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DOE OSTI2026

AGFormer: Adaptive Spatiotemporal graph informed transformer for multi-reservoir inflow forecasting

Accurate reservoir inflow forecasting is crucial for effective water resource management, yet most machine learning models focus on single-reservoir prediction and overlook spatial dependencies among hydrologically connected reservoirs. Here, we propose AGFormer (Adaptive Graph-Informed Transformer), an end-to-end framework that integrates adaptive graph learning with temporal sequence modeling for multi-reservoir inflow forecasting. A shared encoder and graph attention mechanism generate reservoir-specific embeddings, which are then processed by the Transformer-based encoder–decoder for multi-step inflow forecasting. We also introduce a pretraining paradigm to learn robust temporal embeddings from misaligned historical records. Evaluated on 30 reservoirs in the Upper Colorado River Basin, AGFormer achieves superior seven-day-ahead forecasts, with NSE > 0.75 for 20 reservoirs—outperforming Encoder–Decoder LSTM, GCN+LSTM, and Transformer baselines. Adaptive graph learning captures dynamic inter-reservoir dependencies, and feature attribution aligns with snowmelt-driven hydrology. Incorporating forecasted meteorological inputs further enhances accuracy, demonstrating AGFormer’s potential to support reservoir management under dynamic hydrological conditions.

Adaptive graph learning↗

DOE OSTI2021

Gasoline fuels properties for multi-mode operation – Observations in a GDI and the CFR engine

The combustion behavior of five full boiling range RON98 gasoline blends was evaluated for multi-mode operation in a GDI and the CFR octane rating engine. The GDI engine tests were conducted with stoichiometric air-fuel ratio in spark-ignition (SI), and with air-diluted homogeneous charge compression ignition (HCCI) mode. In the CFR engine, the knocking combustion was analyzed under standard RON testing conditions at both peak knocking lambda and stoichiometric air-fuel ratios, whereas compression ignited operation was characterized by utilizing the HCCI number test protocol. Disparate knock limited SI and HCCI combustion behavior was observed for the test fuels, despite four of the fuels having the same RON and octane sensitivity. It was found that knock-limited combustion phasing in the GDI engine did not align well with the RON. However, a detailed comparison of knock-limited SI operation in the GDI and CFR engine revealed that a more appropriate effective RON based on a common knock intensity metric (MAPO) and stoichiometric air-fuel ratio resulted in comparable knock characterization between the two engine platforms. Furthermore, the critical intake air temperature and the critical compression ratio were proposed to characterize knock-limited SI operation, while the minimum intake air heating and compression ratio were used to define a fuel's autoignition propensity for compression ignition operation in the GDI and CFR engine, respectively. Finally, each fuel's characteristic compression ratio needed to obtain knock-limited SI (KLSI) and HCCI operation was used to calculate an effective multi-mode octane number (MM-ON) based on the primary reference fuel blends.

33 ADVANCED PROPULSION SYSTEMS↗

DOE OSTI2022

Fuel property impacts on gaseous and PM emissions from a multi-mode single-cylinder engine

The U.S. Department of Energy’s Co-Optima initiative has focused on improving fuel economy and vehicle performance while reducing emissions through the simultaneous development of emerging sustainable fuels with beneficial properties and advanced combustion strategies. A major thrust has been the development of advanced compression ignition (ACI) combustion strategies of gasoline range fuels in combination with spark-ignited (SI) combustion in a single engine capable of multi-mode operation to achieve high power density with enhanced part load efficiency. The aim of this study was to further the understanding of how emissions from both ACI and SI strategies operating on the same fuels in the same engine are impacted by different fuel properties. This investigation focused on particulate matter (PM) and gaseous hydrocarbon emissions from 6 different fuels across 3 different combustion modes on the same single-cylinder engine designed for multi-mode operation: SI combustion, partial fuel stratification (PFS), and spark-assisted compression ignition (SACI). In each of these modes, 3 different CA50 phasings were studied such that all 6 fuels could be studied at the same phasings. Three of the six different fuels used were specially formulated in a previous investigation to study the impact of fuel distillation and aromatic content while maintaining the research octane number (RON) and octane sensitivity. Additionally, neat isooctane and two ethanol containing fuels (RD5-87 and Co-Optima E30) were studied. Different fuel and phasing impacts on emissions were observed across the three combustion modes. Fuel properties were found to impact soot PM and particle number more than the CA50 phasing, while the phasing had more impact on NOx emissions. The NOx emissions were reduced in the PFS mode for all fuels compared to SI combustion, but the SACI combustion mode did not reduce NOx emissions. Although PFS produced low soot PM emissions like SI, total PM mass emissions were significantly higher due to large organic carbon (OC) PM mass contribution. Both PFS and SACI had greater particle number emission than SI operation with small nuclei mode particles dominating in PFS compared to large agglomeration particles in SACI.

