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At least 91 records · Page 5

Effect of Si Content on Extreme Fast Charging Behavior in Silicon–Graphite Composite Anodes

Commercial Li-ion batteries typically incorporate a small amount of high-capacity silicon (Si)-based materials in the composite graphite-based anode to increase the energy density of the battery. However, very little is known about the effects of Si on the fast-charging behavior of composite anodes. Herein, we examine the effects of the Si/graphite ratio in the composite anode on the fast-charging behavior of full cells. We show that addition of Si increases the rate capability from 1C to 8C and improves the capacity retention in early cycles at 6C due to reduced overpotential in constant current charging cycles. The impacts of Si content on fast-charging aging were identified by Post-Test characterization. Despite realizing benefits of available capacity and reduced Li plating at 6C, silicon–electrolyte interactions lead the time-dependent cell performance to fade quickly in the long term. The Post-Test analysis also revealed the thickening of the electrode and nonuniform distribution of electrolyte decomposition products on the Si-containing anodes, as well as the organic-rich solid electrolyte interphase (SEI), which are the factors behind cell degradation. Our study sheds insight on the advantages and disadvantages of Si/graphite composite anodes when they are used in fast-charging applications and guides further research in the area by designing an optimized composition of Si incorporated in a mature graphite matrix.

25 ENERGY STORAGE↗

A compact dication source for Ba 2+ tagging and heavy metal ion sensor development

Here, we present a tunable metal ion beam that delivers controllable ion currents in the picoamp range for testing of dry-phase ion sensors. Ion beams are formed by sequential atomic evaporation and single or multiple electron impact ionization, followed by acceleration into a sensing region. Controllability of the ionic charge state is achieved through tuning of electrode potentials that influence the retention time in the ionization region. Barium, lead, and cadmium samples have been used to test the system, with ion currents identified and quantified using a quadrupole mass analyzer. Realization of a clean Ba 2+ ion beam within a bench-top system represents an important technical advance toward the development and characterization of barium tagging systems for neutrinoless double beta decay searches in xenon gas. This system also provides a testbed for investigation of novel ion sensing methodologies for environmental assay applications, with dication beams of Pb 2+ and Cd 2+ also demonstrated for this purpose.

47 OTHER INSTRUMENTATION↗

Lepidocrocite Titanate–Graphene Composites for Sodium-Ion Batteries

To overcome electronic transport issues of layered titanates in sodium-ion batteries, we have designed and synthesized composites of lepidocrocite titanates with reduced graphene oxide through a solution-based self-assembly approach. The parent lepidocrocite titanate (K 0.8 [Ti 1.73 Li 0.27 ]O 4 ) was exfoliated by a soft-chemical approach and mechanical shaking. Exfoliated layered titania sheets (LTO) were then combined with reduced graphene oxide (rGO) layers to assemble into composites through flocculation. Countercations (i.e., Mg 2+ ) were used for the self-assembly of negatively charged titania and rGO nanosheets via flocculation. The carbon content in the composites was tuned from 1 to 17% by changing the ratio of titania and rGO sheets in the mixed colloidal suspensions. Electrodes were processed with as-prepared LTO-rGO composites without any carbon additives and tested in sodium half-cell configurations. Mg + -coagulated LTO-rGO composite electrodes deliver higher capacities than electrodes prepared with coagulated titania sheets and 10% acetylene black in sodium half-cells and display good capacity retention after 50 cycles. Electrochemical impedance spectroscopy results indicate lower charge transfer resistance for LTO-14.5%rGO composites than that of coagulated titania sheets with 10% acetylene black. A power law analysis of cells containing the composites indicate a hybrid mechanism consisting of both surface and diffusional processes. A comparison with a similar system, that of dopamine-derived LTO-C heterostructures, reveal significant differences. While capacities showed a strong dependence on carbon content for the dopamine-derived materials, this was not true for the LTO-rGO composites. Instead, the highest capacity was obtained for the 14.5% rGO sample, with a lower value obtained for the 17% rGO sample. A greater proportion of the redox processes were surface rather than diffusional in nature for the LTO-rGO composites as well.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Enhanced fatigue and retention in ferroelectric thin film memory capacitors by post-top electrode anneal treatment

