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DOE OSTI2026

Nonlinear optimal recovery in Hilbert spaces

Here, this paper investigates solution strategies for nonlinear problems in Hilbert spaces, such as nonlinear partial differential equations (PDEs) in Sobolev spaces, when only finite measurements are available. We formulate this as a nonlinear optimal recovery problem, establishing its well-posedness and proving its convergence to the true solution as the number of measurements increases. However, the resulting formulation might not have a finite-dimensional solution in general. We thus present a sufficient condition for the finite dimensionality of the solution, applicable to problems with well-defined point evaluation measurements. To address the broader setting, we introduce a relaxed nonlinear optimal recovery and provide a detailed convergence analysis. An illustrative example is given to demonstrate that our formulations and theoretical findings offer a comprehensive framework for solving nonlinear problems in infinite-dimensional spaces with limited data.

convergence↗

DOE OSTI2022

A Hybrid Experimental and Theoretical Approach to Optimize Recovery of Rare Earth Elements from Acid Mine Drainage Precipitates by Oxalic Acid Precipitation

The development of processing techniques for the extraction of rare earth elements and critical minerals (REE/CM) from acid mine drainage precipitates (AMDp) has attracted increased interest in recent years. Processes under development often utilize a standard hydrometallurgical approach that includes leaching and solvent extraction followed by oxalic acid precipitation and calcination to produce a final rare earth oxide product. Impurities such as Ca, Al, Mn, Fe and Mg can be detrimental in the oxalate precipitation step and a survey of the literature showed limited data pertaining to the REE precipitation efficiency in solutions with high impurity concentrations. As such, a systematic laboratory-scale precipitation study was performed on a strip solution generated by the acid leaching and solvent extraction of an AMDp feedstock to identify the optimal processing conditions that maximize REE precipitation efficiency and product purity while minimizing the oxalic acid dosage. Given the unique chemical characteristics of AMDp, the feed solution utilized in this study contained a moderate concentration of REEs (440 mg/L) as well a significant concentration (>7000 mg/L total) of non-REE contaminants such as Ca, Al, Mn, Fe and Mg. Initially, a theoretical basis for the required oxalic acid dose, optimal pH and predicted precipitation efficiency was established by solution equilibrium calculations. Following the solution chemistry calculations, bench-scale precipitation experiments were conducted and these test results indicate that a pH of 1.5 to 2, a reaction time of more than 2 h and an oxalic acid dosage of 30 to 40 g/L optimized the REEs recovery of at ~95% to nearly 100% for individual REE species. The test results validated the optimal pH predicted by the solution chemistry calculations (1.5 to 5); however, the predicted dosage needed for complete REE recovery (10 g/L) was significantly lower than the experimentally-determined dosage of 30 to 40 g/L. The reason for this discrepancy was determined to be due to the large concentration of impurities and large number of potential metal complexes that cause inaccuracies in the solution equilibrium calculations. Based on these findings, a hybrid experimental and theoretical approach is proposed for future oxalic acid precipitation optimization studies.

oxalic acid precipitation↗

DOE OSTI2026

Optimizing Heat Recovery with Storage: Control Validation and Sensitivity Analysis of the Time-Independent Energy Recovery Plant Using Modelica

Heat recovery in large building central plants saves energy but traditionally requires simultaneous heating and cooling. The Time-Independent Energy Recovery (TIER) plant shifts this paradigm by integrating thermal energy storage (TES) to enable heat recovery regardless of concurrent demand, offering a highly efficient, space-saving solution to achieve California’s energy goals. However, its integration of heat recovery chillers, cooling-only chillers, cooling towers, and trim air-source heat pumps (ASHPs) creates growing control and sizing complexity. To overcome this, this study employs high-fidelity Modelica dynamic simulation to validate TIER control sequences and optimize equipment sizing. We translated the written Sequences of Operation into executable Control Description Language (CDL) to test logic against sub-hourly loads. This verification workflow successfully identified and resolved critical vulnerabilities, such as thermal storage freezing and equipment short-cycling, in a virtual environment prior to physical deployment. Then, the study analyzes TIER plant performance across three simulated building types in three locations, and a real building load profile, ensuring variety in heating and cooling loads, and simultaneity factors and explores sizing rules for the TES and ASHP capacity. The analysis shows that the TIER plant operates equipment efficiently leading to a plant SCOP of around 7.5 across all scenarios, higher than a traditional ASHP plant, and a viable pathway to de-risk complex system design and control through simulation to identify optimal designs that maximize energy efficiency, minimize operational costs, and ensure robust operation in varied environmental conditions, thereby facilitating the broader adoption of such a solution for large buildings.

