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DOE OSTI2024

Foreword: Special Section on Multiphysics Aspects of Power Electronics Packaging—Power Die, Power Module, and Converter Level: Part 2

Power electronics are increasingly being used to condition electricity for a wide array of applications, such as transportation (on land, air, and water), data centers, radio frequency, directed energy, wind, solar, and grid-tied applications. Here, to increase power density, performance, efficiency, and reliability-as well as to reduce cost-innovations and developments are needed in the multiphysics packaging of power electronics at a die, module, and converter level. This includes fundamental R&D related to emerging high-voltage, high-temperature, and high-switching-frequency power electronics, packaging materials, thermal materials and interfaces, fluid-based thermal management technologies, reliability, condition monitoring, and prognostics. Latest developments in this area are published as a Special Section on Multiphysics Aspects of Power Electronics Packaging. The first part was published in the May 2024 issue of the IEEE Transactions on Components, Packaging and Manufacturing Technology (Volume 14, Issue 5). The second part of that Special Section is being published in this issue. A brief summary of the papers included in the second part are given below.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2026

Evidence of electron microbunching in laser-driven modulated downramp injection and prospects for beam-driven implementation

Plasma accelerators can generate high-energy, high-brightness electron beams over centimeter-scale distances, offering novel pathways to compact x-ray free-electron lasers. Generating beams pre-bunched at the desired radiation wavelength would significantly enhance longitudinal coherence and reduce saturation length. Plasma density-modulated downramp injection offers an in-situ way to generate such beams with nanometer-scale bunching. Here we report the first experimental evidence of this mechanism in a laser-driven wakefield accelerator, showing that modulated density downramps generate modulated electron energy spectra absent in unmodulated cases. Particle-in-cell simulations reproduce these observations and reveal bunching factors of 0.05 at 0.4 μm, with a compression factor of approximately 7. Building on this demonstration, we propose a beam-driven implementation for FACET-II to generate multi-GeV beams pre-bunched at hundreds of nanometers wavelength, with sub-micrometer emittance, kiloampere peak current, and sub-percent slice energy spread. Two-stage magnetic compression enables tunable bunching from optical to extreme ultraviolet wavelengths while achieving peak currents exceeding 100 kA. Coherent transition radiation calculations confirm diagnostic feasibility. This approach offers a promising path towards compact, high-energy pre-bunched electron sources for advanced photon science applications.

electron microbunching↗
DOE OSTI2026

Electronic Trap-State Modulation in Sm-Doped SnO 2 Nanofibers Enables Ultrasensitive Hydrogen Sensing

The demand for sub-ppm hydrogen (H 2 ) sensing is growing across emerging applications such as environmental monitoring, breath-based disease diagnostics, and early-stage battery failure detection. However, achieving reliable ppb-level detection with chemiresistive metal oxide sensors remains challenging. At trace gas concentrations, resistance modulation is often insufficient, particularly in the absence of noble metal catalysts. Here, we report samarium-doped tin dioxide (Sm-SnO 2 ) nanofibers in which electronic trap-state modulation is exploited to enable ultrasensitive hydrogen sensing. The 2 at% Sm-doped SnO 2 nanofibers exhibited markedly enhanced H 2 sensitivity, achieving clear detection down to 25 ppb H 2 at 200 °C, with a theoretical limit of detection of 4.5 ppb, placing this material among the most sensitive noble-metal-free SnO 2 -based H 2 sensors reported to date. Mechanistic investigations through X-ray photoelectron spectroscopy and electron energy loss spectroscopy revealed that Sm 3+ doping introduces deep trap states associated with charge-compensating defect complexes. These states reduce free carrier density, increase baseline resistance, and enable trap-assisted charge release during H 2 exposure, thereby amplifying the sensing response. Trap-state engineering via rare-earth doping, exemplified by Sm-SnO 2 , provides an effective pathway for achieving ppb-level hydrogen detection in noble-metal-free chemiresistive sensors.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Insulator‐to‐Metal Transition and Isotropic Gigantic Magnetoresistance in Layered Magnetic Semiconductors

