Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Separators”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Predicting Liquid–Liquid Phase Separation of Submicrometer Proxies for Atmospheric Secondary Aerosol

Liquid–liquid phase separation (LLPS) of atmospheric aerosols can significantly impact climate, air quality, and human health. However, their complex composition, small size, and history-dependent properties result in great uncertainty in the modeling of aerosol phase state and atmospheric processes. Herein, using cryogenic transmission electron microscopy (cryo-TEM), we examined model submicron aerosols composed of organic compounds and ammonium sulfate, and established a parameterization for the separation relative humidity (SRH) that accounts for chemical composition, particle size, and equilibration time. We evaluated different variables that describe chemical composition: O/C ratio, partition coefficient, solubility, molar mass, and polarizability. The O/C ratio fits the SRH of micrometer droplets best, and by using a scaling factor to translate the micrometer SRH parameterization to submicron aerosols, we incorporate the effects of size and equilibration time. The measured scaling factor for the submicron mean SRH (30nm – 1μm, 20 min equilibration times) is 0.80, the factor becomes 1 with equilibration time over 1 hour, and is equal to 0, meaning that SRH is absent, when the aerosol dry diameter is smaller than 30 nm. Furthermore, our parameterization will aid in universal SRH modeling, potentially leading to more accurate predictions of aerosol mass, optical properties, hygroscopicity, and heterogeneous chemistry.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Cost‐Effective and Scalable Approach for the Separation and Direct Cathode Recovery from End‐of‐Life Li‐Ion Batteries

Li-ion battery recycling presents a promising opportunity to decrease dependence on foreign sources of materials and harvest precious materials within the United States. Herein, a superior complete direct recycling process on individual end-of-life cells is reported where the recovered high-purity cathode active material, as well as electrolyte salt Li hexafluorophosphate (LiPF 6 ) can be reused without significant processing. This new process utilizes a series of mechanical separation steps that enable the separation of the cathode and anode active materials while they are still attached to their current collectors. Using this type of process can significantly reduce metal contamination and enable a clean cathode that can be directly recycled. The process if implemented commercially can greatly reduce the environmental burden of batteries as the greenhouse gas emissions of 8.25 kg CO 2 e kg −1 from the direct recycling process are 64% lower compared to those from virgin production of cathode material. During electrochemical testing of the recovered LiNi 0.6 Mn 0.2 Co 0.2 O 2 a discharge capacity of ≈160 mAh g −1 and good cyclability of over 250 cycles at 0.33C are achieved. This success paves a new pathway to explore and optimize existing Li-ion battery recycling procedures.

electrolyte reuse↗
DOE OSTI2026

Fluorinated ionic liquids as gas chromatographic stationary phases for the separation of volatile per- and polyfluoroalkyl substances

Background Here, the production of fluorinated organic compounds in the manufacturing, semiconductor, and pharmaceutical industries has increased exponentially over the past decade. This rapid growth has created an urgent need for efficient chromatographic platforms capable of selectively separating these compounds from complex mixtures, not only to support industrial quality control and waste management practices, but also to enable reliable environmental monitoring of volatile fluorinated contaminants. Conventional GC stationary phases lack the fluorophilic interactions needed for highly fluorinated analytes. Consequently, there is a clear demand for specialized stationary phases designed to improve chromatographic retention and selectivity for these compounds. Results Three stationary phases composed of fluorinated ionic liquids (ILs) with varied extent of fluorination were prepared to study fluorophilic interactions with fluorinated/non-fluorinated probe molecules by gas chromatography (GC). IL stationary phases featuring linear and branched perfluoroalkyl moieties, as well as a branched alkyl moiety, were systematically investigated. Chromatographic performance was examined using fluorinated compounds and their hydrocarbon analogs, including CF 3 -substituted aromatics, aliphatic alcohols, fluorotelomer alcohols (FTOHs), and perfluoroalkenes. Measurements on 5 m and 20 m columns revealed that the IL possessing branched alkyl provided stronger dispersive and hydrogen bonding interactions toward non-fluorinated aromatic and long-chain alcohols, whereas the fluorinated ILs enhanced retention of highly fluorinated FTOHs and perfluorodecene. Comprehensive two-dimensional GC (GC × GC), using a nonpolar primary column coupled with secondary columns featuring cross-bonded poly(trifluoropropylmethyl siloxane) (Rtx-200 ms), the branched fluorinated IL, or the branched non-fluorinated IL, highlighted complementary selectivity with the branched fluorinated IL providing the strongest interactions with fluorinated analytes. Significance These results demonstrate that fluorinated IL stationary phases are promising alternatives to conventional polysiloxane stationary phases for improving the separation of per- and polyfluoroalkyl substances and related fluorinated compounds. By correlating IL structure with fluorophilic interactions, this work establishes design principles for GC stationary phases that enable enhanced selectivity for highly fluorinated analytes while maintaining complementary interactions with non-fluorinated compounds.

