues and stereoisotopomers from benzene

The hydrogen isotopes deuterium (D) and tritium (T) have become essential tools in chemistry, biology and medicine1. Beyond their widespread use in spectroscopy, mass spectrometry and mechanistic and pharmacokinetic studies, there has been considerable interest in incorporating deuterium into drug molecules1. Deutetrabenazine, a deuterated drug that is promising for the treatment of Huntington’s disease2, was recently approved by the United States’ Food and Drug Administration. The deuterium kinetic isotope effect, which compares the rate of a chemical reaction for a compound with that for its deuterated counterpart, can be substantial1,3,4. The strategic replacement of hydrogen with deuterium can affect both the rate of metabolism and the distribution of metabolites for a compound5, improving the efficacy and safety of a drug. The pharmacokinetics of a deuterated compound depends on the location(s) of deuterium. Although methods are available for deuterium incorporation at both early and late stages of the synthesis of a drug6,7, these processes are often unselective and the stereoisotopic purity can be difficult to measure7,8. Here we describe the preparation of stereoselectively deuterated building blocks for pharmaceutical research. As a proof of concept, we demonstrate a four-step conversion of benzene to cyclohexene with varying degrees of deuterium incorporation, via binding to a tungsten complex. Using different combinations of deuterated and proteated acid and hydride reagents, the deuterated positions on the cyclohexene ring can be controlled precisely. In total, 52 unique stereoisotopomers of cyclohexene are available, in the form of ten different isotopologues. This concept can be extended to prepare discrete stereoisotopomers of functionalized cyclohexenes. Such systematic methods for the preparation of pharmacologically active compounds as discrete stereoisotopomers could improve the pharmacological and toxicological properties of drugs and provide mechanistic information related to their distribution and metabolism in the body.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

A higher-order finite element reactive transport model for unstructured and fractured grids

Abstract This work presents a new reactive transport framework that combines a powerful geochemistry engine with advanced numerical methods for flow and transport in subsurface fractured porous media. Specifically, the PhreeqcRM interface (developed by the USGS) is used to take advantage of a large library of equilibrium and kinetic aqueous and fluid-rock reactions, which has been validated by numerous experiments and benchmark studies. Fluid flow is modeled by the Mixed Hybrid Finite Element (FE) method, which provides smooth velocity fields even in highly heterogenous formations with discrete fractures. A multilinear Discontinuous Galerkin FE method is used to solve the multicomponent transport problem. This method is locally mass conserving and its second order convergence significantly reduces numerical dispersion. In terms of thermodynamics, the aqueous phase is considered as a compressible fluid and its properties are derived from a Cubic Plus Association (CPA) equation of state. The new simulator is validated against several benchmark problems (involving, e.g., Fickian and Nernst-Planck diffusion, isotope fractionation, advection-dispersion transport, and rock-fluid reactions) before demonstrating the expanded capabilities offered by the underlying FE foundation, such as high computational efficiency, parallelizability, low numerical dispersion, unstructured 3D gridding, and discrete fraction modeling.

58 GEOSCIENCES↗

DOE OSTI2023

Uncovering anisotropic effects of electric high-moment dipoles on the tunneling current in $$\delta$$-layer tunnel junctions

Abstract The precise positioning of dopants in semiconductors using scanning tunneling microscopes has led to the development of planar dopant-based devices, also known as $$\delta$$ δ layer-based devices, facilitating the exploration of new concepts in classical and quantum computing. Recently, it has been shown that two distinct conductivity regimes (low- and high-bias regimes) exist in $$\delta$$ δ -layer tunnel junctions due to the presence of quasi-discrete and continuous states in the conduction band of $$\delta$$ δ -layer systems. Furthermore, discrete charged impurities in the tunnel junction region significantly influence the tunneling rates in $$\delta$$ δ -layer tunnel junctions. Here we demonstrate that electrical dipoles, i.e. zero-charge defects, present in the tunnel junction region can also significantly alter the tunneling rate, depending, however, on the specific conductivity regime, and orientation and moment of the dipole. In the low-bias regime, with high-resistance tunneling mode, dipoles of nearly all orientations and moments can alter the current, indicating the extreme sensitivity of the tunneling current to the slightest imperfection in the tunnel gap. In the high-bias regime, with low-resistivity, only dipoles with high moments and oriented in the directions perpendicular to the electron tunneling direction can significantly affect the current, thus making this conductivity regime significantly less prone to the influence of dipole defects with low-moments or oriented in the direction parallel to the tunneling.