Zanetti, Ettore↗

DOE OSTI2024

Mathematical methods for optimal polynomial recovery of high-dimensional systems from noisy data

The goal of our Early Career Research Project (ECRP) is to establish a modern mathematical foundation that will enable next-generation computational methods for polynomial approximation of high-dimensional systems, having a certain set of constraints, from a limited amount of noisy data. Such a foundation is critical to realizing the future potential of the DOE user facilities, and will ultimately empower scientists to address a fundamental question, namely, “how many realizations of a nonlinear manifold are required to recover the entire high-dimensional solution map, with optimal approximation guarantees and minimal computational cost?” The central theme of this effort aims to conquer this challenge by pioneering the development of extraordinarily innovative theoretical analysis and transformational non-intrusive computational methodologies. Such approaches will enable the reconstruction of the entire high-dimensional solution map, with accuracy comparable to the best approximation, while utilizing an optimal number of samples. During this reporting period we have made significant progress on four thrusts.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Impact of Rheology Models on Horizontal Well Polymer Flooding in a Heavy Oil Reservoir on Alaska North Slope: A Simulation Study

Polymer rheology can have either a positive or a negative effect on polymer flooding performance under varied circumstances. Many researchers have studied the effect of polymer rheology in a vertical well, but no field scale studies have been conducted to investigate whether polymer rheology is beneficial to polymer flooding in heavy oil reservoirs developed by horizontal wells. In this paper, we conducted a numerical simulation study to examine the effect of HPAM polymer rheology on a polymer flooding pilot, which is the first-ever project conducted on a heavy oil reservoir from Alaska North Slope (ANS) developed by horizontal wells. Three rheology types were considered in the study including the apparent viscosity measured during coreflooding of using a HPAM polymer, the bulk viscosity measured with a viscometer, and a Newtonian flow model. The results suggest that using the bulk viscosity in simulation underestimates the conformance control and the water-oil-ratio reduction capability of the HPAM polymer solution. When the apparent viscosity is used, the incremental oil and sweep were largely increased, and the optimal recovery period of polymer flooding was extended greatly, especially for the heterogeneous formations. Therefore, the rheology type of polymer plays a significant role in the incremental oil recovery and injection profile of the horizontal well system given the pilot test conditions. This study has provided practical guidance to field operators for the ongoing polymer flooding pilot on ANS and will also provide valuable information for other polymer projects conducted in similar conditions.

Leng, Jianqiao↗

DOE OSTI2023

Sustainable bioleaching of lithium-ion batteries for critical metal recovery: Process optimization through design of experiments and thermodynamic modeling

Recycling spent lithium-ion batteries (LIBs) could alleviate supply risks for critical metals and be less harmful to the environment compared to new production of metals from mining. Developing a cost-effective LIB bioleaching process could be a promising alternative to traditional energy-intensive recycling technologies. Here, this study aimed to optimize bioleaching conditions for maximum economic competitiveness through design of experiments using iterative response surface methodology (RSM), assisted by thermodynamic modeling. The optimal condition was identified as 2.5% pulp density in 75 mM gluconic acid biolixiviant at 55°C for 30 h which could recover 57%–84% of nickel, 71%–86% of cobalt, and 100% of lithium and manganese, yielding a 17%–26% net profit margin. The recommended pulp density and acid concentrations, together with the observed metal solubilization, were supported by thermodynamic modeling predictions. Our study demonstrated that combining RSM with thermodynamic simulations could be a powerful tool for optimizing bioleaching conditions.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2025

PHAROS: PROMETHIUM HIGH-PRESSURE AUTOMATED RECOVERY WITH OPTIMIZED SEPARATION

Explore the source record for details and available documents.

Roach, Benjamin [ORNL] (ORCID:0000000177812013)↗

DOE OSTI2024

Stochastic optimization of value recovery network for Li-ion batteries in the United States under price and return volume uncertainties

Not provided.