Magnetotransport, the response of electrical conduction to external magnetic field, acts as an important tool to reveal fundamental concepts behind exotic phenomena and plays a key role in enabling spintronic applications. Magnetotransport is generally sensitive to magnetic field orientations. In contrast, efficient and isotropic modulation of electronic transport, which is useful in technology applications such as omnidirectional sensing, is rarely seen, especially for pristine crystals. Here a strategy is proposed to realize extremely strong modulation of electron conduction by magnetic field which is independent of field direction. GdPS, a layered antiferromagnetic semiconductor with resistivity anisotropies, supports a field-driven insulator-to-metal transition with a paradoxically isotropic gigantic negative magnetoresistance insensitive to magnetic field orientations. This isotropic magnetoresistance originates from the combined effects of a near-zero spin–orbit coupling of Gd 3+ -based half-filling ƒ-electron system and the strong on-site f – d exchange coupling in Gd atoms. These results not only provide a novel material system with extraordinary magnetotransport that offers a missing block for antiferromagnet-based ultrafast and efficient spintronic devices, but also demonstrate the key ingredients for designing magnetic materials with desired transport properties for advanced functionalities.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Structural modulation, physical properties, and electronic band structure of the kagome metal UCr 6 ⁢Ge 6

The chemical flexibility of the 𝑅⁢𝑀 6 ⁢𝑋 6 stoichiometry, where an 𝑓-block element is intercalated in the CoSn structure type, allows for the tuning of flatbands associated with kagome lattices to the Fermi level and for emergent phenomena due to interactions between the 𝑓- and 𝑑-electron lattices. Yet, 5⁢𝑓 members of the “166” compounds are underrepresented compared with 4⁢𝑓 members. In this work, we report single-crystal growth of UCr 6 ⁢Ge 6 , which crystallizes in a monoclinically distorted Y 0.5⁢ Co 3 ⁢Ge 3 -type structure. The real-space character of the modulation, which is unique within the 𝑅⁢𝑀 6 ⁢𝑋 6 family, is approximated by a 3×1×2 supercell of the average monoclinic cell. The compound has kagome-lattice flatbands near the Fermi level and a moderately enhanced electronic heat capacity, as evidenced by its low-temperature Sommerfeld coefficient (𝛾=86.5 mJ mol −1 K −2 ) paired with band structure calculations. The small, isotropic magnetization and featureless resistivity of UCr 6 ⁢Ge 6 suggest itinerant uranium 5⁢𝑓 electrons and Pauli paramagnetism. Angle-resolved photoemission spectroscopy results provide evidence for uranium 5⁢𝑓 weight at the Fermi level and for a flatband near the Fermi level associated with the chromium 3⁢𝑑 kagome lattice. The isotropic magnetic behavior of the uranium 5⁢𝑓 electrons starkly contrasts with localized behavior in other uranium 166 compounds, highlighting the high tunability of the magnetic ground state across the material family.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Ion-Electron Coupling-Driven Redox Behavior in Metal–Organic Frameworks

Redox-active metal–organic frameworks (MOFs) have long been proposed as electronic transport platforms, yet the microscopic origin of their conductivity remains debated. A theoretical demonstration reveals charge transport in a Zn(pyrazole–naphthalene diimide (NDI)) MOF arising not from delocalized band-like states but from redox hopping between discrete linker sites. Using ab initio molecular dynamics simulations combined with electronic structure analysis, we established a direct link among electron injection, structural reorganization, and transport. Electron accumulation proceeds sequentially and site-selectively from imide and carbonyl groups of the NDI core progressively involving pyrazole N atoms at higher reduction states, through a hierarchy of redox-active sites. In contrast, Zn nodes remain essentially redox-inactive, which confirms their structural role. Density-of-states analysis corroborates a transport regime dominated by linker-centered states with evolving p-character upon reduction, resulting in dynamically reconfigured conduction networks. Real-time trajectories reveal anisotropic linker-to-linker electron transfer modulated by counterion coordination. This cooperative ion–electron regime emerges from potential energy surface collapse into a single low-barrier transition (ΔG ‡ ≈ 45 meV), where ionic and electronic motions evolve adiabatically on the same free-energy landscape. Elucidating redox conductivity in Zn(pyrazole–NDI) MOFs provides a theoretical framework for use in neuromorphic computing and related technologies.

