Frequency and Harmonic Computing Advancements (2016-2026): State-of-the-Art Feats
Focus: Physics-driven milestones in frequency/harmonic/wave-based/oscillatory/resonant computing (oscillatory neural networks (ONNs), wave-based analog processors, frequency-domain neural nets, spin-wave/magnonic computing, photonic frequency multiplexing, complex-frequency excitations, harmonic resonance systems); strong physics ties preferred (nonlinear wave equations, phase/frequency locking, Floquet engineering, dispersion/nonlinearity balance, resonance amplification, complex-plane poles/residues); last decade only.

1. Oscillatory Neural Networks (ONNs) Theoretical & Simulation Foundations (2016-2020+)
Process: Coupled nonlinear oscillators (van der Pol/Hopf) encode data in phase/frequency; synchronization for pattern recognition, associative memory, image processing.
Physics Explanations: Strong - phase/frequency locking via Kuramoto dynamics; collective oscillation as computation primitive.
Source: Csaba/Porod IEEE papers; neuromorphic reviews.
PARAMETERS: Theoretical/simulation study. Oscillator types: van der Pol, Hopf bifurcation models. Coupling via Kuramoto dynamics. Spin-torque oscillators (STOs) studied for nanoscale implementations. Typical simulation scale: arrays of 4-100+ coupled oscillators. Phase encoding: 0-2pi continuous. Frequency range depends on implementation (GHz for STOs, MHz-kHz for CMOS ring oscillators).
REFERENCE: Csaba, G. & Porod, W. "Coupled oscillators for computing: A review and perspective." Applied Physics Reviews 7(1), 011302 (2020). DOI: https://doi.org/10.1063/1.5120412

2. Spin-Wave (Magnonic) Logic Gates & Interference Computing (2016-2020+)
Process: Spin waves in ferromagnetic films perform Boolean logic via interference; frequency-selective propagation for gates.
Physics Explanations: Strong - magnon dispersion relation; wave interference at GHz frequencies for low-power ops.
Source: AIP/JAP; magnonics roadmaps.
PARAMETERS: Material: Yttrium Iron Garnet (YIG) on Gadolinium Gallium Garnet (GGG) substrate. Film thickness: 54 nm (thin film) to 18 um (thick film LPE). Waveguide width: 100 um typical. Excitation frequency: ~3.95 GHz at effective magnetic field Heff = 1394 Oe. Isolation ratio: 19 dB at ~2.80 kOe. Spin-wave wavelength: ~8.9 um. Device length: ~53 um. Gilbert damping: as low as 5x10^-4. Logic demonstrated: XNOR, NOT, OR, NOR, AND, NAND, half-adder.
REFERENCE: Mahmoud, A. et al. "Introduction to spin wave computing." J. Appl. Phys. 128(16), 161101 (2020). DOI: https://doi.org/10.1063/5.0019328 | Kanazawa et al. "Three port logic gate using forward volume spin wave interference in a thin yttrium iron garnet film." Sci. Rep. 9, 16645 (2019). DOI: https://doi.org/10.1038/s41598-019-52889-w

3. Optical Wave-Based Analog Computing with Metamaterials (2016-2021+)
Process: Metasurfaces perform spatial Fourier transforms, convolutions, edge detection via diffraction in engineered media.
Physics Explanations: Strong - spatial frequency filtering; wave propagation parallelism at light speed.
Source: Applied Sciences (Cheng 2021 review); Nature Photonics collections.
PARAMETERS: Theoretical/review study. Covers two fundamental approaches: metasurface approach (subwavelength meta-atoms for transfer function design) and Green's function approach (bulk metamaterial slabs). Operations demonstrated: spatial differentiation, integration, convolution, edge detection. Operating wavelengths: visible to microwave depending on implementation. Speed: light-speed parallel processing. Power: passive (no external power for computation).
REFERENCE: Cheng, K. et al. "Optical Realization of Wave-Based Analog Computing with Metamaterials." Applied Sciences 11(1), 141 (2021). DOI: https://doi.org/10.3390/app11010141

4. Frequency-Domain Physical-Informed Neural Networks (FPINNs) (2023-2025)
Process: PINNs operate in Fourier domain for PDE solving/nonlinear dynamics; spectral methods + neural nets.
Physics Explanations: Strong - frequency-domain constraints enforce physics; spectral convergence for wave/PDE problems.
Source: Engineering Applications of AI (Qian 2023); extensions.
PARAMETERS: Architecture: CliqueNet backbone with cyclic convolution feature structure + Fourier Spectral Method (FSM). Training: coupling of physical governing equations with neural network in frequency domain. Applications: nonlinear system dynamic prediction, ODE systems. Addresses limited feature expression and low time-domain computational efficiency of existing PINNs. Based on Hamiltonian neural networks framework.
REFERENCE: Qian, K. et al. "Frequency-domain physical constrained neural network for nonlinear system dynamic prediction." Engineering Applications of Artificial Intelligence (2023). DOI: https://doi.org/10.1016/j.engappai.2023.106197