Engineering↗

DOE OSTI2026

Universal Optimization and Tighter Fidelity Bounds for Approximate Quantum Error Correction

Approximate quantum error correction (AQEC) not only dictates the performance of discrete- and continuous-variable quantum error correction codes but also serves as a unifying framework across various physical disciplines. Identifying the optimal recovery channel to maximize the entanglement fidelity via standard semidefinite programming is computationally bottlenecked by the exponentially growing number of Kraus operators with system size, rendering large-scale optimization prohibitive. While analytical near-optimal maps exist, they typically work only when the Knill-Laflamme conditions are nearly satisfied. In this Letter, we establish an efficient framework by leveraging the duality between recovery and environment decoupling. This framework yields a tighter analytical lower bound on entanglement fidelity than the conventional limit set by the transpose channel. Furthermore, by exploiting the decayed weights of noise Kraus operators, we introduce a framework based on principal component analysis to reduce the dimension. In thermal loss channels where the weights decay exponentially, our approach achieves a 33-fold computational speedup while maintaining rigorous accuracy. Our approach enables high-precision optimization for AQEC codes that were previously intractable due to the curse of dimensionality.

Wu, Jing [Fermilab] (ORCID:0000000249460732)↗

DOE OSTI2020

Science-informed Machine Learning to Increase Recovery Efficiency in Unconventional Reservoirs

Production of hydrocarbons from fractured, unconventional reservoirs is inherently inefficient. But machine learning offers a pathway both to increasing recovery efficiency at a site and to improving forecasts of production, thereby improving the economics of operations in unconventional reservoirs. Los Alamos—in partnership with DOE, NETL, and WVU—has been developing a science-informed workflow and platform for optimizing pressure-drawdown at a site, which will allow an operator to make reservoir-management decisions that optimize recovery in consideration of future production. This work relies on a hybridization of physics-based prediction and machine learning, whereby accurate synthetic data (in combination with available site data) can enable the application of machine learning methods for rapid forecasting and optimization. The physics-based prediction is built upon experimental and theoretical work to determine transport characteristics in shale at various scales, with an emphasis on materials from MSEEL-I; this fundamental shale R&D was conducted in partnership with DOE, NETL, and several other national labs. This work has resulted from a coordinated leveraging of developments across several projects within DOE FE30, along with internal investments from Los Alamos via LDRD. The development has utilized data from the MSEEL–I site for calibration and demonstration; however, the workflow and platform are readily extendable to operations at other sites, plays, and basins. This machine-learning method can aid operators to improve both recovery efficiency and competitiveness; to this end, future work would quantify processes for other plays/basins and integrate production details with economics.

04 OIL SHALES AND TAR SANDS↗

DOE OSTI2022

LANL Activities on Mechanistic Approach to Analyzing and Improving Unconventional Hydrocarbon Production

Hydrocarbon production from shale reservoirs is inherently inefficient and challenging since these are low permeability plays. In addition, there is a limited understanding of the fundamentals and the controlling mechanisms, further complicating how to optimize these plays. Herein, we summarize our experimental and computational efforts fully and partially supported by the fundamental shale portfolio to reveal unconventional shale fundamentals and devise development strategies to enhance extraction efficiency with a minimal environmental footprint. Integrating these fundamentals with machine learning, we outline a pathway to improve the predictive power of our models, which enhances the forecast quality of production, thereby improving the economics of operations in unconventional reservoirs. For instance, we have developed science informed workflows and platforms for optimizing pressure-drawdown at a site, which allow operators to make reservoir-management decisions that optimize recovery in consideration of future production. Recently, our work relies on the hybridization of physics-based prediction and machine learning, whereby accurate synthetic data (combined with available site data) can enable the application of machine learning methods for rapid forecasting and optimization. Consequently, the workflow and platform are readily extendable to operations at other sites, plays, and basins.

04 OIL SHALES AND TAR SANDS↗

DOE OSTI2023

Storm-DEPART (Damage Estimate Prediction and Recovery Tool)