Comprehensive two-dimensional GC↗
DOE OSTI2024

The production and separation of 161 Tb with high specific activity at the University of Utah

Targeted radiotherapy (TRT) is an increasingly prominent area of research in nuclear medicine, particularly in the context of treating cancerous tumors. One radionuclide of considerable interest for TRT is terbium-161 (t 1/2 = 6.95 days), which undergoes beta emission and shares similar decay properties as 177 Lu (FDA-approved as LUTATHERA® and PLUVICTO®). Besides beta emission, 161 Tb also emits a significant number of conversion and Auger electrons further enhancing its therapeutic potential. Terbium-161 can be produced using nuclear reactors through an indirect neutron capture reaction, $^{160}_{64}$Gd(n,γ) $^{161}_{64}$Gd → (3.7 min, β – ) $^{161}_{65}$Tb, from 160 Gd targets. However, a key challenge in utilizing 161 Tb for TRT lies in effectively separating target and product materials to attain high specific activity for radiolabeling. Here, we detail the production of no-carrier added 161 Tb using low flux research reactors (mean thermal (< 0.625 eV) neutron flux: 1.356 ×10 12 n • cm –2 • s –1 ) like the University of Utah TRIGA Reactor, using enriched 160 Gd 2 O 3 targets (1.5 ± 0.3 µCi of 161 Tb per mg of 160 Gd target per hour of irradiation). We also developed a separation technique based on cation exchange and extraction chromatography, suitable for mCi level irradiations with targets exceeding 200 milligrams. In a simulated full-scale irradiation, 161 Tb was successfully isolated from large mass targets using cation exchange (AG 50W-X8, with 2-hydroxyisobutyric acid at 70 mM, pH 4.75) and extraction chromatography (LN Resin, 0.5 – 0.75 M HNO 3 ) methods. Here, this resulted in high apparent molar activities of [ 161 Tb]Tb-DOTA (113 ± 3 MBq/nmol), demonstrating high purity 161 Tb relevant for potential future preclinical applications.

161Tb↗
DOE OSTI2024

A sustainable cobalt separation with validation by techno-economic analysis and life-cycle assessment

Sustainable, cost-effective cobalt/nickel separations chemistry contributes to the realization of economically competitive lithium-ion battery recycling, as well as primary mining of cobalt and nickel. Such improvements can address supply chain challenges for cobalt, a critical element. Herein, we disclose a simple method for separating Co/Ni by second coordination-sphere molecular recognition. Selective cobalt precipitation is achieved using carbonate ions in an ammonia solution due to the outer-sphere, hydrogen bonding interactions between [Co(NH 3 ) 6 ] 3+ and CO 3 2− , evaluated with density functional theory calculations. We demonstrate this method on mixtures of Co/Ni chlorides comprising a 10-fold excess of Ni and provide comparisons with ore-processing systems. High purities (99.4(3)% Co; 98.2(4)% Ni) and recoveries (77(8)% Co; ∼100% Ni) were observed for both Co- and Ni-enriched products using optimized conditions. In conclusion, this method is potentially economically competitive based on initial techno-economic analysis (TEA) and life-cycle assessment (LCA) that also illustrate advantages in terms of sustainability.

cobalt↗
DOE OSTI2026

Evaluation of chromatographic resins for high efficacy separation of radium from chemical analogues