5. Analog Implementation of Harmonic Oscillator Recurrent Neural Network (HORN) (2025)
Process: Electronic circuits realize HORN with transient oscillatory dynamics for efficient sequence processing.
Physics Explanations: Strong - van der Pol-like oscillators; phase/frequency encoding in analog transients.
Source: arXiv analog demo (2025).
PARAMETERS: Network size: 4-node HORN. Task: sequential MNIST (sMNIST) classification. Training: in silico (digital twin), parameters transferred to analog hardware. Hardware: analog electronic circuit with signal generator, analog computer, data logger. Classification accuracy: ~74% (reservoir mode with SVM readout at 789 pixels). Digital-analog agreement: 28.39% with direct readout transfer (precision mismatch). Mismatch cause: precision difference between analog hardware and floating-point representation.
REFERENCE: arXiv:2509.04064 (2025). Published as: Phys. Rev. Applied 24, 064055 (2025). DOI: https://doi.org/10.1103/PhysRevApplied.24.064055

6. Programmable Wave-Based Meta-Computer (2024)
Process: Reconfigurable metamaterials perform matrix-vector multiplication, DFT, filtering in EM wave space.
Physics Explanations: Strong - analog wave propagation; electromagnetic interference for parallel ops.
Source: Advanced Functional Materials (Yang 2024).
PARAMETERS: Two microwave-frequency prototypes designed and fabricated. Operations demonstrated: matrix-vector multiplication, discrete Fourier transform, filtering, solving complex matrix equations. Real-time analog computation in EM wave space. Re-programmable meta-structure elements. Validated through numerical simulations and experiments.
REFERENCE: Yang, H. et al. "Programmable Wave-Based Meta-Computer." Advanced Functional Materials (2024). DOI: https://doi.org/10.1002/adfm.202404457

7. Neuromorphic Frequency-Domain Wave Computing in Photonics (2023-2025)
Process: Nonlinear photonic nets use supercontinuum/frequency multiplexing for reservoir computing.
Physics Explanations: Strong - nonlinear wave dynamics; frequency-domain parallelism via optical channels.
Source: Advanced Science (2023); photonic NN reviews.
PARAMETERS: Platform: highly nonlinear optical fiber. Mechanism: coherent higher-order soliton fission for broadband frequency generation. Input: femtosecond pulse (~140 fs at fiber input) with spectral phase encoding via programmable filter. Processing: nonlinear wave mixing generates new frequency bands. Readout: linear mapping of spectral intensities to prediction labels. Off-the-shelf fiber-optic components. Energy-efficient, scalable architecture.
REFERENCE: Fischer, B. et al. "Neuromorphic Computing via Fission-based Broadband Frequency Generation." Advanced Science 10, 2303835 (2023). DOI: https://doi.org/10.1002/advs.202303835

8. Time-Frequency Analysis with Spiking Neural Networks (SNNs) (2024)
Process: SNNs perform spectrogram-like processing via oscillatory spikes/frequency-selective neurons.
Physics Explanations: Strong - temporal coding; frequency-tuned spiking for signal analysis.
Source: IOP Neuromorphic Computing (Bensimon 2024).
PARAMETERS: Architecture: Spike-Continuous-Time-Neuron (SCTN) based network functioning as frequency resonators. Learning rule: modified supervised Spike-Timing-Dependent Plasticity (STDP). Application: EEG signal analysis with 5 SCTN-based resonators per EEG subband. Acts as spectral analyzer competitive with classical time-frequency analysis tools. Code available: https://github.com/NeuromorphicLabBGU/Time-Frequency-Analysis-Using-Spiking-Neural-Network
REFERENCE: Bensimon, M. et al. "Time-frequency analysis using spiking neural network." Neuromorphic Computing and Engineering 4, 044001 (2024). DOI: https://doi.org/10.1088/2634-4386/ad7d30

9. Local Active Memristive Oscillators for Frequency Extraction (2025)
Process: Mott memristors create tunable oscillators; extract/classify frequency info (e.g., speech).
Physics Explanations: Strong - nonlinear oscillations near chaos; frequency locking/amplification.
Source: PMC/Nature (Wang 2025).
PARAMETERS: Device: VO2 Mott memristor exhibiting insulator-to-metal transition (IMT). Operating regime: edge-of-chaos (EOC). Single oscillator's virtual nodes replace massive arrays of passive devices. Computing capacity: frequency-domain feature extraction and non-linear response. Compact model based on local active principle and thermodynamic analysis. Applications: speech frequency classification, reservoir computing.
REFERENCE: Wang, Y. et al. "Local active memristive oscillator enables controllable complex behaviours and frequency domain extraction." National Science Review 13(2), nwaf546 (2026). DOI: https://doi.org/10.1093/nsr/nwaf546

10. Frequency Multiplexed Photonic Reservoir Computing (2025)
Process: WDM reservoirs use multiple optical frequencies for parallel computation.
Physics Explanations: Strong - optical frequency channels; massive wave parallelism.
Source: SPIE (Lupo 2025).
PARAMETERS: Platform: fiber-based photonic reservoir computing. Method: wavelength division multiplexing (WDM) with frequency comb encoding. Two-layer deep reservoir computing with fully analog inter-layer connection. 5 wavelengths improve classification to 92.3% accuracy with only 9 spatial output ports. Fully analog connection between reservoir layers via frequency domain.
REFERENCE: Lupo, A. et al. "Deep photonic reservoir computer based on frequency multiplexing with fully analog connection between layers." Optica 10, 1478-1485 (2023). DOI: https://doi.org/10.1364/OPTICA.489501 | Cox, N. et al. "Photonic frequency multiplexed next-generation reservoir computer." APL Photonics 10(3), 036122 (2025). DOI: https://doi.org/10.1063/5.0255084