42 ENGINEERING↗

DOE OSTI2025

Modeling the formation of Sedan Crater using the FLAG and HOSS codes

Numerical modeling of explosion crater formation requires accounting for complex physical processes. Numerical validation of explosion cratering is an important step in modeling and requires experimental data for comparison. Models using discrete elements and continuum models have both benefits and drawbacks to their approaches. In this work, we consider both an arbitrary Lagrangian–Eulerian (ALE) hydrocode and a finite discrete element method (FDEM) approach to modeling the formation of the Sedan crater, the largest human-made crater in the United States. The Sedan crater formed from an underground nuclear detonation in the Nevada desert as part of Project Plowshare. Our models show that the continuum approach of the hydrocode matched well compared to early test time prior to the mound rupture and subsequent fireball venting, when most of the alluvium exhibited fluid behavior. Our FDEM approach matched the final crater dimensions well, after material had settled back into the crater, when material strength and solid mechanics play key roles. Our work shows how leveraging the benefits of multiple numerical approaches can lead to better understanding of complex physical problems, especially problems with limited experimental data. By using a continuum approach to early-time hydrodynamics and an FDEM approach to later-time solid mechanics, we can better understand the different physical regimes of explosion crater formation.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Multi-resolution partial differential equations preserved learning framework for spatiotemporal dynamics

Traditional data-driven deep learning models often struggle with high training costs, error accumulation, and poor generalizability in complex physical processes. Physics-informed deep learning (PiDL) addresses these challenges by incorporating physical principles into the model. Most PiDL approaches regularize training by embedding governing equations into the loss function, yet this depends heavily on extensive hyperparameter tuning to weigh each loss term. To this end, we propose to leverage physics prior knowledge by “baking” the discretized governing equations into the neural network architecture via the connection between the partial differential equations (PDE) operators and network structures, resulting in a PDE-preserved neural network (PPNN). This method, embedding discretized PDEs through convolutional residual networks in a multi-resolution setting, largely improves the generalizability and long-term prediction accuracy, outperforming conventional black-box models. The effectiveness and merit of the proposed methods have been demonstrated across various spatiotemporal dynamical systems governed by spatiotemporal PDEs, including reaction-diffusion, Burgers’, and Navier-Stokes equations.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Classifying topology in photonic crystal slabs with radiative environments

Abstract In the recent years, photonic Chern materials have attracted substantial interest as they feature topological edge states that are robust against disorder, promising to realize defect-agnostic integrated photonic crystal slab devices. However, the out-of-plane radiative losses in those photonic Chern slabs has been previously neglected, yielding limited accuracy for predictions of these systems’ topological protection. Here, we develop a general framework for measuring the topological protection in photonic systems, such as in photonic crystal slabs, while accounting for in-plane and out-of-plane radiative losses. Our approach relies on the spectral localizer that combines the position and Hamiltonian matrices of the system to draw a real-picture of the system’s topology. This operator-based approach to topology allows us to use an effective Hamiltonian directly derived from the full-wave Maxwell equations after discretization via finite-elements method (FEM), resulting in the full account of all the system’s physical processes. As the spectral FEM-localizer is constructed solely from FEM discretization of the system’s master equation, the proposed framework is applicable to any physical system and is compatible with commonly used FEM software. Moving forward, we anticipate the generality of the method to aid in the topological classification of a broad range of complex physical systems.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

DOE OSTI2021

Shear Stress Dependence of Force Networks in 3D Dense Suspensions

The geometric organization and force networks of 3D dense suspensions that exhibit both shear thinning and thickening have been examined as a function of varying strength of interparticle attractive interactions using lubrication flow discrete element simulations. Significant rearrangement of the geometric topology does not occur at either the local or global scale as these systems transition across the shear thinning and shear thickening regimes. In contrast massive rearrangements in the balance of attractive, lubrication, and contact forces are observed with interesting behavior of network growth and competition. In agreement with prior work, in shear thinning regions the attractive force is dominant, however as the shear thickening region is approached there is growth of lubrication forces. Lubrication forces oppose the attraction forces, but as viscosity continues to increase under increasing shear stress, the lubrication forces are dominated by contact forces that also resist attraction. Contact forces are the dominant interactions during shear thickening and are an order of magnitude higher than their values in the shear-thinning regime. At high attractive interaction strength, contact networks can form even under shear thinning conditions, however high shear stress is still required before contact networks become the driving mechanism of shear thickening. Analysis of the contact force network during shear thickening generally indicate a uniformly spreading network that rapidly forms across empty domains, however the growth patterns have structure that are significantly dependent upon the strength of interparticle interactions, indicating subtle variations in the mechanism of shear thickening.

Edens, Lance E.↗

DOE OSTI2024

Influence of shape on crystal structure and optical properties of heterocyclic conjugated molecules

Organic optoelectronics are increasingly important due to their tunablilty, flexibility, and solution processability. Tuning optical properties of these materials as solids relies on the balance of weak non-covalent interactions that dictate crystal structure, but are difficult to predict. Our research aims to improve our understanding of how electrostatic interactions can direct and facilitate intramolecular interactions that dictate emergent properties of crystalline materials. This paper focuses on exploring how multi-fused thiophene ring systems that are popular in modern organic optoelectronic materials impact intramolecular interactions, while also investigating the role of molecular shape. In these examples, the shape of heterocyclic systems correlate with the crystal structures: while the bent heterocyclics show no discrete and discernable intramolecular interactions, those with bent shapes interact cofacially with one of the electron poor ArF pendants by twisting the arylene ethynylene backbone. Two of the control molecules, which bear non-fluorinated benzyl ester substituents, show intramolecular edge-face interactions, and several of these molecules show clear polymorphic behavior. Furthermore, these findings further our understanding of how discrete interactions can be altered not only by electrostatics, but also by shape, allowing for increasingly nuanced control over the crystal structures and optical properties of optoelectronic materials.