The separation of Radium (Ra) from interfering chemical analogues is of major importance for both the accurate measurement of Ra-226 in environmental samples and the preparation of radium targets destined for medical isotope production. The adsorption behavior of Ra, Barium (Ba), and Strontium (Sr) was investigated on multiple crown-ether-based proprietary extraction chromatographic resins developed by TrisKem Int. Among these, the TK101 resin, characterized by a novel room-temperature ionic liquid (RTIL) dual extractant–solvent system, demonstrated enhanced affinity and selectivity, particularly at low acid concentrations, achieving a D w of 3477 ± 73 for Ra in 0.04 M HNO₃, whereas the maximum Ra D w obtained with the traditional Sr resin in 8 M HNO 3 was only 12.33 ± 0.4. In 0.04 M HNO 3 , a Ra distribution ratio (D w ) of 776 was achieved within 1 min, indicating rapid uptake kinetics. The adsorption capacities were estimated at 19.6 ± 0.1 mg/g for Ba and 12.0 ± 0.2 mg/g for Sr. However, competing alkali metals significantly reduced alkaline earth metal uptake, indicating that the TK101 resin is best suited for radium purification following a preconcentration step to minimize matrix effects in high salinity samples. Dynamic column studies confirmed the strong chromatographic performance of the TK101 resin, with no significant Ba or Sr breakthrough in the Ra fraction and a Ra recovery of 87 ± 2.8%. These results demonstrate the potential of the TK101 resin for selective radium separation in analytical and radiochemical applications.

and nuclear chemistry↗
DOE OSTI2024

Nonvolatile electrochemical memory at 600°C enabled by composition phase separation

Silicon-based microelectronics are limited to ~150°C and therefore not suitable for the extremely high temperatures in aerospace, energy, and space applications. While wide-band-gap semiconductors can provide high-temperature logic, nonvolatile memory devices at high temperatures have been challenging. In this work, we develop a nonvolatile electrochemical memory cell that stores and retains analog and digital information at temperatures as high as 600°C. Through correlative scanning transmission electron microscopy, we show that this high-temperature information retention is a result of composition phase separation between the oxidized and reduced forms of amorphous tantalum oxide. This result demonstrates a memory concept that is resilient at extreme temperatures and reveals phase separation as the principal mechanism that enables nonvolatile information storage in these electrochemical memory cells.

42 ENGINEERING↗
DOE OSTI2024

A directional electrode separator improves anodic biofilm current density in a well-mixed single-chamber bioelectrochemical system

In this study, a directional electrode separator (DES) was designed and incorporated into a single-chamber bioelectrochemical system (BES) to reduce migration and reoxidation of hydrogen. This issue arises when H 2 , generated at the cathode, travels to the anode where anodic biofilms use H 2 . To test the feasibility of our design, a 3D-printed BES reactor equipped with a DES was inoculated with anaerobic digestor granules and operated under fed-batch conditions using fermented corn stover effluent. The DES equipped reactor achieved significantly higher current densities (~53 A/m²) compared to a conventional single-chamber BES without a separator (~16 A/m²), showing a 3.3 times improvement. Further, control abiotic electrochemical experiments revealed that the DES exhibited significantly higher proton conductivity (456±127 µS/mm) compared to a proton exchange membrane (67±21 µS/mm) with a statistical significance of P=0.03. The DES also effectively reduced H 2 migration to the anode by 21-fold relative to the control. Overall, incorporating a DES in a single-chamber BES enhanced anodic current density by reducing H 2 migration to the anode.

3D printed BES↗
DOE OSTI2024

Machine learning-guided discovery of polymer membranes for CO 2 separation with genetic algorithm

Designing polymer membranes with high gas permeability and selectivity is a difficult multi-task constrained problem due to the trade-off between these two properties. In this work, we present a machine learning (ML) driven genetic algorithm to tackle the design problem of polymer membranes for CO 2 separation from N 2 and O 2 . Using literature data of permeability for three gases, we constructed multiple ML models with different fingerprinting featurization schemes to predict gas permeabilities. Then, we employed a genetic algorithm to design new polymers and evaluated their performance using our ML models. We were able to identify new polymer membranes that are promising for both CO 2 /N 2 and CO 2 /O 2 separations. Further, the top discovered polymers are predicted to have high glass transition temperatures. Similarly, the pyridine functionality was found in ≈20% of the predicted polymers. This framework can be used to design polymers for any application involving constrained optimization. Finally, we outlined the challenges and opportunities with using ML guided data-driven inverse design of polymers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Surface engineering of polymeric membranes with metal oxides for improved fouling resistance and superior oil-water separation