Thin film ferroelectric capacitors comprising a ferroelectric film sandwiched between electrodes for nonvolatile memory operations are rendered more stable by subjecting the capacitors to an anneal following deposition of the top electrode. The anneal is done so as to form the interface between the ferroelectric film and the top electrode. Heating in an air oven, laser annealing, or electron bombardment may be used to form the interface. Heating in an air oven is done at a temperature at least equal to the crystallization temperature of the ferroelectric film. Where the ferroelectric film comprises lead zirconate titanate, annealing is done at about 550 to 600 C for about 10 to 15 minutes. The formation treatment reduces the magnitude of charge associated with the nonswitching pulse in the thin film ferroelectric capacitors. Reduction of this charge leads to significantly more stable nonvolatile memory operations in both digital and analog memory devices. The formation treatment also reduces the ratio of change of the charge associated with the nonswitching pulse as a function of retention time. These improved memory devices exhibit greater performance in retention and reduced fatigue in memory arrays.

Thakoor, Sarita↗

Layered oxide cathode-inspired secondary hard carbon microsphere anode material for high-power and long-life rechargeable batteries

A new anode material that will provide lithium ion (Li-ion) batteries with high energy and power density is urgently needed. In this work, a layered oxide cathode-inspired secondary hard carbon microsphere (CMS) anode material was designed, and exhibited excellent rate performance and long cyclability. Polyacrylonitrile/poly(styrene-co-acrylonitrile) (PAN/SAN) compositions displaying the meatball-like shape of the PAN precursor were carbonized into CMSs having turbostratic microstructures. The CMS carbonized at 1,000°C (CMS1000) displayed high specific capacity at the highest current density of 1,000mAg -1 , i.e., 77.6 % of its average charge capacity at 100 mA g -1 , and considerable cycling retention after 500 cycles, i.e., 83.8 % of the specific capacity at cycle 25. In conclusion, our work demonstrates that the design of new anode materials is a fruitful route to improve commercial Li-ion batteries.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Nanoscale Compositional Mapping of Commercial LiNi 0.8 Co 0.15 Al 0.05 O 2 Cathodes Using Atom Probe Tomography

Nickel-rich cathodes provide improved specific capacity that lead to higher gravimetric energy density, critical for electric vehicles. However, poor long-term capacity retention at elevated temperatures/high C-rates (the rate of charge and discharge on a battery) stem from material issues: surface phase changes, corrosive side reactions with the electrolyte, ion dissolution and propagation of cracks. Introducing dopants, developing nanoscale surface coatings and graded core-shell structures have all improved the electrochemical performance of nickel-rich cathodes. However, a material level understanding on the effect of Li composition and distribution in Ni-rich cathodes is limited, due to a lack of characterization methods available that can directly image Li at the nanoscale. Hence, it is critical to establish methods such as atom probe tomography (APT), having both nanometer scale spatial resolution and high compositional sensitivity to quantitatively analyze battery cathodes. To fully realize its potential as a method for quantitative compositional analysis of commercial Li-ion batteries, we provide a comprehensive description of the challenges in sample preparation and analyze the dependency of the analysis parameters, specifically laser pulse energy on the measured stoichiometry of elements in a high Ni content cathode material; LiNi 0.8 Co 0.15 Al 0.05 O 2 (NCA). In this work, our findings show the stoichiometry variations cannot be explained by charge state ratios or Ga implantation damage alone during FIB preparation, indicating that additional factors such as crystallographic orientation may need to be considered to achieve quantitative nanoscale compositional analysis of such battery cathodes using APT.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Revealing key structures for reversible sulfur redox in amorphous polymeric sulfur

Amorphous polymeric sulfur cathodes, such as sulfurized polyacrylonitrile (SPAN), enable high-energy lithium-sulfur batteries without cobalt or nickel, leveraging abundant sulfur. However, the limited in situ understanding of their synthesis and electrochemistry has impeded targeted optimization. Here, in this study, we integrate operando high-energy total scattering with sulfur K-edge X-ray absorption spectroscopy to monitor SPAN's formation and cycling in real time. Our results show that S-C bond formation halts further fusion of cyclized polyacrylonitrile, fostering π-π stacking and a transition from long-chain to short-chain sulfur-critical for reversible sulfur redox. These features synergistically minimize polysulfide dissolution and charge-transfer resistance, enabling optimized SPAN to achieve high capacity retention over 1,000 cycles. Operando X-ray absorption spectroscopy reveals that residual protons drive thiol-thione tautomerism, with lithium replacement during the first discharge causing ~20% irreversible capacity loss. To enhance performance, minimizing -NH groups and expanding pyridine networks are key. These findings transform SPAN optimization from empirical tuning to mechanism‑guided engineering and point the way towards sulfur loadings and energy densities competitive with state‑of‑the‑art Li‑ion cathodes.