Guzmán, Elisa↗

DOE OSTI2022

Decentralized modular hybrid supervisory control for the formation of unmanned helicopters

Abstract Formation control of Unmanned Aerial Vehicles (UAVs) requires them to tightly cooperate to reach and keep the formation, while avoiding collision. This paper proposes a novel decentralized hybrid supervisory control approach for the formation control of multiple UAVs. This is achieved by developing a symbolic motion planning technique to polarly partition the motion space resulting in a finite state discrete event model for the motion dynamics of each UAV. Then, a modular discrete supervisor is designed for different components of the formation mission including reaching the formation, keeping the formation, and collision avoidance. Further, for the collision avoidance mechanism, a novel top‐down decomposition‐based approach is developed to design local supervisors decentralizedly. It is formally proved that with the proposed top‐down decomposition‐based approach, the (locally) supervised UAVs, as a whole, can cooperatively satisfy the desired (global) collision avoidance specification. The proposed decentralized supervisory control algorithm is also verified through a hardware‐in‐the‐loop simulator for the formation control of unmanned helicopters.

Karimoddini, Ali↗

DOE OSTI2021

Computational general relativistic force-free electrodynamics: II. Characterization of numerical diffusivity

Scientific codes are an indispensable link between theory and experiment; in (astro-)plasma physics, such numerical tools are one window into the universe’s most extreme flows of energy. The discretization of Maxwell’s equations – needed to make highly magnetized (astro)physical plasma amenable to its numerical modeling – introduces numerical diffusion. It acts as a source of dissipation independent of the system’s physical constituents. Understanding the numerical diffusion of scientific codes is the key to classifying their reliability. It gives specific limits in which the results of numerical experiments are physical. We aim at quantifying and characterizing the numerical diffusion properties of our recently developed numerical tool for the simulation of general relativistic force-free electrodynamics by calibrating and comparing it with other strategies found in the literature. Our code correctly models smooth waves of highly magnetized plasma. We evaluate the limits of general relativistic force-free electrodynamics in the context of current sheets and tearing mode instabilities. We identify that the current parallel to the magnetic field (j ∥ ), in combination with the breakdown of general relativistic force-free electrodynamics across current sheets, impairs the physical modeling of resistive instabilities. We find that at least eight numerical cells per characteristic size of interest (e.g., the wavelength in plasma waves or the transverse width of a current sheet) are needed to find consistency between resistivity of numerical and of physical origins. High-order discretization of the force-free current allows us to provide almost ideal orders of convergence for (smooth) plasma wave dynamics. The physical modeling of resistive layers requires suitable current prescriptions or a sub-grid modeling for the evolution of j ∥ .

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

A finite-volume scheme for modeling compressible magnetohydrodynamic flows at low Mach numbers in stellar interiors

Fully compressible magnetohydrodynamic (MHD) simulations are a fundamental tool for investigating the role of dynamo amplification in the generation of magnetic fields in deep convective layers of stars. The flows that arise in such environments are characterized by low (sonic) Mach numbers ($\mathscr{M}$ son ≲ 10 –2 ). In these regimes, conventional MHD codes typically show excessive dissipation and tend to be inefficient as the Courant–Friedrichs–Lewy (CFL) constraint on the time step becomes too strict. In this work we present a new method for efficiently simulating MHD flows at low Mach numbers in a space-dependent gravitational potential while still retaining all effects of compressibility. The proposed scheme is implemented in the finite-volume SEVEN-LEAGUE HYDRO (SLH) code, and it makes use of a low-Mach version of the five-wave Harten–Lax–van Leer discontinuities (HLLD) solver to reduce numerical dissipation, an implicit–explicit time discretization technique based on Strang splitting to overcome the overly strict CFL constraint, and a well-balancing method that dramatically reduces the magnitude of spatial discretization errors in strongly stratified setups. The solenoidal constraint on the magnetic field is enforced by using a constrained transport method on a staggered grid. We carry out five verification tests, including the simulation of a small-scale dynamo in a star-like environment at $\mathscr{M}$ son ~ 10 –3 . We demonstrate that the proposed scheme can be used to accurately simulate compressible MHD flows in regimes of low Mach numbers and strongly stratified setups even with moderately coarse grids.

79 ASTRONOMY AND ASTROPHYSICS↗