11. Complex-Valued Optical Convolution Accelerator (2025+)
Process: Photonic chip handles phase-sensitive data (radar) at >2 TOPS via complex waves.
Physics Explanations: Strong - complex-valued wave processing; frequency/phase encoding.
Source: Nature collections.
PARAMETERS: Computing speed: 2.0512 TeraOPS (single-kernel), 3x faster than prior photonic convolution accelerators. Application: synthetic aperture radar (SAR) image recognition (Sentinel-1 satellite data). Accuracy: 83.8% experimental (500 images), close to in-silico results. Complex-valued processing preserves both amplitude and phase information. Institution: Beijing University of Posts and Telecommunications.
REFERENCE: Bai, Y. et al. "TOPS-speed complex-valued convolutional accelerator for feature extraction and inference." Nature Communications 16, 292 (2025). DOI: https://doi.org/10.1038/s41467-024-55321-8

12. NSF/ERVA Wave-Based Computing Workshop & Roadmap (2025-2026)
Process: Explores wave devices for AI/signal processing; analog parallelism.
Physics Explanations: Strong - linear/nonlinear wave phenomena for computation.
Source: NSF-ERVA workshop reports.
PARAMETERS: Workshop organized by Engineering Research Visioning Alliance (ERVA) under NSF. Covers analog VLSI, wave-based computing devices, quantum-enabled technologies. Related roadmap: "Roadmap for Unconventional Computing with Nanotechnology" published in Smart Materials and Structures (2025). Topics: wave-based AI acceleration, analog signal processing, neuromorphic wave devices.
REFERENCE: NSF-ERVA Workshop Reports. https://www.ervacommunity.org/ | Stepney, S. et al. "Roadmap for Unconventional Computing with Nanotechnology." DOI: https://doi.org/10.1088/1361-6528/ad9e00

13. Magnonic Hybrid Quantum Systems (2020s-2026)
Process: Magnons coupled to qubits for wave-based quantum info.
Physics Explanations: Strong - spin-wave frequency manipulation; low-power quantum ops.
Source: Nature collections.
PARAMETERS: Key experiment: single magnon detection using superconducting qubit as quantum sensor. Material: millimeter-sized ferromagnetic crystal (YIG sphere). Quantum efficiency: up to ~0.71. Magnon-qubit coupling: dipolar interactions. Qubit type: superconducting transmon. Cavity microwave photon acts as coherent data bus for magnon-qubit entanglement. Operating temperature: millikelvin (dilution refrigerator). Frequency: GHz range (microwave).
REFERENCE: Lachance-Quirion, D. et al. "Entanglement-based single-shot detection of a single magnon with a superconducting qubit." Science 367, 425-428 (2020). DOI: https://doi.org/10.1126/science.aaz9236

14. Harmonic Amplitude Summation in Frequency-Tagging (2021+)
Process: Sum baseline-corrected harmonics for robust brain frequency-tagging.
Physics Explanations: Strong - frequency-domain reconstruction; phase-insensitive harmonic summation.
Source: Journal of Cognitive Neuroscience (Retter 2021).
PARAMETERS: Method: baseline-corrected amplitude summation across harmonics (F, 2F, 3F, etc.). Application: steady-state visual evoked potentials (SSVEPs) / frequency-tagging of brain responses. Validated against root-mean-square summation and individual harmonic analysis. Provides phase-insensitive combination of harmonic responses. Benchmark: EEG frequency-tagging paradigms for face perception, attention, etc.
REFERENCE: Retter, T.L., Rossion, B. & Schiltz, C. "Harmonic Amplitude Summation for Frequency-tagging Analysis." Journal of Cognitive Neuroscience 33(11), 2372-2393 (2021). DOI: https://doi.org/10.1162/jocn_a_01763

15. Bound States in Continuum Boosted High-Harmonic Generation (2019+)
Process: Nanoscale metasurfaces enhance HHG efficiency for frequency up-conversion.
Physics Explanations: Strong - BIC resonances; nonlinear frequency multiplication.
Source: Phys. Rev. Research (Carletti 2019).
PARAMETERS: Platform: dielectric metasurfaces with bound states in the continuum (BIC) resonances. Mechanism: BIC-enhanced electromagnetic field confinement boosts nonlinear frequency conversion efficiency. Scale: nanoscale structures. Process: high-harmonic generation (third harmonic and beyond). Enhancement: orders-of-magnitude improvement over non-resonant substrates. Applications: frequency up-conversion, nonlinear optics.
REFERENCE: Carletti, L. et al. "High-harmonic generation at the nanoscale boosted by bound states in the continuum." Physical Review Research 1(2), 023016 (2019). DOI: https://doi.org/10.1103/PhysRevResearch.1.023016

16. Frequency-Domain Compressed Sensing for Power Harmonics (2022)
Process: IoT + dynamic CS for grid harmonic monitoring.
Physics Explanations: Partial - sparse frequency recovery; HO-FF algorithm.
Source: Energy Reports (Niu 2022).
PARAMETERS: Framework: IoT-based real-time harmonic monitoring with dynamic compressed sensing. Sensing node: continuous sampling with sliding time window compression. Edge node: Homotopy Optimization with Fundamental Filter (HO-FF) algorithm for iterative recovery. Fundamental filtering scheme improves signal recovery accuracy. Application: distributed power system harmonic analysis. Reduces computational complexity for real-time grid monitoring.
REFERENCE: Niu, Y. et al. "Harmonic analysis in distributed power system based on IoT and dynamic compressed sensing." Energy Reports 8, 2363-2375 (2022). DOI: https://doi.org/10.1016/j.egyr.2022.01.119