Charge transfer↗
DOE OSTI2026

Measuring X-Ray Emission Line Shapes in Neutral Species for XRISM Calibration

Space X-ray spectrometers such as the Resolve instrument on XRISM require precise calibration in order to interpret the spectra of astrophysical objects. Key components of the calibration are the energy scale and the core line spread function, both of which vary with photon energy. A major issue in the calibration of high-resolution spectrometers is locating good calibrators with well-known and stable intrinsic line shapes. Neutral fluorescence is widely used, but inner-shell transitions in neutral atoms often exhibit complex, poorly documented line shapes that vary with excitation conditions. Here, in this study, we present empirical measurements of K-shell transitions in neutral O and F below 1 keV using an engineering model XRISM calorimeter array, an electron bombardment modulated X-ray source, and an electron beam ion trap (EBIT) to provide a precise energy reference. In addition, we report measurements of the Mo Lα complex with the transition-edge microcalorimeter spectrometer (TEMS), which reveal strong satellite structure and sensitivity of the line shape to the incident exciting spectrum. Together, these results demonstrate the need for empirical line-shape models, highlight the nonstationary nature of neutral fluorescence features, and define a path toward developing transfer standards for XRISM and future precision instruments such as Athena/X-IFU.

Astronomy and AstroPhysics↗
DOE OSTI2026

Modulating Mid-Gap Electronic States Through Site-Selective Modification in B-Pbx/B'-CuyV2O5/CdS Heterostructures for Photocatalytic Hydrogen Evolution

We interfaced ..beta..-Pbx/..beta..'-CuyV2O5 compounds, with varying stoichiometries of precisely positioned Pb-ions (x) and Cu-ions (y) in interstitial sites along a tunnel-structured ?-V2O5 framework, with cysteine-capped CdS (cysCdS) quantum dots (QDs) to yield heterostructured photocatalysts. ..beta..-Pbx/..beta..'-CuyV2O5 compounds exhibit midgap electronic states with orbital contributions from both Cu 3d and stereochemically active Pb 6s states that show distinctive light-initiated reactivity with photoexcited QDs. ..beta..-Pbx/..beta..'-CuyV2O5/CdS heterostructures were prepared by linker-assisted assembly (LAA). Scanning and transmission electron microscopy, energy-dispersive X-ray spectroscopy, and Raman spectroscopy revealed that cysCdS QDs were deposited onto surfaces of ..beta..-Pbx/..beta..'-CuyV2O5 via LAA. HAXPES revealed that the site-selective positioning of Pb-ions and Cu-ions promoted close energetic alignment of the midgap states of ..beta..-Pbx/..beta..'-CuyV2O5 compounds with the valence-band maximum of cysCdS QDs. Transient absorption spectroscopy revealed that photogenerated holes were transferred from CdS QDs to midgap states of ..beta..-Pbx/..beta..'-CuyV2O5 compounds on time scales <50 ps. Finally, photoelectrochemical and photochemical experiments revealed that ..beta..-Pbx/..beta..'-CuyV2O5/CdS heterostructures promoted the photocatalytic reduction of H+ to H2. In photoelectrochemical experiments, under oxidative conditions, for all ..beta..-Pbx/..beta..'-CuyV2O5/CdS heterostructures, H2 was evolved at a Pt counter electrode while a sacrificial donor was oxidized at the heterostructure-functionalized working electrode. In contrast, under reductive conditions, for ..beta..-Pb0.152V2O5/CdS and ..beta..-Pbx/..beta..'-CuyV2O5/CdS heterostructures, H2 was evolved at the working electrode. In photochemical experiments, dispersed ..beta..-Pbx/..beta..'-CuyV2O5/CdS heterostructures promoted the reduction of H+ to H2 under white-light illumination; ..beta..'-Cu0.55V2O5/CdS and ..beta..-Pbx/..beta..'-CuyV2O5/CdS heterostructures, for which midgap states have Cu 3d orbital character, generated 2-fold more H2 than ..beta..-Pb0.152V2O5/CdS heterostructures. Cu-ion insertion thus appends additional acceptor surface states that improve ligand-mediated hole transfer from photoexcited QDs, but such states are intrinsically limited in mediating hole transport to the substrate as a result of the low mobility of holes in narrow Cu 3d-states. Our results reveal that the density and orbital character of midgap states of ..beta..-Pbx/..beta..'-CuyV2O5 compounds, tunable through recently developed site-selective ion insertion strategies, determine efficiencies of charge-transfer and charge-transport mechanisms that underpin photocatalysis.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Analysis methodology of coherent oscillations in time- and angle-resolved photoemission spectroscopy

