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DOE OSTI2025

Colloidal Behavior of Plutonium Oxide in Concentrated Electrolyte Solutions

The Hanford Site in Washington State manages legacy high-level radioactive waste streams that display major chemistry and engineering challenges, including the high salt levels and pH values that correspond to conditions under which many classical concepts describing chemical reactivity cannot be applied. One particular challenge that needs to be tackled at Hanford is that Pu concentrations, [Pu], in the soluble phases of the tank wastes are higher than expected based on the solubility of crystalline PuO2, which is widely accepted to be caused by the formation of PuO2 colloid, consisting of nano- to submicron-sized particles (PuO2 NPs). Fundamental research underpinning the behavior of PuO2 NPs under conditions not only relevant to the Hanford tank waste but at high ionic strength in general is needed to reliably predict the chemical reactivity of PuO2 NPs and develop engineering solutions to safely and efficiently process high-level radioactive waste into forms suitable for long-term storage. In this work, we study the behavior of PuO2 NPs (particle size ~100 nm) under high ionic strength conditions by reacting it with highly concentrated (up to 5 M) salt solutions. We explore different electrolyte compositions to elucidate the impact of different anions (NO3-, Cl-, ClO4-, SO42-, C2O42-, CO32-) on the stability of PuO2 NP in the acidic and alkaline pH regime. PuO2 NP aggregation and precipitation as function electrolyte concentration is tracked by a combination of liquid scintillation counting, dynamic light scattering for determination of particle size distributions, and zeta potentials as a proxy for particle charge. At acidic pH, electrolytes containing non-coordinating anions, such as NaNO3, NaCl, and NaClO4 mostly stabilize PuO2 NPs over a large electrolyte concentration range, showing only subtle differences in their reactivity. Other electrolyte anions show a more pronounced effect on the PuO2 NP stability: SO42-, binds directly to the particles’ surface, reverses the particle charge, and precipitates the PuO2 NPs efficiently even at intermediate sulfate concentrations (>0.1 M). In contrast, C2O42- is found to lead to high [Pu] in solution, in the milli-molar range, even at mildly acidic pH (~4). Thermodynamic modeling of the dissolved Pu concentrations using PHREEQC is unable to predict the observed [Pu] in the acidic pH regime, supporting the influence of colloids in maintaining elevated [Pu]. It is noteworthy that the current thermodynamic databases do not include constants for colloidal Pu phases and cannot accurately predict many of the high ionic strength solutions relevant to this work. The mechanisms and models responsible for these observations will need further investigation in the future. At high pH values (~12), PuO2 NPs exhibits classical sol-gel chemistry, meaning that upon destabilization of the colloidal sol, for example by addition of concentrated NaOH, highly porous and viscid PuO2 coagulates are formed that consist of a three-dimensional network likely held together by physical interactions. The PuO2 NP coagulate shows no significant reversibility of the aggregation when contacted with concentrated brines; however, PuO2 NPs can be efficiently resuspended in solution by addition of diluted electrolytes, alkaline solutions containing high amounts of carbonate, or simple addition of water. Especially carbonate is shown to stabilize PuO2 NPs in solution at high pH, characterized by stable colloidal suspensions that are resistant against sedimentation during centrifugation. Thermodynamic modeling of the carbonate system was able to predict an increasing dissolved Pu concentration with increasing carbonate concentration. However, the model was profoundly sensitive to the fixed redox potential and does not include any thermodynamic constants for colloidal Pu species.

Neumann, Julia↗

DOE OSTI2024

Purification of U from U-10Mo scrap generated during the fabrication of high performance research reactor fuel

A low enriched U-Mo alloy fuel is under development to replace highly enriched U fuels currently used in United States high performance research reactors. The alloy casting and fuel fabrication processes will generate scrap streams containing low enriched U (LEU) which must be recovered. Solvent extraction processes were designed using the Argonne Model for Universal Solvent Extraction (AMUSE) to purify solutions containing 20 and 50 g/L U. The feed for the solvent extraction processes was prepared from solutions generated from the dissolution of U-10Mo-Zr foils and U-10Mo-Zr-Al mini-plates. The U purification processes were demonstrated using two, 16-stage banks of miniature mixer-settlers. The solvent extraction experiments demonstrated that all design objectives for the U purification processes could be met. The U recovery in the product stream for each flowsheet was ≥99.9%. The flowsheet demonstrations also showed that the purity of the U Product will meet the requirements of the ASTM International C1462-21 specification for LEU metal enriched to less than 20% 235 U. In conclusion, the AMUSE modeling for both flowsheet demonstrations was validated by comparing predicted and measured concentrations of U, Mo, and Zr in the exit streams and stage samples at steady-state conditions in the mixer-settlers.