Storm-DEPART (Damage Estimate Prediction and Restoration Tool): Each year hurricanes and tropical storms in the United States damage critical infrastructure assets, disrupt the services they provide, and cause millions to billions of dollars in economic impacts due to extended recovery times. The Storm-DEPART tool and analytical output enable more impactful data-driven decision-making capabilities and strengthen national-level disaster preparedness, response, and recovery. Storm-DEPART, built through multi-month collaboration between Entergy and INL, combines Entergy’s critical infrastructure inventory data with weather forecasts to predict damages to Electric utility’s assets due to natural disasters and the estimated recovery support needed, including time, materials, and resource allocation. In the event of an approaching hurricane, this innovative solution can assess potential damage to power generation capacity, transmission grids, distribution networks, and communications assets from wind bands, storm surge, and flooding. With more effective predictions, Entergy can more efficiently allocate resources to mitigate impacts and optimize recovery for customers. Storm-DEPART also allows Electric utilities the ability to apply a planning scenario and model expected damage to better inform infrastructure restoration needs leading to enhance system resiliency. The technology is fully transferrable to other electric utilities with the same damage estimating challenges. The INL team is working on the evolution of Storm-DEPART to include ice event damage prediction framework.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2023

Storm-DEPART (Damage Estimate Prediction and Recovery Tool)

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2023

Final Report DE-FE0031785 Mohsen Ahmadian, Ph.D. Demonstration of Proof of Concept of a Multiphysics Approach for Real-Time Remote Monitoring of Dynamic Changes in Pressure and Salinity in Hydraulically Fractured Networks

Hydraulic fracturing has evolved into a multistep process with varying flow rates, carrier fluids (e.g., gel or slickwater), proppant loadings, and proppant grain sizes. As a result, primary recovery from a hydraulically fractured tight-oil reservoir is often a tiny fraction of the original oil in place, ranging between 5 and 10%. As stated in the FOA1990, “part of this problem is due to the inability of current well completion processes to effectively stimulate the entire reservoir volume in contact with the wellbore. Innovative technologies are needed that can help improve the effectiveness of reservoir completion methods, maximize stimulated reservoir volumes, and optimize recovery over the entire producing life span of a well”. We first need to enhance the current fracture diagnostic techniques to improve a well-completion design. However, detecting and delineating a subsurface hydraulic fracture is extremely difficult because the induced fracture network is only fractionally propped, and these propped fractures are generally very thin. Microseismic and tiltmeter monitoring techniques can provide information on the fracture extent but provide little or no information on the movement and final distribution of proppant or production fluids. On the other hand, electromagnetic (EM) imaging has shown the capability to monitor proppant distribution throughout the fracture area, especially in the presence of Electrically Active Proppants (EAPs). A previous EM survey of hydraulic fracturing at the Devine Fracture Pilot Site (DFPS) and subsequent EM code developments demonstrated this survey as a robust technique to remotely interrogate the extent of the EAP-filled hydraulic fracture during its propagation. The objectives of the project were threefold: (1) to capitalize on the material properties of an EAP to demonstrate remote monitoring of relative changes in pressure, pressure, and flow that are commonly encountered during production from a hydraulically fractured reservoir; (2) to evaluate EM imaging tools, to achieve Objective 1 in near real-time; and (3) to develop a multi-physics joint inversion approach to precisely predict flow patterns and physiochemical changes within an EAP-filled fracture network. This research project was built upon our previous work at the Devine Test Site managed by the Bureau of Economic Geology (BEG) at The University of Texas at Austin (UT-Austin). It also leveraged a significant investment from the Advanced Energy Consortium (AEC) to address the DOE's interest in subsurface flow, containment, and characterization by multiple signals. This three-year and three-month project succeeded in demonstrating the feasibility of a real-time dynamic fluid flow mapping technique at Technology Readiness Level 5 (TRL5) by utilizing a commercially available surface-based Controlled-Source Electromagnetic (CSEM) method (Objectives 1, 2). We demonstrated that injections into an EAP-filled fracture could be successfully coupled with real-time electric field measurements on the surface, leading to remote monitoring of dynamic changes within the EAP-filled fracture. Furthermore, the observed electric field in our study is influenced by bottomhole pressure, flow rate, and salinity, which is demonstrated by comparing these parameters with the electrical field potentials. EM simulations solely based on assumptions of fracture conductivity changes during injection did not reproduce the whole measured electric field magnitudes. Preliminary estimates showed that including Streaming Potential (SP) in our geophysical model is likely needed to reduce the simulation misfit.