42 ENGINEERING↗

DOE OSTI2020

Multi-agent motion planning with sporadic communications for collision avoidance

Here, a novel multi-vehicle motion planning and collision avoidance algorithm is proposed and analyzed. The algorithm aims to reduce the amount of onboard calculations and inter-agent communications needed for each vehicle to successfully navigate through an environment with static obstacles and reach their goals. To this end, each agent first calculates a path to the goal by means of an asymptotically optimal rapidly-exploring random tree (RRT*) with respect to the static obstacles. Then, other agents are treated as dynamic obstacles and potential collisions are determined by means of collision cones. Collision cones depend on the position and velocity from other agents and are grown conservatively between inter-agent communications. Based on the available information, each agent determines if a deconfliction maneuver is needed, if it can continue along its current path, or if communication is needed to make a decision about a conflict. With probability one, our algorithm guarantees that the agents keep from colliding with each other. Under an assumption on the existence of a solution for a vehicle to its goal, this algorithm also solves the planning problem with probability one. Simulations illustrate a group of agents successfully reaching their goal configurations and examine how the uncertainty affects the communication frequency of the multi-agent system.

33 ADVANCED PROPULSION SYSTEMS↗

DOE OSTI2021

Seismic monitoring of a small CO 2 injection using a multi-well DAS array: Operations and initial results of Stage 3 of the CO 2 CRC Otway project

Active time-lapse seismic is widely employed for monitoring CO 2 geosequestration due to its ability to track the distribution of fluids in space and time. However, standard 4D seismic monitoring suffers from several challenges, including high cost, disruption to other land uses, and, consequently, relatively large intervals between monitor surveys. Some of these challenges can be mitigated using permanently installed sources and receivers. Such an approach was tested at the CO 2 CRC Otway site by continuous offset VSP monitoring of 15,000 t of supercritical CO 2 injected into an aquifer 1,500 m deep with nine permanent seismic sources (surface orbital vibrators or SOVs) and five downhole fibre-optic receivers. This continuous monitoring is complemented by multi-well 4D VSP using a mobile vibroseis source and the same DAS receivers, which included one baseline and two monitor surveys after injection of 4,000 and 12,000 t of CO 2 . The continuous DAS-SOV monitoring detected an abrupt increase of travel times below the injection interval on the second day of injection (after injection of 300 t of CO 2 ) and tracked the growth of the areal CO 2 plume by mapping changes of reflection amplitudes. The plume is also detected by time-lapse changes of reflection amplitudes in multi-well 4D VSPs. The plume images obtained from continuous offset VSP and 4D VSP are broadly consistent with each other but with some differences due to differences in illumination, lateral variations of velocities and seismic anisotropy. Furthermore, these differences also serve as a measure of uncertainty of 4D VSP images.

4D VSP↗

DOE OSTI2023

Constraint energy minimizing generalized multiscale finite element method for multi-continuum Richards equations

In fluid flow simulation, the multi-continuum model is a useful strategy. When the heterogeneity and contrast of coefficients are high, the system becomes multiscale, and some kinds of reduced order methods are demanded. Combining these techniques with nonlinearity, we will consider in this paper a dual-continuum model which is generalized as a multi-continuum model for a coupled system of nonlinear Richards equations as unsaturated flows, in complex heterogeneous fractured porous media; and we will solve it by a novel multiscale approach utilizing the constraint energy minimizing generalized multiscale finite element method (CEM-GMsFEM). In particular, such a nonlinear system will be discretized in time and then linearized by Picard iteration (whose global convergence is proved theoretically). Subsequently, we tackle the resulting linearized equations by the CEM-GMsFEM and obtain proper offline multiscale basis functions to span the multiscale space (which contains the pressure solution). More specifically, we first introduce two new sources of samples, and the GMsFEM is used over each coarse block to build local auxiliary multiscale basis functions via solving local spectral problems, that are crucial for detecting high-contrast channels. Second, per oversampled coarse region, local multiscale basis functions are created through the CEM as constrainedly minimizing an energy functional. Various numerical tests for our approach reveal that the error converges with the coarse-grid size and that only few oversampling layers as well as basis functions are needed.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Feature-adjacent multi-fidelity physics-informed machine learning for partial differential equations