modified PUREX process↗

DOE OSTI2025

Scalable Hyperpolarized MRI Enabled by Ace‐SABRE of [1‐ 13 C]Pyruvate

Abstract Hyperpolarized (HP) MRI using [1– 13 C]pyruvate is emerging as a promising molecular imaging approach. Among hyperpolarization methods, Signal Amplification By Reversible Exchange (SABRE) is attractive because SABRE polarizes the substrates directly in room‐temperature solutions avoiding complex hardware. Most SABRE experiments have historically been performed in methanol, a relatively toxic and difficult‐to‐remove solvent. Here we demonstrate the use of a 80/20 acetone/water (A/W) solvent system (Ace‐SABRE) to provide hyperpolarized [1– 13 C]pyruvate with up to 17% polarization, then implement a solvent processing protocol to achieve injectable solutions retaining 74% of the initial polarization, and lastly we demonstrate HP in vivo spectroscopy and imaging using the Ace‐SABRE platform to showcase metabolic tracking in a hepatocellular carcinoma (HCC) tumor as well as HP‐MRI, both in direct comparison to dissolution dynamic nuclear polarization (d‐DNP) experiments. The Ace‐SABRE technique promises faster adoption of SABRE hyperpolarization in biological experiments, overall lowering the barriers to entry for HP‐NMR and HP‐MRI.

Chemistry↗

DOE OSTI2024

Hydrologic connectivity and dynamics of solute transport in a mountain stream: Insights from a long-term tracer test and multiscale transport modeling informed by machine learning

The movement of solutes in a watershed is a complex process with multiple interactions and feedbacks across spatial and temporal scales. Modeling the dynamics of solute transport along diverse hydrologic pathways within watersheds – from hillslopes to stream channels and in and out of the hyporheic zones – is challenging but critically important, as these processes integrate and contribute to the biogeochemical functioning of the river corridor up to the river network scale. Here we use results from a long-term network-scale tracer test at the H.J. Andrews experimental forest in western Cascade Mountains, Oregon, USA to inform a multiscale framework for transport in stream corridors. The framework uses a Lagrangian-based subgrid model to represent the effects of hyporheic exchange flow and advective transport at stream network scales. The spatially and temporally resolved stream discharge needed for the transport model is imputed across the river system by an entity-aware long short-term memory network. Modeled concentrations show good agreements with the observations and exhibit power scaling laws indicative of a very wide range of timescales over which hyporheic exchange flow occurs. Our results demonstrate a data-informed modeling framework that links dynamical processes occurring at small scales to a network context to help understand how changes at reach scale cascade into network-scale effects, providing a useful tool for sustainable river basin management.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2025

Advanced Brine Processing to Enable U.S. Lithium Independence (CRADA Report)

Current production of LiOH, which is needed to make Li-ion battery cathode active materials, utilizes a multistep process including solar evaporation, precipitation with Na 2 CO 3 and then conversion to LiOH using Ca(OH) 2 . This process requires a large amount of land area for solar evaporation, the right weather conditions, and chemicals for the conversion process that result in NaCl and CaCO 3 waste products. The production of Ca(OH) 2 is very energy intensive and evolves significant quantities of CO 2 . An alternative process flow utilizing direct lithium extraction techniques, followed by a chemical free conversion process can have benefits in reducing the needed land requirements and chemicals for traditional brine processing. There are many potential direct lithium extraction technologies that are currently being developed. The direct lithium extraction process from typical brine sources will produce a LiCl solution with some impurities including typically high concentrations of Na. This brine then needs to be converted to LiOH for use in battery cathode production. Ideally this conversion could occur without the use of additional chemicals. Electrochemistry can do this conversion either via electrolysis or bipolar membrane electrodialysis (BPED) to produce LiOH and HCl in solution. BPED utilized bipolar membranes to split water, which has a reduced potential as compared to splitting water at electrodes into hydrogen and oxygen gas. This reduced potential required results in a significant energy savings for BPED over electrolysis methods. This CRADA project aimed to develop such an integrated process using direct lithium extraction followed by BPED to produce a LiOH solution. That solution can then be crystallized into battery grade LiOH. In particular, Albemarle utilized a direct lithium extraction process to produce a concentrated LiCl solution that could be used for the BPED process. The BPED process was first tested using various LiCl solutions with impurity ions added at bench scale to understand the effects of impurities and determine processing parameters. Then testing was performed using the direct lithium extracted brine at the bench scale before scaling the process up. After the process was scaled up a long duration test was carried out to estimate the lifetime of the membranes, which is key to the economics of the BPED process.