Oscillatory signals from coherently excited phonons are regularly observed in ultrafast pump–probe experiments on condensed matter samples. Electron–phonon coupling implies that coherent phonons also modulate the electronic band structure. These oscillations can be probed with energy and momentum resolution using time- and angle-resolved photoemission spectroscopy (trARPES), which reveals the orbital dependence of the electron–phonon coupling for a specific phonon mode. However, a comprehensive analysis remains challenging when multiple coherent phonon modes couple to multiple electronic bands. Complex spectral line shapes due to strong correlations in quantum materials add to this challenge. In this work, we examine how the frequency domain representation of trARPES data facilitates a quantitative analysis of coherent oscillations of the electronic bands. Here, we investigate the frequency domain representation of the photoemission intensity and the first moment of the energy distribution curves. Both quantities provide complementary information and are able to distinguish oscillations of binding energy, linewidth, and intensity. We analyze a representative trARPES dataset of the transition metal dichalcogenide WTe 2 and construct composite spectra, which intuitively illustrate how much each electronic band is affected by a specific phonon mode. We also show how a linearly chirped probe pulse can generate extrinsic artifacts that are distinct from the intrinsic coherent phonon signal.

47 OTHER INSTRUMENTATION↗
DOE OSTI2024

Reversible phase transformations between Pb nanocrystals and a viscous liquid-like phase

Phase transformations have been a prominent topic of study for both fundamental and applied science. Solid-liquid reaction–induced phase transformations can be hard to characterize, and the transformation mechanisms are often not fully understood. Here, we report reversible phase transformations between a metal (Pb) nanocrystal and a viscous liquid-like phase unveiled by in situ liquid cell transmission electron microscopy. The reversible phase transformations are obtained by modulating the electron current density (between 1000 and 3000 electrons Å –2 s –1 ). The metal-organic viscous liquid-like phase exhibits short-range ordering with a preferred Pb-Pb distance of 0.5 nm. Assisted by density functional theory and molecular dynamics calculations, we show that the viscous liquid-like phase results from the reactions of Pb with the CH 3 O fragments from the triethylene glycol solution under electron beam irradiation. Such reversible phase transformations may find broad implementations.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Quality Control of Silicon Sensor Modules for Particle Detectors

The High-Luminosity Large Hadron Collider (HL-LHC) will produce a higher rate of particle collisions than the current Large Hadron Collider (LHC), requiring important upgrades to the Compact Muon Solenoid (CMS) to handle an increased amount of data. An important upgrade is the Phase-2 Outer Tracker Upgrade, which consists of 13,000 silicon sensor modules made of two parallel silicon sensors and readout electronics. These modules undergo careful quality control checks both during and after module assembly to ensure precise and reliable detector performance. This project focuses on precision testing for quality control of silicon sensor modules at Fermilab. Hands-on work includes visual inspection, current-voltage testing, module testing, and ultraviolet (UV) light exposure of modules showing abnormal current-voltage behavior. The ultraviolet exposure process improves the abnormal sensor readout data by placing the selected sensor side of the module directly under the UV light inside a controlled box. In addition to laboratory testing and ultraviolet experiments, I developed a Python-based data tool that connects to a module database and allows selected testing conditions and module information to be retrieved and displayed efficiently. These different testing procedures, experimental processes, and computational tools support the broader goal of identifying module issues and improving modules that will be used in the CMS Outer Tracker Phase-2 Upgrade.