17. Plucker Conoid Geometry for Wave-Based Systems (2025)
Process: Conoid structures for broadband/directional wave control in computing.
Physics Explanations: Strong - geometric waveguiding; spectral bandwidth manipulation.
Source: Preprints (2025).
PARAMETERS: Concept: Plucker conoid-inspired geometry (PCIG) as wave modulation strategy. Proposed device: optical transistor where guided beams interact with conoid-profiled surfaces. Mechanism: sinusoidally modulated geometry introduces phase shifts for passive signal control (transmission, reflection, redirection). No electronic components, electrical power, or nonlinear media required. Simulation results: significant increases in phase variance and bandwidth expansion vs. planar waveguides.
REFERENCE: Preprints.org (2025). DOI: https://doi.org/10.20944/preprints202504.1531.v1

18. State-Resonant Energy Transmission Law (SRETL) Concepts (2026)
Process: Phi = nu_0 R(E) for resonant energy flux in materials; wave-particle duality.
Physics Explanations: Strong - activation frequency + transmission function; harmonic resonance.
Source: OAEPublish (Zhu 2026).
PARAMETERS: Governing equation: Phi = nu_0 * R(E), where Phi = macroscopic energy flux, nu_0 = intrinsic activation frequency, R(E) = dimensionless transmission function dependent on accessible energy states E. Unifies classical migration-limited transport and wave-like resonance-mediated transmission as complementary regime limits. Application: energy materials, confined and field-structured systems. Author: Dr. Bin Zhu, Dept. Chemical Engineering, Loughborough University.
REFERENCE: Zhu, B. "A state-resonant energy transmission law for energy materials and beyond." Energy Z 2, 200001 (2026). https://www.oaepublish.com/articles/energyz.2026.03

19. Neural Oscillatory Circuits Paradigm (2025+)
Process: Brainwave-mimicking circuits for efficient AI computation.
Physics Explanations: Strong - oscillatory dynamics; phase/frequency as info carrier.
Source: TechRxiv (Roberts/O'Rourke).
PARAMETERS: Not publicly available - specific TechRxiv preprint by Roberts/O'Rourke could not be located in public databases. Concept: brainwave-mimicking electronic circuits that use oscillatory dynamics for AI computation. Related work on oscillatory recurrent gated neural integrator circuits (ORGaNICs) exists in PNAS.
REFERENCE: Roberts & O'Rourke, TechRxiv (2025). Preprint not independently verified. Related: Herz, D.M. et al., PNAS (2019). DOI: https://doi.org/10.1073/pnas.1911633116

20. Oscillatory Neural Networks Optimized by Machine Learning (2024)
Process: ML tunes ONN parameters for synchronization/computation.
Physics Explanations: Partial - synchronization optimization.
Source: Frontiers in Neuroscience (Rudner 2024).
PARAMETERS: Method: Backpropagation Through Time (BPTT) for determining coupling resistances between ring oscillators. Circuit model: ring oscillator-based ONN. Applications demonstrated: associative memories, multi-layered ONN classifiers. Result: ML-designed ONNs show superior performance vs. Hebbian learning. Enables significant circuit topology simplification.
REFERENCE: Rudner, T., Porod, W. & Csaba, G. "Design of oscillatory neural networks by machine learning." Frontiers in Neuroscience 18 (2024). DOI: https://doi.org/10.3389/fnins.2024.1307525

21. Formalism for Computing with Oscillators (2024)
Process: Mathematical framework for ONN capability/synchronization.
Physics Explanations: Strong - Hopf/van der Pol models; phase dynamics for computation.
Source: Nature (Todri-Sanial 2024).
PARAMETERS: Comprehensive review covering: computational capability analysis, synchronization occurrence conditions, mathematical formalism (Hopf/van der Pol/Kuramoto models). Circuit implementations: VO2 memristors, CMOS ring oscillators, spin-torque oscillators. Applications: pattern retrieval, combinatorial optimization, machine learning. Perspectives on broadening ONN applications and mathematical understanding.
REFERENCE: Todri-Sanial, A. et al. "Computing with oscillators from theoretical underpinnings to applications and demonstrators." npj Unconventional Computing 1(1) (2024). DOI: https://doi.org/10.1038/s44335-024-00015-z

22. Acoustic Logic Gates via Valley-Locked Topological Waves (2025)
Process: 2D metamaterials for acoustic frequency-selective logic.
Physics Explanations: Strong - topological wave protection; frequency-dependent routing.
Source: J. Sound Vib. (Liu 2025).
PARAMETERS: Platform: 2D metamaterial heterostructures with topological valley edge states. Logic gates demonstrated: AND, OR gates via valley-locked waveguides and tunneling phenomena. Robustness: verified under wide valley-locked layers, impurities, disorder, and bends. Mechanism: local resonant metamaterials for low-frequency valley-locked waveguides. Reconfigurable platforms for waveguide state logic.
REFERENCE: Liu et al. "Topological valley-locked acoustic logic gates." Related publications in J. Sound and Vibration / Int. J. Mech. Sci. (2023-2025). DOI: https://doi.org/10.1016/j.ijmecsci.2023.108725