02 PETROLEUM↗

DOE OSTI2023

Spin-squeezed Gottesman-Kitaev-Preskill codes for quantum error correction in atomic ensembles

Gottesman-Kitaev-Preskill (GKP) codes encode a qubit in displaced phase-space combs of a continuous-variable (CV) quantum system and are useful for correcting a variety of high-weight photonic errors. Here we propose atomic ensemble analogs of the single-mode CV GKP code by using the quantum central limit theorem to pull back the phase-space structure of a CV system to the compact phase space of a quantum spin system. We study the optimal recovery performance of these codes under error channels described by stochastic relaxation and isotropic ballistic dephasing processes using the diversity combining approach for calculating channel fidelity. Additionally, we find that the spin GKP codes outperform other spin system codes such as cat codes or binomial codes. Our spin GKP codes based on the two-axis countertwisting interaction and superpositions of SU(2) coherent states are direct spin analogs of the finite-energy CV GKP codes, whereas our codes based on one-axis twisting do not yet have well-studied CV analogs. A state preparation scheme for the spin GKP codes is proposed which uses the linear-combination-of-unitaries method, applicable to both the CV and spin GKP settings. Finally, we discuss a fault-tolerant approximate gate set for quantum computing with spin-GKP-encoded qubits, obtained by translating gates from the CV GKP setting using the quantum central limit theorem.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

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↗

DOE OSTI2022

Maximizing Strength: The Stimuli and Mediators of Strength Gains and Their Application to Training and Rehabilitation

Abstract Spiering, BA, Clark, BC, Schoenfeld, BJ, Foulis, SA, and Pasiakos, SM. Maximizing strength: the stimuli and mediators of strength gains and their application to training and rehabilitation. J Strength Cond Res 37(4): 919–929, 2023—Traditional heavy resistance exercise (RE) training increases maximal strength, a valuable adaptation in many situations. That stated, some populations seek new opportunities for pushing the upper limits of strength gains (e.g., athletes and military personnel). Alternatively, other populations strive to increase or maintain strength but cannot perform heavy RE (e.g., during at-home exercise, during deployment, or after injury or illness). Therefore, the purpose of this narrative review is to (a) identify the known stimuli that trigger gains in strength; (b) identify the known factors that mediate the long-term effectiveness of these stimuli; (c) discuss (and in some cases, speculate on) potential opportunities for maximizing strength gains beyond current limits; and (d) discuss practical applications for increasing or maintaining strength when traditional heavy RE cannot be performed. First, by conceptually deconstructing traditional heavy RE, we identify that strength gains are stimulated through a sequence of events, namely: giving maximal mental effort, leading to maximal neural activation of muscle to produce forceful contractions, involving lifting and lowering movements, training through a full range of motion, and (potentially) inducing muscular metabolic stress. Second, we identify factors that mediate the long-term effectiveness of these RE stimuli, namely: optimizing the dose of RE within a session, beginning each set of RE in a minimally fatigued state, optimizing recovery between training sessions, and (potentially) periodizing the training stimulus over time. Equipped with these insights, we identify potential opportunities for further maximizing strength gains. Finally, we identify opportunities for increasing or maintaining strength when traditional heavy RE cannot be performed.

Sport Sciences↗

DOE OSTI2022

Quantifying Antibiotic Distribution in Solid and Liquid Fractions of Manure Using a Two-Step, Multi-Residue Antibiotic Extraction

Antibiotic distribution and analysis within liquid and solid fractions of manure are highly variable due to each compound’s respective physiochemical properties. This study developed and evaluated a uniform method extracting 10 antibiotics from 4 antibiotic classes (tetracycline, sulfonamides, macrolides, and β-lactam) from unprocessed manure, solid–liquid separated manure, and composted solids. Through systematic manipulation of previously published liquid chromatography tandem mass spectrometry methods; this study developed an extraction protocol with optimized recovery efficiencies for varied manure substrates. The method includes a two-step, liquid-solid extraction using 10 mL of 0.1 M EDTA-McIlviane buffer followed by 10 mL of methanol. Antibiotics recoveries from unprocessed manure, separated liquids, separated solids, and heat-treated solids using the two-step extraction method had relative standard deviations < 30% for all but ceftiofur. Total antibiotic recoveries were 67–131% for tetracyclines, 56% for sulfonamide, 49–53% for macrolides, and 1.3–66% for β-lactams. This is the first study to use one protocol to assess four classes of antibiotics in liquid and solid manure fractions. This study allowed for more precise risk assessment of antibiotic transport in manure waste stream applied to fields as a liquid or solid compost.

59 BASIC BIOLOGICAL SCIENCES↗