25 ENERGY STORAGE↗

The role of oxygen in automotive grade lithium-ion battery cathodes: an atomistic survey of ageing

The rising demand for high-performance lithium-ion batteries, pivotal to electric transportation, hinges on key materials like the Ni-rich layered oxide LiNi x Co y Al z O 2 (NCA) used in cathodes. The present study investigates the redox mechanisms, with particular focus on the role of oxygen in commercial NCA electrodes, both fresh and aged under various conditions (aged cells have performed >900 cycles until a cathode capacity retention of ~80%). Our findings reveal that oxygen participates in charge compensation during NCA delithiation, both through changes in transition metal (TM)–O bond hybridization and formation of partially reversible O 2 , the latter occurs already below 3.8 V vs. Li/Li + . Aged NCA material undergoes more significant changes in TM–O bond hybridization when cycling above 50% SoC, while reversible O 2 formation is maintained. Nickel is found to be redox active throughout the entire delithiation and shows a more classical oxidation state change during cycling with smaller changes in the Ni–O hybridization. By contrast, Co redox activity relies on a stronger change in Co–O hybridization, with only smaller Co oxidation state changes. The Ni–O bond displays an almost twice as large change in its bond length on cycling as the Co–O bond. The Ni–O 6 octahedra are similar in size to the Co–O 6 octahedra in the delithiated state, but are larger in the lithiated state, a size difference that increases with battery ageing. These contrasting redox activities are reflected directly in structural changes. The NCA material exhibits the formation of nanopores upon ageing, and a possible connection to oxygen redox activity is discussed. The difference in interaction of Ni and Co with oxygen provides a key understanding of the mechanism and the electrochemical instability of Ni-rich layered transition metal oxide electrodes. Our research specifically highlights the significance of the role of oxygen in the electrochemical performance of electric-vehicle-grade NCA electrodes, offering important insights for the creation of next-generation long-lived lithium-ion batteries.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Enhanced fatigue and retention in ferroelectric thin film memory capacitors by post-top electrode anneal treatment

Thin film ferroelectric capacitors (10) comprising a ferroelectric film (18) sandwiched between electrodes (16 and 20) for nonvolatile memory operations are rendered more stable by subjecting the capacitors to an anneal following deposition of the top electrode (20). The anneal is done so as to form the interface (22) between the ferroelectric film and the top electrode. Heating in an air oven, laser annealing, or electron bombardment may be used to form the interface. Heating in an air oven is done at a temperature at least equal to the crystallization temperature of the ferroelectric film. Where the ferroelectric film comprises lead zirconate titanate, annealing is done at about 550.degree. to 600.degree. C. for about 10 to 15 minutes. The formation treatment reduces the magnitude of charge associated with the non-switching pulse in the thin film ferroelectric capacitors. Reduction of this charge leads to significantly more stable nonvolatile memory operations in both digital and analog memory devices. The formation treatment also reduces the ratio of change of the charge associated with the non-switching pulse as a function of retention time. These improved memory devices exhibit greater performance in retention and reduced fatigue in memory arrays.

Thakoor, Sarita↗

Bilayer hybrid graphite anodes via freeze tape casting for extreme fast charging applications

Extreme fast charging (XFC) of lithium-ion batteries is critical for continuous market adoption of electric vehicles. However, mass transport limitations and sluggish kinetics lead to lithium plating in graphite anodes under fast charging conditions. One approach to address the mass transport limitation in graphite is to design low-tortuosity electrodes to enhance ionic transport. In this study, a bilayer hybrid structured electrode with directionally aligned channels was developed via freeze tape casting, which enables faster lithium ion diffusion through the graphite electrode. A scalable roll-to-roll process was designed in which slurry can be cast on any substrates for simple processing. Additionally, electrochemical impedance spectroscopy measurements indicated that the bilayer hybrid coating had both low tortuosity and short diffusion pathways, enabling XFC charging. Rate testing for the bilayer hybrid electrode indicated superior performance over the other coatings, exhibiting a ~20% improvement in the charge capacity compared with the conventional coating at 5C and 10 min total charging time. The bilayer hybrid electrode also demonstrated a 10% improvement in capacity retention compared with the conventional electrode after 1000 cycles at XFC conditions. This study demonstrates freeze tape casting as a scalable way to fabricate low-tortuosity electrodes for XFC applications.