23. Revival of Wave-Based Analog Computing (2020s)
Process: Metamaterials for Fourier/optical analog ops.
Physics Explanations: Strong - diffraction/interference parallelism at light speed.
Source: Various reviews.
PARAMETERS: General trend covering multiple implementations: electromagnetic metamaterial processors, photonic Fourier transform devices, acoustic analog computers. Key advantage: light-speed parallel processing. Operations: differentiation, integration, convolution, edge detection. Platforms: metasurfaces, photonic crystals, phononic crystals. Power: passive devices (no external energy for computation).
REFERENCE: Zangeneh-Nejad, F. et al. "Analogue computing with metamaterials." Nature Reviews Materials 6, 207-225 (2021). DOI: https://doi.org/10.1038/s41578-020-00243-2

24. Harmonic Resonance Computing (HRC) Emerging Concepts (2025-2026)
Process: Vibrational/harmonic patterns as computational primitives.
Physics Explanations: Speculative strong - resonance as info processing; wave functions.
Source: Emerging speculative works (Klock 2025).
PARAMETERS: Not publicly available in peer-reviewed literature. Concept: vibrational fields as dynamic information storage (not static data). Proposed mechanisms: harmonic wave computation, resonant feedback loops, near-zero energy loss via resonance self-stabilization. Claims: real-time harmonic intelligence processing. Status: self-published/speculative; no peer-reviewed experimental validation found.
REFERENCE: Klock, B.J. "The Science of Harmonic Resonance Computing." Self-published (2025). https://bjklock.com/p/the-science-of-harmonic-resonance | ResearchGate preprint (2025). DOI: https://doi.org/10.13140/RG.2.2.18855.07848

25. Frequency-Domain Time Series Transformers (2023-2025)
Process: FEDformer/FiLM/FreTS/Fredformer use Fourier ops in transformers.
Physics Explanations: Strong - spectral decomposition; global frequency modeling.
Source: arXiv/ICLR papers.
PARAMETERS: FEDformer: seasonal-trend decomposition + frequency-enhanced attention using sparse Fourier representation. Benchmarks: 6 datasets, reduces multivariate prediction error by 14.8%, univariate by 22.6%. Architecture: Transformer with Fourier-enhanced blocks. Training: standard backpropagation. Code: https://github.com/MAZiqing/FEDformer
REFERENCE: Zhou, T. et al. "FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting." ICML 2022, PMLR 162:27268-27286. https://proceedings.mlr.press/v162/zhou22g.html | arXiv:2201.12740

26. Reservoir Computing with Physical Waves (2020s)
Process: Photonic/acoustic/spin-wave reservoirs for chaotic dynamics.
Physics Explanations: Strong - nonlinear wave chaos as reservoir.
Source: Photonics/magnonics reviews.
PARAMETERS: Platforms: photonic (silicon microresonators, fiber optics), magnonic (spin-wave interference in YIG), acoustic (phonon-magnon coupling). Key mechanism: nonlinear wave dynamics provide rich high-dimensional state space. Performance: spin-wave reservoir computing enhanced by physical conditions (field, temperature). Photonic reservoirs: >200 TOPS demonstrated (silicon photonic, 2024).
REFERENCE: Photonic: Vandoorne, K. et al. "Photonic neuromorphic information processing and reservoir computing." APL Photonics 5, 020901 (2020). DOI: https://doi.org/10.1063/1.5129762 | Magnonic: Papp, A. et al. Phys. Rev. Applied 19, 034047 (2023). DOI: https://doi.org/10.1103/PhysRevApplied.19.034047

27. Neuromorphic Frequency Extraction with Memristors (2025)
Process: Oscillators classify speech via frequency domain.
Physics Explanations: Strong - edge-of-chaos frequency extraction.
Source: Wang 2025.
PARAMETERS: Same study as Entry 9. Device: VO2 Mott memristor at edge-of-chaos. Single oscillator virtual nodes for frequency-domain feature extraction. Applications: speech frequency classification. Compact thermodynamic model based on local active principle.
REFERENCE: See Entry 9. Wang, Y. et al. National Science Review 13(2), nwaf546 (2026). DOI: https://doi.org/10.1093/nsr/nwaf546

28. Programmable Metastructures for Wave-Based Analog (2025)
Process: Reconfigurable metasurfaces design themselves for computation.
Physics Explanations: Strong - wave propagation self-optimization.
Source: Nature Communications (Tzarouchis 2025).
PARAMETERS: Architecture: reconfigurable metastructure performing analog complex mathematical computations using EM waves. Operations: matrix inversion, root finding, constrained optimization/inverse design. Both stationary and non-stationary algorithms. Authors: Tzarouchis, Edwards, Engheta (Univ. of Pennsylvania). Experimentally verified concept.
REFERENCE: Tzarouchis, D.C., Edwards, B. & Engheta, N. "Programmable wave-based analog computing machine: a metastructure that designs metastructures." Nature Communications 16, 908 (2025). DOI: https://doi.org/10.1038/s41467-025-56019-1

29. Pulse-Driven Neural Architecture with Oscillatory Dynamics (2026)
Process: PDNA augments RNNs with learnable oscillations for sequence processing.
Physics Explanations: Strong - internal oscillatory state evolution; frequency robustness.
Source: arXiv (2026).
PARAMETERS: Not publicly available - specific 2026 arXiv paper with "PDNA" acronym could not be independently located. Concept: continuous-time RNNs with learnable oscillatory dynamics for robust sequence processing. Related work: Coupled Oscillatory RNN (coRNN) uses second-order ODEs modeling nonlinear oscillator networks. Deep Pulse-Coupled Neural Networks (arXiv:2401.08649) use spatio-temporal backpropagation.
REFERENCE: Specific PDNA paper not independently verified. Related: Rusch, T.K. et al. "Coupled Oscillatory Recurrent Neural Network (coRNN)." arXiv:2010.00951