25 ENERGY STORAGE↗

DOE OSTI2026

Designing a Robust MEA-Based Post-Combustion Carbon Capture Process with Capture Rate Guarantees

This work presents an application of the nonlinear two-stage robust optimization solver PyROS to the model-based design and operation of a monoethanolamine scrubbing process for CO2 capture under epistemic uncertainty. Through this application, risk-averse process designs are successfully obtained for CO2 capture targets ranging from 90% to over 99%. In particular, the risk-averse solutions for CO2 capture targets of up to 98% are shown to be only marginally more expensive than their nominally optimal counterparts. Thus, the results demonstrate the utility of recently developed nonlinear robust optimization approaches for the solution of large-scale chemical process models under uncertainty.

20 FOSSIL-FUELED POWER PLANTS↗

DOE OSTI2026

Establishment of a Vertically Integrated Domestic Manufacturing Process for Production of Substrates Needed for Manufacture of Gas Diffusion Layers

In this project, AvCarb, LLC evaluated the baseline performance metrics of commercial carbon veils and their corresponding Gas Diffusion Layers (GDLs) with the goal of establishing an optimized, vertically integrated production system for wet-laid nonwoven substrates used in gas diffusion media for electrochemical energy storage and conversion devices. Mechanical testing and microstructural characterization were conducted and used to develop a multiscale computational model capable of simulating and predicting the performance of GDLs in fuel cells. Although the project successfully generated foundational transport and modeling data, it was terminated prior to identifying the critical GDL design parameters necessary for full optimization. The program aimed to improve carbon veil fabrication through enhanced fiber dispersion, fiber-fiber adhesion control, and improved web formation, enabling the production of high-quality, uniform substrates. Simulations were intended to guide mixing and solution delivery system design and process conditions, followed by production-scale trials to evaluate fiber dispersion, web uniformity, and mechanical robustness. At full deployment, the proposed production line would have been capable of producing approximately 650,000 m² of carbon veil annually. This capability remains strategically important, as the United States currently lacks a domestic source of wet-laid nonwoven carbon substrates that satisfy the stringent quality requirements for fuel-cell GDLs and electrolyzers representing an ongoing supply-chain vulnerability. Beyond supply-chain benefits, the project established a robust benchmarking dataset for existing commercial carbon veils while advancing next-generation material concepts targeting improved performance and manufacturing consistency.

Olson, Cynthia Lemay↗

DOE OSTI2024

Adsorption Thermodynamics for Process Simulation

Adsorption has rapidly evolved in recent decades and is an established separation technology extensively practiced in gas separation industries and others. However, rigorous thermodynamic modeling of multicomponent adsorption equilibrium remains elusive, and industrial practitioners rely heavily on expensive and time-consuming trial-and-error pilot studies to develop adsorption units. Here, this article highlights the need for rigorous adsorption thermodynamic models and the limitations and deficiencies of existing models such as the extended Langmuir isotherm, dual-process Langmuir isotherm, and adsorbed solution theory. It further presents a series of recent advances in the generalization of the classical Langmuir isotherm of single-component adsorption by deriving an activity coefficient model to account for the adsorbed phase adsorbate–adsorbent interactions, substituting adsorbed phase adsorbate and vacant site concentrations with activities, and extending to multicomponent competitive adsorption equilibrium, both monolayer and multilayer. Requiring a minimum set of physically meaningful model parameters, the generalized Langmuir isotherm for monolayer adsorption and the generalized Brunauer–Emmett–Teller isotherm for multilayer adsorption address various thermodynamic modeling challenges including adsorbent surface heterogeneity, isosteric enthalpies of adsorption, BET surface areas, adsorbed phase nonideality, adsorption azeotrope formation, and multilayer adsorption. Also discussed is the importance of quality adsorption data that cover sufficient temperature, pressure, and composition ranges for reliable determination of the model parameters to support adsorption process simulation, design, and optimization.