Physics-informed neural networks have emerged as an alternative method for solving partial differential equations. However, for complex problems, the training of such networks can still require high-fidelity data which can be expensive to generate. To reduce or even eliminate the dependency on high-fidelity data, we propose a novel multi-fidelity architecture which is based on a feature space shared by the low- and high-fidelity solutions. In the feature space, the projections of the low-fidelity and high-fidelity solutions are adjacent by constraining their relative distance. The feature space is represented with an encoder and its mapping to the original solution space is effected through a decoder. In conclusion, the proposed multi-fidelity approach is validated on forward and inverse problems for steady and unsteady problems described by partial differential equations.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Multi-head physics-informed neural networks for learning functional priors and uncertainty quantification

In numerous applications, the integration of prior knowledge and historical information is essential, particularly for tasks requiring the solution of ordinary or partial differential equations (ODEs/PDEs) in data-sparse or noisy environments. For instance, achieving accurate solutions to time-dependent PDEs with limited initial condition measurements necessitates an effective strategy for embedding prior knowledge. Hard-parameter sharing architectures in neural networks (NNs) have demonstrated success in both traditional and scientific machine learning domains, facilitating the learning of informative representations. Here, in this study, we introduce a novel, yet efficient, method to enhance physics-informed neural networks (PINNs) by incorporating a multi-head structure that enables the learning of functional priors from both empirical data and governing physical laws. This prior information can then be used to address data sparsity and high-level noise in solving ODE/PDE problems with uncertainty quantification (UQ). The approach, termed Multi-Head PINN (MH-PINN), consists of a shared body NN and multiple head NNs, each corresponding to an individual PINN instance. Our framework for functional prior learning is carried out in two stages: (1) training the MH-PINNs to develop a shared body NN alongside multiple head NNs, and (2) employing these trained head NNs to estimate a prior distribution through a normalizing flow-based density estimator. The learned functional prior can then be applied as a regularization mechanism in deterministic contexts or as an informative prior within a Bayesian inference framework, aiding in the resolution of subsequent ODE/PDE tasks. We evaluate the efficacy of MH-PINNs across five benchmark problems, including a high-dimensional parametric PDE, all characterized by data sparsity or substantial noise levels. Our findings reveal that MH-PINNs deliver accurate solutions and robust UQ, demonstrating adaptability across a range of complex and challenging scenarios.

Bayesian inference↗

DOE OSTI2025

Multi-physics melt pool modeling and process optimization for laser direct energy deposition of Nb-based refractory C103: Defect formation, geometric precision, and process mapping

Recent developments in additive manufacturing (AM) technology have reignited interest in the fabrication of the Nb-based refractory C103 alloy offering solutions to the challenges posed by traditional manufacturing methods. However, the limited numerical and experimental studies on laser direct energy deposition (DED) of C103 have hindered the understanding of the relationships between process parameters and build quality. This has made it challenging to consistently produce parts with the desired quality and microstructure suitable for critical applications. In this study, we focus on optimizing the laser DED process for C103 by employing a hybrid approach that combines experimental techniques and computational fluid dynamics (CFD). This approach facilitates the development of process maps for defect detection and geometric precision. To achieve this, multi-layer C103 samples were fabricated using laser DED under various process parameters, enabling the creation of a process map for defect detection. Additionally, a multi-physics, multiphase simulation framework was developed within a high-performance computing (HPC) environment to establish process maps for geometric precision. Using these process maps, printability windows were identified for achieving both the desired geometric accuracy and defect-free prints. It was observed that prints with a power-to-velocity (P/V) ratio close to unity resulted in defect-free outcomes. This study provides a foundation for reducing design lead time and rejected parts, ultimately optimizing the laser DED process for C103.

Defect formation and geometric precision↗

DOE OSTI2020

Numerical study of the effect of propped surface area and fracture conductivity on shale gas production: Application for multi-size proppant pumping schedule design

Hydraulic fracturing is a technique extensively used in the oil and gas industry, where water, proppant (sand) and additives are injected into unconventional reservoirs to enhance the recovery of shale hydrocarbon. Although some previous studies have developed pumping schedules that maximize gas production for a single-size proppant, there are very few studies that consider the effect of varying proppant diameters across pumping stages on shale gas production. Motivated by this, we carried out an extensive sensitivity analysis to determine the effect of different proppant diameters on the average fracture conductivity (FC), average propped surface area (PSA) and cumulative shale gas production volume. We found out that the cumulative shale gas production volume depends on both the average PSA and average FC. We also found out that small-diameter proppant resulted in higher average PSA and lower average FC, whereas large-diameter proppant resulted in lower average PSA and higher average FC. Hence, we designed a multi-size proppant pumping schedule considering both of these parameters into account for simultaneously propagating multiple fractures to maximize shale gas production from unconventional reservoirs. Since the size of injected proppant particles determines the average PSA and average FC for the propped hydraulic fractures, we developed a novel framework called Sequentially Interlinked Modeling Structure (SIMS) to predict the average PSA, average FC and cumulative shale gas production volume at the end of 10 years for a given pumping schedule. Then, we used this SIMS framework to obtain a multi-size proppant pumping schedule that maximizes shale gas production. In closing, we demonstrated that the obtained pumping schedule gives a cumulative shale gas production volume greater than the values obtained from the existing pumping schedules.