Rapid industrial growth has increased the need for efficient membranes to separate oil-water emulsions. Polyvinylidene fluoride (PVDF) membranes, although widely used due to their chemical inertness and favorable mechanical properties, suffer from fouling due to their intrinsic hydrophobicity. Modifying these membranes after fabrication offers a practical solution as it easily fits into existing large-scale manufacturing processes. Atomic layer deposition (ALD), an atomically-precise vapor phase surface modification technique, can create ultrathin metal oxide layers that greatly improve membrane hydrophilicity without significantly affecting the original pore size. However, PVDF's lack of reactive chemical moieties makes ALD challenging. Here, in this study, we present a simple alkali treatment that greatly enhances ALD nucleation and growth on PVDF membranes. This treatment imparts exceptional oil-water emulsion separation capabilities and antifouling behavior in PVDF membranes after just a few ALD cycles, surpassing the performance of PVDF membranes coated with hundreds of ALD cycles. This dramatic reduction in the number of ALD cycles required could enable cost-effective modification of commercial PVDF membranes at scale using spatial, roll-to-roll ALD. These modified membranes outperform reported modified PVDF membranes, with >99 % permeance recovery and <1 % irreversible loss of permeance and >98 % oil rejection from oil-water emulsions over 100 h continuous operation, making them promising for advanced water purification technologies.

Atomic layer deposition↗
DOE OSTI2026

A high-voltage MR-ToF mass spectrometer and separator for the study of exotic isotopes at FRIB

The Facility for Rare Isotope Beams (FRIB) delivers a wide variety of rare isotopes as fast, stopped, or reaccelerated beams to enable forefront research in nuclear structure, astrophysics, and fundamental interactions. To expand the scientific potential of FRIB’s stopped and reaccelerated beam programs, we are designing a Multi-Reflection Time-of-Flight mass spectrometer and separator (MR-ToF MS). It will enable high-precision mass measurements of short-lived isotopes, improve beam diagnostics, and deliver isobarically and isomerically purified beams to downstream experimental stations. It is designed to store ions at a kinetic energy of 30 keV, significantly enhancing ion throughput while maintaining high mass resolving power. In conclusion, we present the scientific motivation, technical design, and simulations demonstrating the expected performance of the system, which has the potential to significantly enhance FRIB’s mass measurement, diagnostic, and mass separation capabilities.

Electrostatic ion beam trap↗
DOE OSTI2026

Modeling Flow and Mass Transfer within Hollow Fiber Packaging for Gas Separation

Hollow fiber membrane modules are used for gas purification by their selective permeation properties. Intensification of the process to minimize the retentate loss and gas pressure involves optimization at various scales. In this work, we outline a numerical investigation of the gas separation performance at the scale of fiber bundles and its impact on module performance. Flow channeling and anisotropy govern the mass-transfer coefficient in axial and cross-flow configurations. These effects are quantified in terms of a permeability tensor or an anisotropy ratio and the effective mass-transfer coefficient or the Sherwood number. The results show a trade-off between purification and recovery. While smaller fibers offer a large specific surface area to enable high purification, it comes at a huge penalty on the separation performance due to reduced penetration within bundles. Optimum performance indicators are emphasized.

Fibers↗
DOE OSTI2025

Manufacturing of Continuous Microporous Polymeric Fibers for Separation Applications

