Wave

Powerful technologies labeled ``AI''-without sufficient epistemic caution-are already reshaping political and private life, bringing both new dangers and new opportunities for citizen participation. These range from electoral and legislative engagement to the most ambitious form: political co-creation through citizens' assemblies. Large Language Models (LLMs) could support such processes through moderation, translation, facilitation, summarization, and writing assistance. But this potential remains largely unrealized. The Democratic Commons project takes a fundamentally interdisciplinary approach-from philosophy to computer science-to evaluate LLMs against five proposed democratic principles. At its core, the project is driven by the question of political bias: under what conditions can LLMs be used democratically within forms of citizen participation that are them- selves still largely experimental? Addressing these socio-technical questions requires grounding in political theory and, more broadly, in philosophy-disciplines that provide the normative frameworks without which the democratic evaluation of AI systems cannot be mean- ingfully conducted.

Phase-resolving wave models such as FUNWAVE-TVD are the accuracy standard for nearshore dynamics, resolving the shoaling, refraction, and breaking of individual waves, but their cost rules them out for the ensembles, uncertainty quantification, and real-time warning that operational forecasting demands. Neural operators promise solver-level accuracy at a fraction of that cost, yet on wave-dominated fields the accurate ones are large: hybrid spectral-convolutional operators such as U-FNO (the strongest baseline in our study after DU-NO) buy their fidelity with tens of millions of parameters. We introduce DU-NO (Double U-shaped Neural Operator), a multiscale U-shaped spectral operator that attaches lightweight convolutional U-Net branches only at its two shallowest encoder and decoder levels. The placement follows a sampling argument: high-wavenumber content exists only on fine grids, so the local, full-band pathways go where that content lives, while the coarse, band-limited levels stay purely spectral. A depth-decaying mode schedule holds the model to 3.64M parameters, an order of magnitude below U-FNO. On our publicly released FUNWAVE-TVD benchmark, DU-NO attains the best autoregressive rollout error of six identically trained architectures, improving on U-FNO by 14.9% with 10.8x fewer parameters, and a frequency-band analysis shows the gain holds across all bands, including the high-wavenumber band where truncated-spectral operators collapse. Parameter-matched controls confirm the gain is architectural: rescaled to the same 3.6M budget, the best baseline still trails DU-NO by 28.6%. The advantage carries beyond nearshore waves: DU-NO matches the strongest baselines on 2D Navier-Stokes and wins clearly on PDEBench shallow-water rollouts. Code, trained models, and evaluation artifacts are available at https://anonymous.4open.science/r/duno-code-5A7B/.

Machine learning surrogates based on neural operators have shown broad applicability in solving forward PDE problems. However, eigenvalue problems, in which an eigenparameter and one of several valid eigenmodes must be simultaneously solved, remain difficult because standard operator learning formulations assume a unique input-output map. This work demonstrates that Fourier Neural Operators (FNOs), combined with wavelet-based encodings of PDE inputs, can learn and predict multiple eigenmodes of the elastic wave equation, corresponding to deformation modes of acoustic waves propagating through arbitrary metamaterial geometries. We provide a mechanistic explanation and experimental evidence for why wavelet encodings are well matched to the dual spatial-spectral structure of the FNO, enabling deterministic mode selection on both continuous-valued and binary-valued geometries within a single model, and for why prediction accuracy varies with geometric discontinuities. For metamaterial design, the resulting surrogate accelerates the simulation stage of the design cycle by three orders of magnitude relative to finite element analysis on a consumer-grade CPU, while preserving high fidelity. These results also carry broader implications for designing input encodings in other multi-mode PDE solvers based on spectral neural operators.

The research explores the pioneering integration of Physics-Informed Neural Networks (PINNs) into the domain of Ground-Penetrating Radar (GPR) data prediction. This research presents a detailed development framework for a specialized PINN model, proficient at interpreting and forecasting GPR data, much like how medical imaging models predict tumor behavior. By harnessing the synergy between deep learning algorithms and the physical laws governing subsurface structures or in medical terms, human tissues the model effectively embeds the physics of electromagnetic wave propagation into its architecture. This ensures that predictions not only align with fundamental physical principles but also mirror the precision needed in medical diagnostics for detecting and monitoring tumors. The suggested deep learning structure comprises three components: a CNN, a spatial feature channel attention (SFCA) mechanism, and ConvLSTM, along with temporal feature frame attention (TFFA) modules. The attention mechanism computes channel attention and temporal attention weights using self-adaptation, thereby fine tuning the visual and temporal feature responses to extract the most pertinent and significant visual and temporal features. By integrating physics directly into the neural network, our model has shown enhanced accuracy in forecasting GPR data. This improvement is vital for conducting effective assessments of bridge deck conditions and other evaluations related to civil infrastructure. The use of Physics Informed Neural Networks (PINNs) has demonstrated the potential to transform the field of Non-Destructive Evaluation (NDE) by enhancing the precision of infrastructure deterioration predictions. Moreover, it offers a deeper insight into the fundamental mechanisms of deterioration, viewed through the prism of physics-based models.