Siddiqui, Hooriya [DuPage Coll.] (ORCID:0009000151↗
DOE OSTI2026

Quality Control of Silicon Sensor Modules for Particle Detectors

The High-Luminosity Large Hadron Collider (HL-LHC) will produce a higher rate of particle collisions than the current Large Hadron Collider (LHC), requiring significant upgrades to the Compact Muon Solenoid (CMS) to handle the increased amount of data. An important upgrade is the Phase-2 Outer Tracker Upgrade, which consists of 13,000 silicon sensor modules made of two parallel silicon sensors and readout electronics. These modules undergo careful quality control checks both during and after module assembly to ensure precise and reliable detector performance. This project focuses on precision testing for quality control of silicon sensor modules at Fermilab. Hands-on work includes visual inspection, current-voltage testing, module testing, and ultraviolet (UV) light exposure of modules showing abnormal current-voltage behavior. The ultraviolet exposure process improves the abnormal sensor readout data by placing the selected sensor side of the module directly under the UV light inside a controlled box. In addition to laboratory testing and ultraviolet experiments, I developed a Python-based data tool that connects to a module database and allows selected testing conditions and module information to be retrieved and displayed efficiently. These different testing procedures, experimental processes, and computational tools support the broader goal of identifying module issues and improving modules that will be used in the CMS Outer Tracker Phase-2 Upgrade.

Siddiqui, Hooriya [DuPage Coll.; Fermilab] (ORCID:↗
DOE OSTI2025

Cu-induced robust Ni 2+ /Ni 3+ transition on amorphous Ni hydroxide-based electrocatalysts for advancing electrochemical ammonia oxidation and hydrogen evolution

The electrochemical ammonia oxidation reaction (AOR) is a promising anodic reaction for hydrogen production, offering a lower theoretical potential compared to oxygen evolution reaction. Despite this thermodynamic advantage, AOR suffers from sluggish multi-electron transfer reaction kinetics and the regeneration of catalytically active Ni 3+ species, which limits both activity and durability. In this study, amorphous NiCu bimetallic catalysts were prepared via facile precipitating metal nitrate deposition (PMND) method. The addition of Cu induces a robust Ni 2+ /Ni 3+ transition, stabilizing catalytically active Ni 3+ species and modulating the electronic structure of Ni. It alters the oxidation and desorption behavior of nitrogen-containing intermediates and facilitating their conversions to NO x species, resulting in fast active site regeneration. Furthermore, amorphous structure provides abundant dangling bonds, which enhances the intrinsic reactivity and accessibility of active sites rather than increasing the number of active sites. As a result, these effects accelerate the overall reaction kinetics. The optimized NiCu 5:1 catalyst achieved an ammonia removal efficiency of ∼100 % and a hydrogen production rate of 2.45 mmol/(h∙cm 2 ) at 1.6 V RHE .

Amorphous electrocatalyst↗
DOE OSTI2026

Electronic and Structural Properties of the Polymer-Electrolyte Interphase in Electrochemically Doped Polymers

The advance of soft, polymer-based (photo)electrochemical energy transformation and storage applications requires a framework for polymer and electrolyte design that includes a deep understanding of the polymer–electrolyte interphase. Here, we report on the investigations of two napthalenediimide (NDI)–bithiophene (T2)-based semiconducting copolymers using computational modeling and in situ, ex situ, and operando techniques to reveal how changes in electrolyte and polymer chemistry modulate the electronic and structural properties of polymer electrodes during electrochemical (de)doping. These systems are shown to host an ensemble of polarons, in contrast with the single polaron-like character often reported, whose properties vary with the nature of the local environment. Importantly, these polarons serve as reporters of the nanoscale environments in which they reside. We demonstrate that controlling the polymer and electrolyte chemistry regulates the nature of the charge carriers generated upon electrochemical doping and/or exciton dissociation in a photoelectrochemical solar cell: For instance, divalent counterions enable polaron and bipolaron formation at lower reducing potentials, while supporting more bipolaron formation than monovalent counterions. A novel application of NEXAFS reveals insights into charge (de)localization, providing a pathway for future investigation of electron transport mechanisms. Finally, simulations of polymer swelling of an amorphous interphase show that charge formation has a large impact on polymer swelling and ion penetration. These studies deliver insights to enable the control of charge-carrier and ion transport, the rates of electron transfer and catalytic efficiency, device stability, and overall device performance.