30. Deep Oscillatory Neural Network (DONN) (2025)
Process: Hopf oscillators in complex domain for deep learning; convolutional variants (OCNNs).
Physics Explanations: Strong - oscillatory dynamics in complex plane; brain-like frequency encoding.
Source: Scientific Reports (Rohan 2025).
PARAMETERS: Architecture: neurons exhibit brain-like oscillatory activity via neural Hopf oscillators in complex domain. Combines neural oscillators with sigmoid/ReLU neurons using complex-valued weights and activations. Input modes: resonator, amplitude modulation, frequency modulation. Training: complex backpropagation. Extension: Oscillatory Convolutional Neural Networks (OCNNs). Benchmark: signal and image processing tasks with comparable/improved performance over baselines.
REFERENCE: Rohan, N.R. et al. "Deep oscillatory neural network." Scientific Reports 15, 40968 (2025). DOI: https://doi.org/10.1038/s41598-025-24837-4

31. Structural Constraints for Oscillations in Neural Nets (2024)
Process: Threshold-linear networks require odd inhibitory nodes + strong connections for oscillation emergence.
Physics Explanations: Strong - dynamical system balance; inhibitory-excitatory asymmetry for rhythms.
Source: eLife (Helson 2024).
PARAMETERS: Network type: threshold-linear networks (TLNs). Key finding: odd number of inhibitory nodes + strong enough connections are necessary and sufficient for oscillation emergence in single-cycle networks. Validated in biologically plausible networks with firing-rate and spiking neuron models. Proof via dynamical system theory. Code: https://github.com/jiezang97/Code-for-Structural-constraints-on-the-emergence-of-oscillations
REFERENCE: Zang, J. et al. "Structural constraints on the emergence of oscillations in multi-population neural networks." eLife (2024). DOI: https://doi.org/10.7554/eLife.88777

32. Oscillatory Mechanisms in Intrinsic Brain Networks (2024)
Process: Intracranial evidence for frequency-dependent network coupling (low-freq DMN modulates high-freq FPN).
Physics Explanations: Strong - phase-amplitude coupling; frequency-specific oscillatory communication.
Source: NeuroImage (Luo 2024).
PARAMETERS: Method: intracranial electroencephalography (iEEG). Subjects: 42 participants. Networks studied: default mode network (DMN), frontoparietal network (FPN), salience network (SN). Key finding: low-frequency phase in DMN modulates high-frequency amplitude envelopes within FPN (phase-amplitude coupling). Analysis: local field potentials within intrinsic brain networks.
REFERENCE: Luo, Q. et al. "Oscillatory mechanisms of intrinsic human brain networks." NeuroImage (2024). DOI: https://doi.org/10.1016/j.neuroimage.2024.120702

33. Oscillations in Multi-Population Neural Networks (2024)
Process: Proof that odd inhibitory nodes + strong connections generate oscillations.
Physics Explanations: Strong - threshold-linear dynamics; balance for rhythmic emergence.
Source: eLife reviewed preprints.
PARAMETERS: Same study as Entry 31 (eLife reviewed preprint version). See Entry 31 for full parameters.
REFERENCE: See Entry 31. Zang, J. et al. eLife (2024). DOI: https://doi.org/10.7554/eLife.88777

34. Oscillatory Neural Network Benefits of Multisensory Learning (2018+)
Process: Sparse spatio-temporal encoding for multisensory integration.
Physics Explanations: Strong - oscillatory binding; phase synchronization across modalities.
Source: PMC (Rao 2018 extensions).
PARAMETERS: Model: oscillatory neural network with sparse spatio-temporal encoding. Validates neuroscience observations from Molholm et al. (2002) and Seitz et al. (2006). Demonstrates benefits of multisensory integration through oscillatory binding and phase synchronization across sensory modalities. Institution: Fairleigh Dickinson University.
REFERENCE: Rao, A.R. "An oscillatory neural network model that demonstrates the benefits of multisensory learning." Cognitive Neurodynamics (2018). DOI: https://doi.org/10.1007/s11571-018-9489-x

35. Model of Oscillatory Neural Network with Multilevel Neurons (2019)
Process: High-order synchronization metrics for pattern recognition/computing.
Physics Explanations: Strong - multilevel phase/frequency synchronization.
Source: MDPI Electronics (Velichko 2019).
PARAMETERS: Method: multilevel neuron model using high-order synchronization effects with family of special metrics. Output oscillator: multilevel variations in synchronization value with reference oscillator. Classification: input patterns classified into set of classes. Authors: Velichko, Belyaev, Boriskov (Petrozavodsk State University, Institute of Physics and Technology).
REFERENCE: Velichko, A. et al. "A Model of an Oscillatory Neural Network with Multilevel Neurons for Pattern Recognition and Computing." Electronics 8(1), 75 (2019). DOI: https://doi.org/10.3390/electronics8010075

36. Oscillatory Neural Networks Design via ML (2024)
Process: Backpropagation through time optimizes ONN circuits.
Physics Explanations: Strong - synchronization tuning for enhanced power.
Source: Frontiers in Neuroscience.
PARAMETERS: Same study as Entry 20. See Entry 20 for full parameters.
REFERENCE: See Entry 20. Rudner, T. et al. Frontiers in Neuroscience 18 (2024). DOI: https://doi.org/10.3389/fnins.2024.1307525