Architecture category. Hybrid method: a physics-based analytical pencil-beam (PB) dose engine followed by a 3-D convolutional residual-correction network (RepVGG-U-Net). We addressed the DoseRAD2026 proton dose-prediction task with PyDoseRT Proton, a GPU-accelerated engine implemented in PyTorch and augmented by a learned residual toward Monte Carlo (MC) accuracy. A double-Gaussian PB kernel was calibrated to GATE/Geant4 integrated depth doses in water in two stages: a classical per-energy curve fit, then a gradient-based fit of the full 3-D dose through the PyTorch physics engine as it retains a differentiable execution path for gradient-based optimization of dose-dependent objectives. The engine computes each beamlet on a beam's-eye-view (BEV) lattice with variance-preserving Gaussian splitting, an analytic nuclear halo, and a Fermi-Eyges heterogeneity term, then rotates the result into the patient frame. Additionally, a compact residual U-Net predicts an additive correction in BEV space. It is conditioned on voxelwise material-label embeddings, a discrete energy embedding and spot size. The same model was used for all anatomical sites (thoracic and abdominal). It was trained with a patient-space L1 objective emphasizing the scored high-dose region and multi-scale BEV deep supervision. The submitted CT configuration obtained preliminary-test beamlet MAE 0.0066, image-z IDD distance 0.0025, plan MAE 0.0049, 98.30% gamma pass rate (1%/1 mm), and DVH error 0.460.

Reconstructing oscillatory wave fields from scattered sensors is a severely underdetermined inverse problem. Beyond the challenges of general physical-field reconstruction, wave responses are complex-valued, frequency-sensitive, and highly oscillatory, while costly simulation and sensing often leave only extreme-sparse observations. Existing low-rank, operator, and diffusion approaches are largely designed for real-valued, smoother fields; dense pixel-space diffusion is particularly inefficient for oscillatory complex fields and difficult to scale to 3D. We propose HarmoCore, which places a generative prior in a compact, continuous, and structured wave-field latent. HarmoCore represents joint real--imaginary channels with Functional Tucker cores over shared continuous spatial bases, learns a frequency-conditioned core diffusion prior, and performs Diffusion Posterior Sampling directly in core space. At fixed sensor coordinates, the multilinear decoder induces an explicit likelihood guidance operator, avoiding dense pixel-space correction. Optional target-equation residual guidance further promotes physical consistency. Experiments on 2D Helmholtz, 2D synthetic wave fields, and 3D Helmholtz show substantial gains under 1%--2% sensing while remaining practical in three dimensions.

Conventional neural networks learn predominantly through affine transformations followed by nonlinear activations, while elapsed time is often treated as an auxiliary feature or assumed to be uniformly sampled. This paper introduces Wave Function Backpropagation (WFB), a wave-parameterized learning formulation in which neural responses are represented by learnable amplitude, wavenumber, angular frequency, and phase. The formulation associates an observed state with its temporal interval Delta t through the phase of a differentiable spatiotemporal wave. We derive standard WFB gradients and a spatial-curvature correction based on the Laplacian of the wave response. WFB is instantiated in a deliberately feed-forward trajectory predictor to provide a controlled proof of concept; sequence learning is outside the scope of the present evaluation. With motion features, STD-WFB using real intervals reduces average displacement error (ADE) by 20.4% relative to the original FFN baseline. In a new position-only evaluation that removes temporal leakage through precomputed velocity and acceleration, real-interval WFB reduces ADE by 10.4% relative to the original FFN and remains competitive with parameter-matched ReLU controls, obtaining 2.1% lower mean ADE than the matched FFN with explicit Delta t. Shuffled-interval WFB attains the lowest mean ADE, indicating that the present evidence supports the effectiveness of the wave representation but does not attribute the gain to interval alignment. These results establish WFB as a viable structured feed-forward learning formulation and define a clear basis for subsequent architectural studies.

The sound speed profile in the deep Arctic Ocean causes the surface layer to form a normal mode waveguide. When the depth of the sound source or receiver is near a node of the eigenfunction, the source cannot excite the mode, or the receiver cannot detect it, resulting in the modal amplitude at the receiver being approximately zero. This manifests as a dispersion interruption in the dispersion structure, which can be observed through time-frequency analysis of the received acoustic signal. Based on the interruption frequency identified from the received signal, combined with the relationship between node depth and modal frequency calculated from the ocean sound speed profile, the source depth can be estimated if the receiver depth is known. The phenomenon of dispersion interruption and the method of estimating source depth have been validated through simulations and experiments.