25 ENERGY STORAGE↗

Enhanced cycling stability of Ni-rich Li-metal cells enabled by dual vinylene carbonate and tris(trimethylsilyl)borate electrolyte additives

NMC811 (LiNi 0.8 Co 0.1 Mn 0.1 O 2 ) and other high-Ni chemistries are promising cathode candidates for high-performance electric vehicles, owing to their high energy density and reduced cobalt content. However, their long-term cycling stability is hindered by surface degradation, particularly when paired with conventional electrolytes and a lithium metal anode. Electrolyte additives represent a practical approach to enhance interfacial stability and improve overall battery performance by promoting the formation of a robust electrolyte–electrode interphase (EEI). In this study, we revisit the effects of vinylene carbonate (VC) and tris(trimethylsilyl)borate (TMSB) additives on single-crystal SC-NMC811||Li cells. While TMSB only increases the open-circuit voltage and initial overpotential, it delivers superior capacity retention at C/3 compared to cells containing only VC or a dual additive system (VC and TMSB). Notably, under fast-charging conditions (1C, 2C, and 5C), the dual-additive system significantly outperforms other formulations, achieving markedly enhanced long-term capacity retention. Comprehensive electrochemical and spectroscopic analyses reveal that the VC/TMSB dual-additive system suppresses surface transition in NMC811, mitigates structural degradation by forming a thin, LiF-deficient cathode-electrolyte interface (CEI) layer. Moreover, they promote smooth and dense Li deposition and generate a LiF-deficient solid-electrolyte interphase (SEI). Consequently, the synergistic stabilization of both the CEI and SEI effectively limits the overall cell impedance growth during extended cycling. These findings provide key insights into co-additive strategies for engineering stable interfaces in high-energy Ni-rich Li-metal batteries.

36 MATERIALS SCIENCE↗

High-Entropy and Superstructure-Stabilized Layered Oxide Cathodes for Sodium-Ion Batteries

Layered transition metal oxides are appealing cathodes for sodium-ion batteries due to their overall advantages in energy density and cost. But their stabilities are usually compromised by the complicated phase transition and the oxygen redox, particularly when operating at high voltages, leading to poor structural stability and substantial capacity loss. Here, in this study, an integrated strategy combing the high-entropy design with the superlattice-stabilization to extend the cycle life and enhance the rate capability of layered cathodes is reported. It is shown that the as-prepared high-entropy Na 2/3 Li 1/6 Fe 1/6 Co 1/6 Ni 1/6 Mn 1/3 O 2 cathode enables a superlattice structure with Li/transition metal ordering and delivers excellent electrochemical performance that is not affected by the presence of phase transition and oxygen redox. It achieves a high reversible capacity (171.2 mAh g –1 at 0.1 C), a high energy density (531 Wh kg –1 ), extended cycling stability (89.3% capacity retention at 1 C for 90 cycles and 63.7% capacity retention at 5 C after 300 cycles), and excellent fast-charging capability (78 mAh g –1 at 10 C). This strategy would inspire more rational designs that can be leveraged to improve the reliability of layered cathodes for secondary-ion batteries.