37. Computing with Oscillators: Theory to Demonstrators (2024)
Process: Formalism for ONN synchronization/computational capability.
Physics Explanations: Strong - Hopf/van der Pol; phase dynamics.
Source: Nature (Todri-Sanial 2024).
PARAMETERS: Same study as Entry 21. See Entry 21 for full parameters.
REFERENCE: See Entry 21. Todri-Sanial, A. et al. npj Unconventional Computing 1(1) (2024). DOI: https://doi.org/10.1038/s44335-024-00015-z

38. Oscillations as Fundamental Computational Mechanism (2025)
Process: Networks with oscillatory nodes outperform non-oscillatory ones.
Physics Explanations: Strong - oscillatory dynamics for robust processing.
Source: Human Arenas (Singer 2025).
PARAMETERS: Study type: simulation. Tested recurrent neural networks on standard pattern recognition benchmarks. Networks with oscillating units (HORNs) outperformed non-oscillatory RNNs in: parameter efficiency, task performance, learning speed, noise tolerance. Authors: Wolf Singer and Felix Eenberger. Explores 4 key differences between natural and artificial neural systems: recurrent connections, temporal computation, in-memory computation, analog computation.
REFERENCE: Singer, W. & Eenberger, F. "Oscillations in Natural Neuronal Networks; An Epiphenomenon or a Fundamental Computational Mechanism?" Human Arenas (2025). DOI: https://doi.org/10.1007/s42087-025-00478-x

39. Pulse-Driven Neural Architecture (PDNA) (2026)
Process: Learnable oscillatory dynamics in continuous-time RNNs.
Physics Explanations: Strong - independent internal oscillation; robust sequence handling.
Source: arXiv (2026).
PARAMETERS: See Entry 29. Specific 2026 PDNA paper not independently verified in public databases.
REFERENCE: See Entry 29.

40. Deep Oscillatory Neural Network (DONN) Extensions (2025)
Process: Convolutional oscillatory nets (OCNNs) for signal/image tasks.
Physics Explanations: Strong - complex-domain Hopf oscillators; oscillatory learning.
Source: Scientific Reports.
PARAMETERS: Same study as Entry 30. Extension to convolutional architectures (OCNNs). See Entry 30 for full parameters.
REFERENCE: See Entry 30. Rohan, N.R. et al. Scientific Reports 15, 40968 (2025). DOI: https://doi.org/10.1038/s41598-025-24837-4

41. Frequency-Domain Complex-Valued CNNs (2026)
Process: Fully complex-valued blocks for frequency-domain data.
Physics Explanations: Strong - consistent frequency operation; lightweight residual architecture.
Source: Expert Systems with Applications (Chakraborty 2026).
PARAMETERS: Architecture: lightweight fully complex-valued residual CNN operating entirely on complex data in frequency domain. Novel activation: Log-Magnitude activation function preserving phase information. Applications: frequency-domain signal/image processing. Authors: Chakraborty, Aryapoor, Daneshtalab (Malardalen University, Sweden).
REFERENCE: Chakraborty, M. et al. "Frequency Domain Complex-Valued Convolutional Neural Network." Expert Systems with Applications (2025). DOI: https://doi.org/10.1016/j.eswa.2025.128893

42. Frequency Transforms in Time Series Forecasting (2025)
Process: Fourier/wavelet in spikformer/SWformer for visual/time-series.
Physics Explanations: Strong - spectral features; multi-scale dependencies.
Source: arXiv (Wang/Fang 2025).
PARAMETERS: FWformer (Wang et al.): replaces traditional self-attention in Spikformer with spike-form Fourier/Wavelet transforms using fixed triangular or wavelet bases. SWformer (Fang et al. 2024): spiking wavelet transformer capturing spatial-frequency characteristics via spike-driven wavelet approach. Applications: visual classification, time series forecasting.
REFERENCE: Wang, J. et al. "Fourier or Wavelet bases as counterpart self-attention in spikformer for efficient visual classification." Frontiers in Neuroscience (2025). DOI: https://doi.org/10.3389/fnins.2024.1516868 | Survey: arXiv:2504.07099

43. Accelerating Inference in Frequency Domain (2024)
Process: Sparse frequency parameters speed up networks.
Physics Explanations: Strong - frequency sparsity exploitation.
Source: ACM (2024).
PARAMETERS: Method: complete inference chain in frequency domain (dual to spatial domain). Transform: discrete cosine transform (DCT) applied to learning kernel of each layer. Non-linearity: non-linear operations applied directly on frequency data. Key insight: networks' frequency-domain parameters are naturally sparse, enabling acceleration. Distinguishes high-frequency from low-frequency signals.
REFERENCE: "Accelerating Inference of Networks in the Frequency Domain." Proc. 6th ACM International Conference on Multimedia in Asia (2024). DOI: https://doi.org/10.1145/3696409.3700171 | arXiv:2410.04342

44. Frequency-Adaptive Interpretable Neural Networks (2025)
Process: Continuous wavelet convolution + DWT for time-series.
Physics Explanations: Strong - adaptive frequency resolution.
Source: JCDE (Fenghao 2025).
PARAMETERS: Architecture: Wavelet Convolution Intelligent Diagnosis Network (WCIDN). Components: continuous wavelet convolution + discrete wavelet transform (DWT). Dynamic kernel mechanism: collaborative optimization of frequency kernel, channel kernel, and filter kernel. Application: intelligent fault diagnosis of high-speed motor bearings. Addresses: feature distribution drift, noise interference, interpretability.
REFERENCE: Sun, F. et al. "A frequency-adaptive and interpretable neural network for intelligent fault diagnosis of high-speed motor bearings." J. Computational Design and Engineering 12(7), 113-128 (2025). DOI: https://doi.org/10.1093/jcde/qwaf059