Future wireless systems are expected to transform the surrounding space from a passive propagation medium into a smart electromagnetic environment, where engineered surfaces control wave propagation, support wireless sensing, and create programmable electromagnetic fingerprints. A key challenge in realizing this vision is the inverse design of metasurfaces for tailored electromagnetic propagation. While forward analysis evaluates the response of a known geometry, the inverse task starts from a prescribed scattering signature and seeks a physically realizable structure that produces it. This inverse task is inherently nonlinear and often high-dimensional, while candidate solutions may be non-unique and provide no direct indication of practical realizability. Here, we introduce a conditional diffusion framework for inverse design of dielectric resonator metasurfaces from target angular scattering patterns. Trained on T-matrix simulated geometry-response pairs, the model learns a conditional distribution of geometries instead of a deterministic mapping, enabling multiple candidate designs for the ill-posed inverse problem. The best generated metasurface achieves a mean percentage error of 1.39%, outperforming CMA-ES optimization (4.1% after 10 h) while requiring only about one minute for after-training inference. The model also produces lower error distributions than deterministic neural baselines for out-of-distribution spectra, highlighting the potential of diffusion models for efficient metasurface design.

Neural operators provide fast surrogates for partial differential equation (PDE) solvers, but their reliability can degrade for high-dimensional spatial inputs and inverse or repeated inference. State-only training constrains solution values but not the learned input--output response. We study sensitivity-constrained neural operators (SC-NOs), which augment standard training with sampled solver-derived Jacobian supervision. Selected sensitivities from differentiable solvers or discrete adjoints are matched during training, allowing response information to be amortized across minibatches without imposing the full Jacobian at every update. We evaluate SC-NO on advection--diffusion and RANS--Spalart--Allmaras benchmarks, input-dimensionality scaling tests, long-horizon autoregressive rollout, and a shallow-water Tohoku tsunami source-inversion case. Sensitivity supervision improves forward prediction and yields larger gains in gradient-based inverse reconstruction of distributed fields. Scaling experiments show an improved accuracy--cost tradeoff for high-dimensional gridded inputs, while ablations indicate that state values and Jacobian information provide complementary supervision. In the tsunami case, SC-FNO reconstructs gridded seafloor deformation from sparse early gauge observations and forecasts subsequent wave propagation in a near-real-time proof-of-concept workflow. These results support sampled sensitivity supervision as a practical way to improve neural PDE surrogates when forward accuracy, inverse stability, robustness, and computational cost must be considered together.

Advancing autonomy for surface vessels requires systematic evaluation of their sensing and perception subsystems. Yet, maritime environments impose unique challenges: sensor installation is constrained by vessel layout, environmental conditions such as fog or sea clutter are difficult to reproduce, and long-duration missions complicate data collection. This work addresses the question: How can we design a modular and reproducible sensor platform for maritime autonomy? We present a comprehensive design blueprint that incorporates diverse modalities - RADAR, LiDAR, IMU, GNSS, AIS, RGB and LWIR cameras, and weather sensors - to enhance environmental awareness and vessel proprioception. Supported by a dedicated ROS2-based software framework for data management, our modular platform enables long-term data collection, hardware-in-the-loop testing, and integration with existing sensors and algorithms. By unifying hardware design and data capture methodology, the platform enhances reproducibility and comparability across vessels and research projects. The proposed framework bridges engineering implementation and research methodology, providing the foundation for standardized, verifiable datasets essential to advancing situational awareness and autonomous maritime navigation.

Strictures caused by esophageal cancer can narrow down the esophageal lumen, leading to dysphagia. Palliation of dysphagia has driven the development of a Robotic Soft Esophagus (RoSE), which provides a novel in vitro platform for esophageal stent testing and food viscosity studies. In RoSE, peristaltic wave generation and control were done in an open-loop manner since the conduit lacked visibility and embedded sensing capability. Hence, in this work, RoSE version 2.0 (RoSEv2.0) is designed with embedded Time Of Flight (TOF) and pressure sensors to measure conduit displacement and air pressure, respectively, for modeling and control. Model Predictive Control (MPC) of RoSEv2.0 is implemented to govern the peristalsis and air pressure profile autonomously. The implemented MPC used Sparse Identification Nonlinear Dynamics with Control (SINDYC) models to estimate the future states of ROSEv2.0. The dynamic models are discovered from the TOF and pressure sensor data. Peristalsis waves of speed 20 mm/s, wavelength 75 mm, and amplitudes 5, 7.5, and 10 mm were successfully generated by the MPC. Additionally, RoSEv2.0 with the MPC was employed to perform stent migration testing with various food bolus consistencies. The major contribution claimed in this paper is the application of SINDYC-based MPC to solve the closed-loop control problem of RoSE for achieving desired peristaltic waves.