25 ENERGY STORAGE↗

Deciphering Chemical/Electrochemical Compatibility of Li 3 InCl 6 in 5.2 V High-Voltage LiCoO 2 All-Solid-State Batteries

Large interfacial resistance is a widely recognized impediment to the advancement of high-voltage, all-solid-state batteries. However, a comprehensive understanding of the fundamental cause behind the interfacial resistance between solid electrolytes and typical layered oxide cathodes has not yet been achieved. Here, we investigated the high-voltage stability of Li 3 InCl 6 and elucidated the underlying interfacial electrochemical reactions between LiCoO 2 and Li 3 InCl 6 . Further, the pairing of Li 3 InCl 6 with LiCoO 2 exhibited a superior capacity retention of 73.6% even at 5.2 V, much higher than 28.2% charged at 4.6 V in lithium-ion batteries after 70 cycles. The enhanced high-voltage stability of ASSBs is attributed to the stable interface formed between LiCoO 2 and Li 3 InCl 6 and the reinforced surface and bulk structure stability. On the other hand, the ultrahigh voltage still causes the partial decomposition of Li 3 InCl 6 and generates interfacial compounds such as InClO and cobalt and indium chlorides/oxides.

25 ENERGY STORAGE↗

Enabling 6C Fast Charging of Li–Ion Batteries with Graphite/Hard Carbon Hybrid Anodes

Li-ion batteries that can simultaneously achieve high-energy density and fast charging are essential for electric vehicles. Graphite anodes enable a high-energy density, but suffer from an inhomogeneous reaction current and irreversible Li plating during fast charging. In contrast, hard carbon exhibits superior rate performance but lower energy density owing to its lower initial coulombic efficiency and higher average voltage. In this work, these tradeoffs are overcome by fabricating hybrid anodes with uniform mixtures of graphite and hard carbon, using industrially-relevant multi-layer pouch cells (>1 Ah) and electrode loadings (3 mAh cm –2 ). By controlling the graphite/hard carbon ratio, this study shows that battery performance can be systematically tuned to achieve both high-energy density and efficient fast charging. Pouch cells with optimized hybrid anodes retain 87% and 82% of their initial specific energy after 500 cycles of 4C and 6C fast-charge cycling, respectively. This is significantly higher than the 61% and 48% specific energy retention with graphite anodes under the same conditions. The enhanced performance is attributed to improved homogeneity of the reaction current throughout the hybrid anode, which is supported by continuum-scale modeling. Furthermore, this process is directly compatible with existing roll-to-roll battery manufacturing, representing a scalable pathway to fast charging.

25 ENERGY STORAGE↗

Jumpstart Opportunities to Unleash Leadership in Energy Storage (JOULES)

Current-generation Li-ion batteries with cobalt- and nickel-containing cathodes and graphite anodes are approaching performance and cost limits. In this program, 24M Technologies, Inc. (24M) is teaming with the Massachusetts Institute of Technology (MIT) and University of Michigan (UM) to develop low cost and fast charging sodium metal batteries with good low-temperature performance and high energy density, building upon previous work performed under ARPA-E programs. Key achievements include optimization of solid electrolyte and anode current collector, optimized cathode active materials, development of high-performance electrolyte formulations, and integration of these components into full cells. The cell design incorporates (1) an ultra-thick cathode (>9 mAh/cm 2 ) comprising advanced cobalt-free, sodium cathode active material, (2) advanced fast-charging electrolyte (up to 12 mS/cm) developed using machine learning and automated high-throughput screening technology by UM, and (3) ceramic modified separator that enable smooth Na transport and deposition, developed at MIT, enabling a high-energy density anode-free configuration and maximizing the energy density of sodium batteries. The team has successfully combined these approaches to sodium chemistry and paved the way to meeting the fast-charging, high-energy density, and low-cost requirements of next-generation drone, electric vertical take-off and -landing, and electric vehicle batteries. Performance for anode-free sodium cells developed under this program is more powerful than the commercial Li-ion batteries. The final deliverable cell design has achieved over 300 Wh/kg and volumetric energy density above 800 Wh/L (Table 1). Additionally, the team has achieved over (1) a lifetime of 340 cycles, (2) 80% capacity retention at -20 °C (compared 25 °C), and (3) the ability to fast charge to 80% SOC in 20 minutes.