45. Continual Learning in Frequency Domain (2024)
Process: Frequency-aware methods preserve knowledge across tasks.
Physics Explanations: Partial - spectral regularization.
Source: NeurIPS (Liu 2024).
PARAMETERS: Framework: Continual Learning in the Frequency Domain (CLFD). First study utilizing frequency-domain features to enhance CL training on edge devices. Improves performance and efficiency. Code: https://github.com/EMLS-ICTCAS/CLFD. Published in: Advances in Neural Information Processing Systems 37, pp. 85389-85411 (2024).
REFERENCE: Liu, R. et al. "Continual Learning in the Frequency Domain." NeurIPS 2024. https://proceedings.neurips.cc/paper_files/paper/2024/hash/9b224ace8963c9385ad5e2b5c9039b97-Abstract-Conference.html

46. Frequency Domain Methods in RNNs for Speech (2010s-2020s)
Process: FFT-based processing in recurrent nets.
Physics Explanations: Strong - spectral efficiency.
Source: Fraunhofer publica.
PARAMETERS: General approach: applying FFT-based processing within recurrent neural network architectures for speech recognition/synthesis. Converts time-domain speech signals to frequency-domain representations for more efficient processing. Institutions: Fraunhofer Institute and various speech processing labs. Specific Fraunhofer publication details not independently verified.
REFERENCE: Not publicly available as specific DOI. General references in Fraunhofer publica repository. Related: various speech processing publications using frequency-domain RNNs.

47. Frequency Domain Neural Network for Image Super-Resolution (2010s-2020s)
Process: CNN-FFT hybrid for fast SR.
Physics Explanations: Partial - frequency-domain upsampling.
Source: GitHub junxuan-li.
PARAMETERS: Architecture: frequency-domain CNN using Hartley transform (avoids complex numbers). Mechanism: convolution theorem casts spatial convolutions as products in frequency domain. Non-linearity: rectifier unit cast as convolution in frequency domain. Training: standard backpropagation. Performance: 1-2 orders of magnitude faster than spatial-domain alternatives with imperceptible quality loss. Code: https://github.com/junxuan-li/A-frequency-domain-neural-network-for-fast-image-super-resolution
REFERENCE: Li, J. et al. "A Frequency Domain Neural Network for Fast Image Super-resolution." IJCNN 2018. arXiv:1712.03037

48. Harmonic Generation Boosted by Nanoscale BICs (2019+)
Process: Metasurfaces enhance nonlinear frequency conversion.
Physics Explanations: Strong - bound states in continuum resonance.
Source: Phys. Rev. Research.
PARAMETERS: Same foundational study as Entry 15. See Entry 15 for full parameters.
REFERENCE: See Entry 15. Carletti, L. et al. Physical Review Research 1(2), 023016 (2019). DOI: https://doi.org/10.1103/PhysRevResearch.1.023016

49. Programmable Circuits for Analog Matrix Computations (2025)
Process: Microwave-integrated circuits for wave-based matrix ops.
Physics Explanations: Strong - high-frequency EM waves; analog parallelism.
Source: Nature Communications.
PARAMETERS: Device: 4-port microwave-integrated circuit. Frequency range: 1.5-3.0 GHz. Power level: hundreds of micro-Watts. Architecture: alternating non-reconfigurable and reconfigurable layers of RF components (cascaded power dividers + programmable phase elements). Operation: universal unitary matrix transformations via controllable multipath interference with active phase control. Institutions: Univ. of Technology Sydney, Rochester Institute of Technology.
REFERENCE: Keshavarz, R. et al. "Programmable circuits for analog matrix computations." Nature Communications (2025). DOI: https://doi.org/10.1038/s41467-025-63486-z

50. Back to Analog: Light-Speed Wave Computing (2025)
Process: Programmable microwave circuits harness waves for matrix transforms.
Physics Explanations: Strong - light-speed analog processing; low latency.
Source: TechXplore (Miri 2025).
PARAMETERS: Same study as Entry 49. See Entry 49 for full parameters. Popular science coverage of Keshavarz/Miri et al. Nature Communications paper.
REFERENCE: See Entry 49. TechXplore coverage: https://techxplore.com/news/2025-10-future-analog-horizon.html

51. Neuromorphic Photonic Computing with Chaotic Frequency Combs (2025)
Process: Nonlinear microresonators for optical neuromorphic processing.
Physics Explanations: Strong - chaotic frequency combs; high-speed low-power.
Source: Phys. Rev. Research (Shishavan 2025).
PARAMETERS: Platform: optical microresonator with chaotic frequency comb formation. Method: delay-line-free reservoir computing using chaotic optical frequency comb as nonlinear reservoir. Performance: accurate prediction of ~1000 symbols in chaotic time series. No dedicated task-specific optimization required. Authors: Shishavan, Manuylovich, Kamalian-Kopae, Perego.
REFERENCE: Shishavan, N.S. et al. "Optical neuromorphic computing based on chaotic frequency combs in nonlinear microresonators." Phys. Rev. Research 7, L042008 (2025). arXiv:2501.17113