03 NATURAL GAS↗

DOE OSTI2022

Multi-pass flow-through reductive catalytic fractionation

Reductive catalytic fractionation (RCF) is a promising lignin-first biorefining strategy that selectively extracts and depolymerizes lignin from whole biomass. Flow-through (FT)-RCF enables physical separation of the biomass and catalyst, but this process configuration typically operates at high solvent-to-biomass ratios. Here, we demonstrate multi-pass FT-RCF, wherein the lignin-enriched solvent obtained after an initial FT-RCF step is recycled and used in subsequent FT-RCF without intermediate lignin recovery. Multi-pass FT-RCF reduces the solvent-to-biomass ratio from 48 to 1.9 L/kg, which is a lower solvent loading than is accessible in batch reactors, without negative impacts on delignification and monomer yield with up to 12 wt % lignin in the solvent. Overall, this work demonstrates that solvent demand in RCF processes, which is a key cost and energy driver to enable this process at scale, can be reduced by recycling lignin oil between RCF reactions.

09 BIOMASS FUELS↗

DOE OSTI2021

Multi-fidelity electrochemical modeling of thermally activated battery cells

Thermally activated batteries undergo a series of coupled physical changes during activation that influence battery performance. These processes include energetic material burning, heat transfer, electrolyte phase change, capillary-driven two-phase porous flow, ion transport, electrochemical reactions, and electrical transport. Several of these processes are strongly coupled and have a significant effect on battery performance, but others have minimal impact or may be suitably represented by reduced-order models. Additionally, assessing the relative importance of these phenomena must be based on comparisons to a high-fidelity model including all known processes. In this work, we first present and demonstrate a high-fidelity, multi-physics model of electrochemical performance. This novel multi-physics model enables predictions of how competing physical processes affect battery performance and provides unique insights into the difficult-to-measure processes that happen during battery activation. We introduce four categories of model fidelity that include different physical simplifications, assumptions, and reduced-order models to decouple or remove costly elements of the simulation. Using this approach, we show an order-of-magnitude reduction in computational cost while preserving all design-relevant quantities of interest within 5 percent. The validity of this approach and these model reductions is demonstrated by comparison between results from the full fidelity model and the different reduced models.

25 ENERGY STORAGE↗

DOE OSTI2022

Characterization of multi-material 316L-Hastelloy X fabricated via laser powder-bed fusion

The aim of this work is to provide firsthand knowledge of 316 L stainless steel (316 L) and Hastelloy X (HX) multi-material processing via laser powder bed fusion (PBF). Specifically, microstructure of the interface is studied using scanning electron microscopy (SEM), energy-dispersive X-ray spectroscopy (EDS), and X-ray diffraction (XRD). Surface metrology is performed to characterize the resulting surface roughness at the interface followed by tensile and flexural testing of multi-material samples to characterize the mechanical properties of the interfaces. Results showed that use of proper process parameters for each individual material led to formation of a compositional gradient at the interface that stretched for 240 μm (10–12 layers) with no evidence of cracking or porosity. The interface exhibited higher surface roughness compared to 316 L or HX as measured by arithmetic mean height, Sa, and maximum valley depth, Sv, parameters. During tensile testing, samples failed in the 316 L region away from the interface, with comparable yield strength, ultimate strength, and ductility. Finally, it was concluded that the “naturally” formed interface created a compositional gradient which was defect free due to similar values of coefficient of thermal expansion, input energy density, and different Marangoni numbers of the materials.