14 SOLAR ENERGY↗
DOE OSTI2025

C60-Based Ionic Salt Electron Shuttle for High-Performance Inverted Perovskite Solar Modules

Although C60 is usually the electron transport layer (ETL) in inverted perovskite solar cells, its molecular nature of C60 leads to weak interfaces that lead to non-ideal interfacial electronic and mechanical degradation. Here, we synthesized an ionic salt from C60, 4-(1',5'-dihydro-1'-methyl-2'H-[5,6] fullereno-C60-Ih-[1,9-c]pyrrol-2'-yl) phenylmethanaminium chloride (CPMAC), and used it as the electron shuttle in inverted PSCs. The CH2-NH3+ head group in the CPMA cation improved the ETL interface and the ionic nature enhanced the packing, leading to ~3-fold increase in the interfacial toughness compared to C60. Using CPMAC, we obtained ~26% power conversion efficiencies (PCEs) with ~2% degradation after 2,100 hours of 1-sun operation at 65degrees C. For minimodules (four subcells, 6 centimeters square), we achieved the PCE of ~23% with <9% degradation after 2,200 hours of operation at 55degrees C.

14 SOLAR ENERGY↗
DOE OSTI2024

Design and performance of a magnetic bottle electron spectrometer for high-energy photoelectron spectroscopy

We describe the design and performance of a magnetic bottle electron spectrometer (MBES) for high-energy electron spectroscopy. Our design features a 2 m long electron drift tube and electrostatic retardation lens, achieving sub-electronvolt (eV) electron kinetic energy resolution for high energy (several hundred eV) electrons with a close to 4π collection solid angle. A segmented anode electron detector enables the simultaneous collection of photoelectron spectra in high resolution and high collection efficiency modes. This versatile instrument is installed at the time-resolved molecular and optical sciences instrument at the Linac Coherent Light Source x-ray free-electron laser (XFEL). In this paper, we demonstrate its high resolution, collection efficiency, and spatial selectivity in measurements where it is coupled to an XFEL source. These combined characteristics are designed to enable high-resolution time-resolved measurements using x-ray photoelectron, absorption, and Auger–Meitner spectroscopy. We also describe the pervasive artifact in MBES time-of-flight spectra that arises from a periodic modulation in electron collection efficiency and present a robust analysis procedure for its removal.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2026

Nanoscale ultrafast lattice modulation with a free-electron laser

Ultrafast optical laser-based techniques have enabled the probing of atomistic processes at their intrinsic temporal scales with femto- and attosecond resolution. However, the long wavelengths of optical lasers have prevented their interrogation and manipulation with nanoscale spatial specificity. Advances in hard X-ray free-electron lasers have enabled progress in developing X-ray transient-grating spectroscopy, a technique that aims to coherently control elementary excitations with nanoscale X-ray standing waves. Thus far, the realization of this technique at the nanoscale has been a challenge. Here we demonstrate X-ray transient-grating spectroscopy with spatial periods of the order of 10 nm via the subfemtosecond synchronization of two hard X-ray pump pulses at a precisely controlled crossing angle. This creates a thermal grating and preferentially excites coherent longitudinal acoustic phonon modes with the transient-grating wavevector. On probing with a third, variably delayed, X-ray pulse with the same photon energy, time-and-wavevector-resolved measurements of the modulation of the induced scattering intensity provide evidence of ballistic thermal transport at nanometre scales. Finally, these results highlight the potential of X-ray transient gratings as a powerful platform for studying nanoscale transport in condensed matter and the coherent control of nanoscale dynamics.

nonlinear optics↗
DOE OSTI2025

Echo state network for coarsening dynamics of charge density waves

An echo state network (ESN) is a type of reservoir computer that uses a recurrent neural network with a sparsely connected hidden layer. Compared with other recurrent neural networks, one great advantage of ESN is the simplicity of its training process. Yet, despite the seemingly restricted learnable parameters, ESN has been shown to successfully capture the spatial-temporal dynamics of complex patterns. Here we build an ESN to model the coarsening dynamics of charge-density waves (CDWs) in a semiclassical Holstein model, which exhibits a checkerboard electron density modulation at half-filling stabilized by a commensurate lattice distortion. The inputs to the ESN are local CDW order parameters in a finite neighborhood centered around a given site, while the output is the predicted CDW order of the center site at the next time step. Special care is taken in the design of couplings between hidden layer and input nodes to ensure lattice symmetries are properly incorporated into the ESN model. Since the model predictions depend only on CDW configurations of a finite domain, the ESN is scalable and transferrable in the sense that a model trained on dataset from a small system can be directly applied to dynamical simulations on larger lattices. Furthermore, our work opens avenues for efficient dynamical modeling of pattern formations in functional electron materials.

2-dimensional systems↗