09 BIOMASS FUELS↗

DOE OSTI2026

Elucidating microstructural evolution and hardness variation across friction self-piercing riveted Al-7055 using synchrotron X-ray scattering and advanced microscopy techniques

Friction self-piercing riveting (FSPR) is a unique hybrid joining technique that combines the advantages of mechanical interlocking, frictional heat, and solid-state joining (if metallurgically compatible) to produce crack free joints in high strength and/or low-ductility alloys at room temperature. Here, in the current study, Al-7055 sheets were joined using FSPR for lightweight automotive applications and significant microhardness variations were observed across the joint cross-section. A detailed microstructural characterization at multiple length scales was carried out using advanced electron microscopy and X-ray scattering techniques to provide a fundamental understanding of the process-structure-property relationships. The relative contributions of microstructural characteristics at various length scales (i.e., grain size, dislocation density, solute concentration, precipitate nature) to strengthening were estimated using existent formulations (i.e., Hall-Petch, Taylor, precipitate bypass/shear equations) and correlated to the observed microhardness values across different regions. Small-angle X-ray scattering and scanning transmission electron microscopy revealed significant changes in the size and volume fraction of precipitate species, i.e., GP-I Zones, η′, and Mg/Zn solute co-clusters, depending on the process region. It was observed that the dissolution of the small η′/GP-I zones (T ∼ 150–200 °C) in the heat-affected zone were the key reason for the hardness drop. Further, it was shown that solid-solution, dislocation, grain size and solute co-cluster strengthening played a key role in the thermo-mechanically affected zone and grain-refined zone (GRZ). Finally, these observations were leveraged along with the Zener-Holloman relationship and grain size in the GRZ to estimate the peak joining temperature of the GRZ (∼ 350 °C) near the steel rivet.

aluminum 7xxx alloy↗

DOE OSTI2026

Plan It Together: Optimizing Across Generation, Transmission, Distribution, and Distributed Energy Resources

Integrated planning holds the promise of unlocking lower total system cost solutions by connecting previously siloed planning processes. This article summarizes the state of bulk and local grid planning today and details multiple new analytical approaches that can enable more holistic planning methods to develop comprehensive solutions to generation, transmission, distribution, and distributed energy resource needs. These include both iterative approaches as well as cooptimization techniques. In addition to the benefits of these methods, the technical and institutional challenges and associated solutions are also discussed.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2024

Ion‐Specific Interactions Engender Dynamic and Tailorable Properties in Biomimetic Cationic Polyelectrolytes

Abstract Biomaterials such as spider silk and mussel byssi are fabricated by the dynamic manipulation of intra‐ and intermolecular biopolymer interactions. Organisms modulate solution parameters, such as pH and ion co‐solute concentration, to effect these processes. These biofabrication schemes provide a conceptual framework to develop new dynamic and responsive abiotic soft material systems. Towards these ends, the chemical diversity of readily available ionic compounds offers a broad palette to manipulate the physicochemical properties of polyelectrolytes via ion‐specific interactions. In this study, we show for the first time that the ion‐specific interactions of biomimetic polyelectrolytes engenders a variety of phase separation behaviors, creating dynamic thermal‐ and ion‐responsive soft matter that exhibits a spectrum of physical properties, spanning viscous fluids to viscoelastic and viscoplastic solids. These ion‐dependent characteristics are further rendered general by the merger of lysine and phenylalanine into a single, amphiphilic vinyl monomer. The unprecedented breadth, precision, and dynamicity in the reported ion‐dependent phase behaviors thus introduce a broad array of opportunities for the future development of responsive soft matter; properties that are poised to drive developments in critical areas such as chemical sensing, soft robotics, and additive manufacturing.