Polyolefin plastic waste, particularly polypropylene, is one of the most prevalent components in the plastic waste stream generated globally. However, only a small fraction of this waste is recycled and reintegrated into second applications. These materials have significant embedded energy that could be used for additional productivity if recycled properly. Therefore, there is a critical need to develop scalable processing techniques with high throughput to effectively recycle it. We report the continuous manufacturing of microporous fibers using waste polypropylene plastic and melt-processable lignin, a plant biomass constituent produced as a byproduct in paper mills or biorefineries, as a template to create pores. Further, these filaments with hierarchical porosity─created by controlled microphase separation during high-speed extensional flow followed by removal of lignin─exhibit exceptional capillary action for hydrophobic liquids. The resulting porous fibers can be used for various separation applications. For example, the oil uptake of the fibers is 9.59 ± 0.82 g/g for applications in oil recovery in bodies of water. In addition, polyethylenimine infiltration within these nanoporous fibers introduces cyclic room temperature sorption and thermal desorption potential of acidic gases such as CO 2 in a bench-scale experiment. The fibers exhibit multiple cycles of CO 2 absorption, with a range of 0.15 to 0.17 mmol/g. Thus, these polyethylenimine-infiltered nanoporous polypropylene fibers can also be used in removing acidic gases from a gas mixture.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Tuning the Selectivity of Carboxylic Acid–Based Eutectic Solvents for the Dissolution and Electrochemical Separation of Metal Oxides

Extracting metals from natural resources and recovering from waste materials with less-hazardous solvents is essential for sustainable technological advancements. The commonly employed method utilizes harsh chemicals for metal dissolution and the ensuing separation. Here, in this study, we examined the potential of eutectic solvents (types III and IV) as alternative media for the selective dissolution of metals and metal oxides and their subsequent electrochemical separation. Notably, type III eutectics composed of betaine:acetic acid and triazole:lactic acid exhibited excellent solubility for cobalt oxide (24.1 g·L –1 ) and copper oxide (30.5 g·L –1 ), respectively. In comparison, the type IV eutectic mixture of Ca(NO 3 ) 2 ·4H 2 O:acetic acid demonstrated the highest conductivity and lowest viscosity with solubility for both copper oxide (6.1 g·L –1 ) and metallic copper (5.4 g·L –1 from a used electronic circuit). Using a Ca(NO 3 ) 2 ·4H 2 O:acetic acid mixture, copper was selectively dissolved from a waste printed circuit board and subsequently electrodeposited onto a nickel electrode. These findings highlight the tunability of DESs for the selective recovery of metals from electronic waste, offering a promising approach for sustainable metal recycling and resource recovery.

electrodeposition↗
DOE OSTI2026

CMPO-Functionalized Silica Sorbents for pH-Tunable Separation and Enrichment of Rare-Earth Elements from Environmental Matrices

Rare-earth elements (REEs) are crucial in many applications, yet mutual separation is challenging due to their similar chemical behavior. Octylphenyl- N,N-diisobutyl carbamoyl methyl phosphine oxide (CMPO) is an organophosphorus ligand originally developed for extracting actinides and lanthanides from spent nuclear fuel. Here, we report a pH-tunable CMPOfunctionalized silica sorbent for selective REE separation from complex aqueous matrices. A CMPO-associated silica gel sorbent was synthesized and characterized by Brunauer−Emmett−Teller (BET) surface area, scanning electron microscopy, and X-ray photoelectron spectroscopy to confirm the surface functionalization and binding behavior. Sorbent performance was evaluated by using a synthetic 46- element solution and a real phosphate rock fertilizer leachate. Notably, REEs were successfully eluted with ultrapure water, demonstrating reversible desorption controlled by pH adjustment. Packed-bed column studies increased the REE mass fraction from 3.6% to 64% (20-fold enrichment), with up to 30-fold enrichment of neodymium. The adsorption process follows the Langmuir isotherm behavior and follows pseudo-second-order kinetics. The uptake capacity of 1 μmol of REEs per 4.2 μmol of CMPO supports the formation of a predominantly 4:1 ligand:rare earth element(III) pseudocomplex. These results demonstrate CMPO-functionalized silica as a selective, water-elutable, and low-chemical-input platform for sustainable REE recovery from environmental and industrial sources.

chelating ligands↗
DOE OSTI2025

Chlorocobaltate-Enabled Selective Separation of CoCl 2 from Mixed Chloride and Nitrate Salts of Mn, Co, and Ni