316L stainless Steel↗

DOE OSTI2025

Synergistic learning with multi-task DeepONet for efficient PDE problem solving

Multi-task learning (MTL) is an inductive transfer mechanism designed to leverage useful information from multiple tasks to improve generalization performance compared to single-task learning. It has been extensively explored in traditional machine learning to address issues such as data sparsity and overfitting in neural networks. In this work, we apply MTL to problems in science and engineering governed by partial differential equations (PDEs). However, implementing MTL in this context is complex, as it requires task-specific modifications to accommodate various scenarios representing different physical processes. To this end, we present a multi-task deep operator network (MT-DeepONet) to learn solutions across various functional forms of source terms in a PDE and multiple geometries in a single concurrent training session. We introduce modifications in the branch network of the vanilla DeepONet to account for various functional forms of a parameterized coefficient in a PDE. Additionally, we handle parameterized geometries by introducing a binary mask in the branch network and incorporating it into the loss term to improve convergence and generalization to new geometry tasks. Our approach is demonstrated on three benchmark problems: (1) learning different functional forms of the source term in the Fisher equation; (2) learning multiple geometries in a 2D Darcy Flow problem and showcasing better transfer learning capabilities to new geometries; and (3) learning 3D parameterized geometries for a heat transfer problem and demonstrate the ability to predict on new but similar geometries. Finally, our MT-DeepONet framework offers a novel approach to solving PDE problems in engineering and science under a unified umbrella based on synergistic learning that reduces the overall training cost for neural operators.

42 ENGINEERING↗

DOE OSTI2021

Multi-modal imaging of a single mouse brain over five orders of magnitude of resolution

Mammalian neurons operate at length scales spanning six orders of magnitude; they project millimeters to centimeters across brain regions, are composed of micrometer-scale-diameter myelinated axons, and ultimately form nanometer scale synapses. Capturing these anatomical features across that breadth of scale has required imaging samples with multiple independent imaging modalities. Translating between the different modalities, however, requires imaging the same brain with each. Here, we imaged the same postmortem mouse brain over five orders of spatial resolution using MRI, whole brain micrometer-scale synchrotron x-ray tomography ($\mu$CT), and large volume automated serial electron microscopy. Using this pipeline, we can track individual myelinated axons previously relegated to axon bundles in diffusion tensor MRI or arbitrarily trace neurons and their processes brain-wide and identify individual synapses on them. This pipeline provides both an unprecedented look across a single brain's multi-scaled organization as well as a vehicle for studying the brain's multi-scale pathologies.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2021

Multi-objective optimization with an integrated electromagnetics and beam dynamics workflow

In particle accelerators, RF cavities are used to accelerate charged particle beams to designed high energy for physical applications. In a typical accelerator design, the optimization of RF cavities and the optimization of beam dynamics are carried out in separate studies. For a more general and unrestricted accelerator design, a coupled optimization of the RF cavities and the beam parameters is required. For this coupled optimization problem, we have developed an integrated electromagnetics and beam dynamics workflow management system. Within this system, the geometries for a set of cavity components are first adjusted; the field modes are then computed with an electromagnetics program, and imported into a beam dynamics program for beam dynamics simulation. This workflow is encapsulated into a parallel multi-objective optimizer to achieve the integrated accelerator design optimization. A multi fidelity strategy is developed to improve the speed of the optimizer. Furthermore, this integrated global optimization capability is illustrated using a photoinjector design example and yields an improved design.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2020

Investigation of the ignition processes of a multi-injection flame in a Diesel engine environment using the flamelet model

In this paper, the first flamelet analysis is conducted of a highly resolved DNS of a multi-injection flame with both auto-ignition and ignition induced by flame-flame interaction. A novel method is proposed to identify the different combustion modes of ignition processes using generalized flamelet equations. The state-of-the-art DNS database generated by Rieth et al. (US National Combustion Meeting, 2019) for a multi-injection flame in a Diesel engine environment is investigated. Three-dimensional flamelets are extracted from the DNS at different time instants with a focus on auto-ignition and interaction-ignition processes. The influences of mixture field interactions and the scalar dissipation rate on the ignition process are investigated by varying the species composition boundary conditions of the transient flamelet equations. Budget analyses of the generalized flamelet equations show that the transport along the mixture fraction iso-surface is insignificant during the auto-ignition process, but becomes important when interaction-ignition occurs, which is further confirmed through a flamelet regime classification method.

42 ENGINEERING↗

DOE OSTI2025

Multi-GPU porting of a phase-change cascaded lattice Boltzmann method for three-dimensional pool boiling simulations

The Lattice Boltzmann method (LBM) has proven effective in simulating phase-change phenomena, such as melting, solidification, evaporation, and boiling. In this work, we develop a highly parallelized multi-GPU implementation of LBM for three-dimensional pool boiling simulations. The code is based on the OpenACC programming model, which enables the code to be deployed efficiently on multi-core CPUs, GPUs, and potentially other accelerators, without the need for architecture-specific rewrites. To support large-scale simulations, the domain is decomposed and distributed across multiple compute nodes using MPI. We demonstrate that the code exhibits excellent scaling properties, with ideal strong-scaling running with up to 256 GPUs on the MareNostrum5 cluster.

97 MATHEMATICS AND COMPUTING↗