Aubrecht, Filip J.↗

DOE OSTI2025

Open‐Air Combustion Synthesis with Rapid Plasma Processing of Large‐Area Transparent Conducting Oxides

A vacuum-free, high-throughput synthesis of indium tin oxide (ITO) via Combustion Oxidation with Rapid Plasma Processing (CORP) utilizes a solution-based exothermic combustion reaction to generate the oxide with tunable control of either amorphous or crystalline phases. A subsequent open-air, forming gas plasma treatment is used to introduce oxygen vacancies and promote crystallization. Here, the evolution of the oxide structure is elucidated by extended X-ray absorption spectroscopy fine structure analysis. Using CORP, fabrication of 300 cm 2 of ITO possessing a champion sheet resistance of 38 Ω sq. −1 , visible transmission of 89%, conductivity stability for over 250 days, roughness < 2nm, and Haacke figure of merit (%T 550nm 10 /R s ) of 0.012 Ω −1 is achieved. Cost modeling of CORP demonstrates up to a 67% reduction in price for TCOs using fully continuous, in-line unit operations compared with vacuum sputtering. The work shows a path toward a low-cost, vacuum-free manufacturing method for TCOs at commercial scales.

42 ENGINEERING↗

DOE OSTI2024

Kernel fusion in atomistic spin dynamics simulations on Nvidia GPUs using tensor core

In atomistic spin dynamics simulations, the time cost of constructing the space- and time-displaced pair correlation function in real space increases quadratically as the number of spins N, leading to significant computational effort. The GEMM subroutine can be adopted to accelerate the calculation of the dynamical spin-spin correlation function, but the computational cost of simulating large spin systems (>40000 spins) on CPUs remains expensive. In this work, we perform the simulation on the graphics processing unit (GPU), a hardware solution widely used as an accelerator for scientific computing and deep learning. Here we show that GPUs can accelerate the simulation up to 25-fold compared to multi-core CPUs when using the GEMM subroutine on both. To hide memory latency, we fuse the element-wise operation into the GEMM kernel using CUTLASS that can improve the performance by 26% ~ 33% compared to implementation based on cuBLAS. Furthermore, we perform the on-the-fly calculation in the epilogue of the GEMM subroutine to avoid saving intermediate results on global memory, which makes the large-scale atomistic spin dynamics simulation feasible and affordable.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

A modeling study of ocean thermal energy conversion resource and potential environmental effects around Kailua-Kona, Hawaii

Ocean Thermal Energy Conversion (OTEC) offers a promising renewable energy solution through a heat exchange process using the temperature difference between warm surface seawater and cold deep seawater. Because accurate resource characterization is critical for the optimal design and implementation of OTEC systems, a high-resolution numerical model is employed to better characterize the OTEC resource at Kona, Hawaii. Our model provides detailed spatial and temporal variability of the thermal gradient, which is essential for assessing the viability and efficiency of OTEC systems. The model results reveal distinct patterns and dynamics not captured by existing observations or models (e.g., lower-resolution information). These findings highlight the importance of using high-resolution models for accurate predictions of thermal gradient variability, ultimately supporting more efficient and sustainable OTEC deployment. Additionally, the study investigates the impacts of mixed water discharge from OTEC plants that can cause shock to organisms living in the surface water and potentially destabilize the water column. Understanding these effects is vital for minimizing any potential negative environmental consequences and ensuring the long-term viability of OTEC operations. Further, our model improves OTEC resource characterization, which can lead to optimal design and deployment of OTEC systems. The analysis of OTEC water discharge impacts can accelerate the development of OTEC technologies, overcoming permitting/consenting challenges. These findings contribute to the broader adoption of high-resolution modeling in ocean energy resource characterization, particularly for OTEC applications.

30 DIRECT ENERGY CONVERSION↗

DOE OSTI2025

Prediction of Redox Potentials for the Late Actinides Cm to Lr Using Electronic Structure Methods

Our previously developed computational method for calculating the aqueous redox potentials of the early actinides has been extended to the later elements in the actinide series: Cm, Bk, Cf, Es, Fm, Md, No, and Lr in multiple oxidation states. These calculations were performed using density functional theory with small-core pseudopotentials and their associated basis sets. Solvation effects were considered via a supermolecule-continuum approach, with 30 water molecules representing two solvation shells. Both the COSMO and SMD implicit solvation models were utilized. The structural parameters and hydration numbers for Cm(III), Bk(III), Bk(IV), and Cf(III) are in reasonable agreement with the available experimental data. For redox processes involving atomic cations in solution, the B3LYP/COSMO approach predicted redox potentials to within ±0.2 V of experiment for most redox couples, consistent with our prior work. Inclusion of spin-orbit corrections in specific redox pairs, especially those with the later actinides in high oxidation states, yields improved results relative to calculations including only scalar-relativistic corrections. The An +m /An(0) redox potentials were calculated using a Born-Haber cycle incorporating sublimation, ionization, and hydration energies. Due to a lack of experimental data, three sets of ionization energies were used for the Born-Haber cycle. The calculated An(III/0) potentials showed better agreement with experimental data when using the COSMO solvation model and the test set comprising the NIST recommended ionization energies. Furthermore, the Md(II/0) potential was better described with the SMD model, whereas No(II/0) was not well described by all methods. Finally, the computational approach was able to predict redox potentials that for most cases agreed with the current available experimental or estimated data.