Described here is the effect of anionic metalates─chlorocobaltate and nitratocobaltate─on the heat-driven separation of the critical element cobalt from potentially competing transition metal salts. Resins bearing the hexadentate glycolamide receptor L (PS-L) exhibit sorption capacities, Q = 1.33 mmol/g for CoCl 2 and Q = 0.66 mmol/g for Co(NO 3 ) 2 , as inferred from sorption isotherm studies. This trend runs counter to the typical Hofmeister series for anion selectivity. Ion chromatographic analysis of a mixed CoCl 2 /Co(NO 3 ) 2 solution revealed an increase in chloride content from 55 mol % to 90 mol % after a single thermally driven catch-and-release cycle. This chloride-selective behavior was recapitulated in a mixed-metal cation, mixed-anion system containing the chloride and nitrate salts of Mn(II), Co(II), and Ni(II) at near-equimolar concentrations. PS-L also displayed enhanced selectivity for Co using this mixed stock solution as observed by ICP-OES. In contrast, for a nitrate-only solution containing Mn(II), Co(II), and Ni(II), PS-L showed increased affinity for Mn, with its proportion rising from 36.6 mol % to 58.1% after a single catch-and-release cycle. Density functional theory calculations support the suggestion that the enhanced uptake of Co(II) in chloride-rich media arises from the high thermodynamic stability of [CoCl 4 ] 2– , which facilitates its outer-sphere coordination to cationic resin-bound cobalt species. Single crystal X-ray crystallographic analyzes of L•MCl 2 (M = Mn, Co, Ni) and L•M(NO 3 ) 2 (M = Mn, Co) confirmed metal complexation by L in the solid state and the concomitant formation of metalate counteranions. Here, the present study highlights a relatively simple approach for separating cobalt from its transition metal congeners.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Suppression of phase separation in AlGaInAs compositionally graded buffers for 1550 nm photovoltaic converters on GaAs

We investigate strategies to suppress phase separation and reduce threading dislocation density (TDD) in AlGaInAs compositionally graded buffers (CGBs) that span the lattice constant range from GaAs to InP. Combining the results from high resolution x-ray diffraction, cathodoluminescence, transmission electron microscopy, and photovoltaic device measurements, we correlate the choices of epitaxial growth conditions with the defect structure of the CGBs and subsequent device performance. Both the use of substrates with high misorientation off (100) toward the (111)A plane and Zn doping instead of Si doping are shown to suppress phase separation and reduce TDD. We demonstrate a 0.74 eV GaInAs device grown on a GaAs substrate offcut 19.5° toward (111)A using a Zn-doped AlGaInAs CGB with TDD = 3.5 ± 0.2 × 10 6 cm -2 that has a bandgap-open circuit voltage offset of only 0.434 V measured under the AM1.5G solar spectrum. We characterized this device under high-intensity irradiance from a 1570 nm laser and measured a 31.9% peak laser power conversion efficiency at 3.6 W/cm 2 irradiance. These results provide a roadmap to the manufacture of laser- and thermal-power conversion devices with the performance and cost-effectiveness needed to drive adoption of these technologies at scale.

14 SOLAR ENERGY↗
DOE OSTI2025

SPIKANs: separable physics-informed Kolmogorov–Arnold networks

Physics-Informed Neural Networks (PINNs) have emerged as a promising method for solving partial differential equations (PDEs) in scientific computing. While PINNs typically use multilayer perceptrons (MLPs) as their underlying architecture, recent advancements have explored alternative neural network structures. One such innovation is the Kolmogorov–Arnold Network (KAN), which has demonstrated benefits over traditional MLPs, including faster neural scaling and better interpretability. The application of KANs to physics-informed learning has led to the development of Physics-Informed KANs (PIKANs), enabling the use of KANs to solve PDEs. However, despite their advantages, KANs often suffer from slower training speeds, particularly in higher-dimensional problems where the number of collocation points grows exponentially with the dimensionality of the system. To address this challenge, we introduce Separable Physics-Informed Kolmogorov–Arnold Networks (SPIKANs). This novel architecture applies the principle of separation of variables to PIKANs, decomposing the problem such that each dimension is handled by an individual KAN. This approach drastically reduces the computational complexity of training without sacrificing accuracy, facilitating their application to higher-dimensional PDEs. Through a series of benchmark problems, we demonstrate the effectiveness of SPIKANs, showcasing their superior scalability and performance compared to PIKANs and highlighting their potential for solving complex, high-dimensional PDEs in scientific computing.

Kolmogorov-Arnold networks↗