25 ENERGY STORAGE↗

A Comprehensive Experimental Study on Microstructure‐Graded Graphite Anodes for Enhancing Fast‐Charging Capability of Lithium‐Ion Batteries

Lithium‐ion batteries with high gravimetric capacity density and improved cycle life performance under fast‐charging conditions are crucial for widespread electric vehicle (EV) adoption. This study investigates how designing graphite anode microstructure, specifically porosity, and particle‐size gradients, improves lithium‐ion (Li + ) transport during fast‐charging conditions. Three‐layered graphite anodes with varying porosity (24%, 36%, 46%) and particle size gradients (3, 5, 10 μm) were compared to a conventional single‐layered electrode in half‐cell configurations. At room temperature and high discharge rate (2C), both gradient structures showed significantly enhanced capacity retention (80% and 67% vs. 50%) compared to the conventional electrode, highlighting the effectiveness of microstructure engineering for fast charging. The study also investigated the temperature's impact on cycle life. After 200 cycles at 2°C and 45°C, all gradient structures demonstrated superior capacity retention (≈80%) compared to the conventional electrode (35%), suggesting the gradients mitigate degradation rate at high temperatures. Electrochemical impedance spectroscopy confirmed superior Li+ diffusion and lower resistivity in gradient electrodes. Simulations explored the influence of gradient profiles on reaction kinetics across the electrode thickness. Overall, this research demonstrates that the fast‐charging capability of graphite electrodes can be greatly enhanced by engineering the electrode microstructure, thereby making EV technology more accessible and appealing.

Ahmadi, Soma↗

Ion Pair Uptake in Ion Gel Devices Based on Organic Mixed Ionic–Electronic Conductors

Abstract In organic mixed ionic–electronic conductors (OMIECs), it is critical to understand the motion of ions in the electrolyte and OMIEC. Generally, the focus is on the movement of net charge during gating, and the motion of neutral anion–cation pairs is seldom considered. Uptake of mobile ion pairs by the semiconductor before electrochemical gating (passive uptake) can be advantageous as this can improve device speed, and both ions can participate in charge compensation during gating. Here, such passive ion pair uptake in high‐speed solid‐state devices is demonstrated using an ion gel electrolyte. This is compared to a polymerized ionic liquid (PIL) electrolyte to understand how ion pair uptake affects device characteristics. Using X‐ray photoelectron spectroscopy, the passive uptake of ion pairs from the ion gel into the OMIEC is detected, whereas no uptake is observed with a PIL electrolyte. This is corroborated by X‐ray scattering, which reveals morphological changes to the OMIEC from the uptake of ion pairs. With in situ Raman, a reorganization of both anions and cations is then observed during gating. Finally, the speed and retention of OMIEC‐based neuromorphic devices are tuned by controlling the freedom of charge motion in the electrolyte.

Quill, Tyler J.↗

A computational pipeline to generate a synthetic dataset of metal ion sorption to oxides for AI/ML exploration

The charged mineral/electrolyte interfaces are ubiquitous in the surface and subsurface–including the surroundings of the geological disposal sites for radioactive waste. Therefore, understanding how ions interact with charged surfaces is critically important for predicting radionuclide mobility in the case of waste leakage. At present, the Surface Complexation Models (SCMs) are the most successful thermodynamic frameworks to describe ion retention by mineral surfaces. SCMs are interfacial speciation models that account for the effect of the electric field generated by charged surfaces on sorption equilibria. These models have been successfully used to analyze and interpret a broad range of experimental observations including potentiometric and electrokinetic titrations or spectroscopy. Unfortunately, many of the current procedures to solve and fit SCM to experimental data are not optimal, which leads to a non-transferable or non-unique description of interfacial electrostatics and consequently of the strength and extent of ion retention by mineral surfaces. Recent developments in Artificial Intelligence (AI) offer a new avenue to replace SCM solvers and fitting algorithms with trained AI surrogates. Unfortunately, there is a lack of a standardized dataset covering a wide range of SCM parameter values available for AI exploration and training–a gap filled by this study. Here, we described the computational pipeline to generate synthetic SCM data and discussed approaches to transform this dataset into AI-learnable input. First, we used this pipeline to generate a synthetic dataset of electrostatic properties for a broad range of the prototypical oxide/electrolyte interfaces. The next step is to extend this dataset to include complex radionuclide sorption and complexation, and finally, to provide trained AI architectures able to infer SCMs parameter values rapidly from experimental data. Here, we illustrated the AI-surrogate development using the ensemble learning algorithms, such as Random Forest and Gradient Boosting. These surrogate models allow a rapid prediction of the SCM model parameters, do not rely on an initial guess, and guarantee convergence in all cases.

Li, Chunhui↗