Actinides↗

DOE OSTI2024

Ensemble Simulations on Leadership Computing Systems

Scientific productivity can be enhanced through workflow management tools, relieving large High Performance Computing (HPC) system users from the tedious tasks of scheduling and designing the complex computational execution of scientific applications. This paper presents a study on the usage of ensemble workflow tools to accelerate science using the Summit and Frontier supercomputing systems. The research aims to connect science domain simulations using Oak Ridge Leadership Computing Facility (OLCF) supercomputing platforms with ensemble workflow methods in order to accelerate HPC-enabled discovery and boost scientific impact. We present the coupling, porting and optimization of Radical-Cybertools on three applications: Chroma, NAMD and LAMMPS. The tools augment traditional HPC monolithic runs with a pilot scheduler. Lessons-learned are discussed for physics, biology and materials science applications. We discuss intrinsic limitations of coupling and porting ensemble workflow tools to applications that run on large HPC systems. The origins of technical challenges and their solutions developed during the implementation process are discussed. Data management strategies, OLCF’s policies for ensembles, and natively supported workflow tools are also summarized.

Georgiadou, Antigoni [ORNL] (ORCID:000000020977631↗

DOE OSTI2026

Salt supplementation-induced metabolic reprogramming in Streptomyces coelicolor

Members of the genus Streptomyces are major producers of a wide variety of secondary metabolites that serve as bioactive compounds. Many secondary metabolites are produced in response to environmental signals such as biotic and abiotic stresses. In this study, we identified salt supplementation as one of the stimuli activating secondary metabolism in the model Streptomyces species, Streptomyces coelicolor. Comparative metabolomics revealed overproduction of several known secondary metabolites, most notably undecylprodigiosin and coelimycin P1, in addition to their biosynthetic intermediates and derivatives, as well as many unknown metabolites. Transcriptomic analysis revealed activation of diverse biological processes including cation uptake, compatible solute production, and the phosphate limitation stress response through conserved and species-specific mechanisms, presumably to overcome the increased salinity. This response leads to activation of a variety of regulatory and metabolic pathways required for production of secondary metabolites including activation of conserved metabolic pathways for energy and substrate supply and species-specific secondary metabolite biosynthetic gene clusters. Furthermore, several promoter sequences contributing to upregulation of secondary metabolism induced by salt supplementation were identified. Overall, our data show how S. coelicolor copes with the increased salinity and tailors the cellular metabolism toward secondary metabolism in a conserved and species-specific manner.

Otani, Hiroshi [USDOE Joint Genome Institute (JGI)↗

DOE OSTI2024

Implementation and (Inverse Modified) Error Analysis for Implicitly Templated ODE-Nets

We focus on learning unknown dynamics from data using ODE-nets templated on implicit numerical initial value problem solvers. First, we perform inverse modified error analysis of the ODE-nets using unrolled implicit schemes for ease of interpretation. It is shown that training an ODE-net using an unrolled implicit scheme returns a close approximation of an inverse modified differential equation (IMDE). In addition, we establish a theoretical basis for hyperparameter selection when training such ODE-nets, whereas current strategies usually treat numerical integration of ODE-nets as a black box. We thus formulate an adaptive algorithm which monitors the level of error and adapts the number of (unrolled) implicit solution iterations during the training process, so that the error of the unrolled approximation is less than the current learning loss. This helps accelerate training while maintaining accuracy. Several numerical experiments are performed to demonstrate the advantages of the proposed algorithm compared to nonadaptive unrollings and validate the theoretical analysis. Here, we also note that this approach naturally allows for incorporating partially known physical terms in the equations, giving rise to what is termed “gray box” identification.

ODE-nets↗