Designing an effective electromagnetic inverse-scattering solver requires faithful enforcement of nonlinear full-wave physics together with an expressive prior on the unknown permittivity contrast. We propose ScoreField, a neural inverse scattering framework that integrates coupled implicit neural representations (INRs) with a pretrained score-based generative prior. ScoreField employs two INRs to parameterize the permittivity contrast and the induced current fields, and jointly optimize them under the Lippmann-Schwinger equations. In addition to the implicit regularization by the INR architecture, the score model provides a learned prior gradient on the contrast, which is propagated to the contrast INR through the chain rule. This formulation enables ScoreField to effectively handle strong multiple scattering, where nonlinear wave interactions require accurate modeling of the coupled full-wave physics. We evaluate ScoreField on simulated weak- and strong-scattering benchmarks, the canonical Austria phantom, and experimental Fresnel measurements. We note that ScoreField significantly improves reconstruction fidelity and suppresses artifacts relative to classical full-wave methods and deep learning baselines, achieving an average PSNR improvement of $1.8 \, \mathrm{dB}$ over the best competing method on real Fresnel data.

Disordered traffic flow is characterized by weak or non-existent lane discipline in the presence of strong vehicle heterogeneity and continuous lateral interactions, challenging traditional lane-based modeling assumptions. This study presents an empirical study of macroscopic and microscopic aspects of disordered traffic using high-resolution UAV trajectory data collected on an urban arterial. A two-dimensional extension of Edie's framework is applied to quantify aggregate traffic variables and produce a two-dimensional fundamental diagram, revealing that traffic states cannot be adequately represented using one-dimensional formulations and highlighting the persistent role of lateral redistribution. The propagation of congestion is estimated directly from the spatiotemporal speed fields, demonstrating the emergence of coherent stop-and-go waves and showing a similar dynamics as conventional lane-based flow, in spite of the heterogeneous vehicle interactions. At the microscopic level, steady-state follower-leader identification is used to examine desired time gaps and minimum lateral spacing, vehicle dimension distributions, and kinematic characteristics, revealing pronounced inter-class heterogeneity that explains disordered traffic behavior. The study provides an empirical framework linking vehicle-level interactions and aggregate traffic dynamics and establishes a data-driven basis for the calibration and validation of traffic models for disordered mixed traffic systems.

Electroencephalography (EEG) is widely used to diagnose neurological conditions, but its analysis usually relies on either predefined spectral features or deep neural networks. Predefined features carry a strong bias, since they fix in advance what counts as informative, while deep neural networks and foundation models are hard to interpret and need large amounts of data and compute. We present bag-of-waves, an interpretable framework that learns a small dictionary of recurring EEG waveform templates, called atoms, using shift-invariant k-means without labels. The continuous EEG is then turned into a sequence of atom tokens, whose counts feed a simple downstream classifier or clustering step. We extend this representation in two ways: we add atom-to-atom transitions, which we call n- grams, to capture temporal structure, and we move from single-channel atoms to regional and cross-channel spatial atoms for the multichannel case. We test the method on three complementary datasets, each probing a different aspect: single-channel mouse genotype clustering with only sixteen animals (the low-data and temporal case), resting-state dementia classification (the spatial case), and the TUEV benchmark, a six-way classification of clinical EEG events (a high-data comparison against strong deep and foundation baselines). Across all three datasets, bag-of-waves achieves performance competitive with state-of-the-art deep and foundation models. Yet, it operates with a fraction of the parameter count and provides full interpretability: because every atom corresponds to an inspectable waveform, the method explicitly recovers known clinical morphologies that a neurophysiologist can directly validate. Its main advantage is that it works in the low-data regime where heavier models are a poor fit.

The Helmholtz equation governs time-harmonic wave propagation, and in dissipative media a complex modulus renders its squared wavenumber $κ^2$ complex. Inferring such fields from sparse, noisy data calls for solvers that also quantify their own uncertainty. Physics-informed Gaussian-process (GP) regression supplies this by returning a posterior over the solution, yet operator-conditioned formulations have been developed almost exclusively for real-valued fields. We extend operator-informed GP regression to complex-valued Helmholtz problems by realifying the complex operator into an equivalent coupled real block, which enables inference with standard real-valued GP conditioning. The construction admits a family of priors, from a proper diagonal prior to coregionalized and multiscale variants, and conditions on PDE residuals and boundary traces. On benchmark problems in one to three dimensions, the solver is competitive with finite-difference and neural-network baselines at a far smaller interior-constraint budget. Unlike those deterministic baselines, it returns a posterior over the complex wavefield rather than a point estimate. Applied to \textit{in vivo} brain magnetic resonance elastography, a proper multiscale prior reconstructs the shear curl field to a correlation of $0.77$ with measurement, above a $0.75$ target. The gain arises from the multiscale kernel rather than from real--imaginary coupling. We further identify a low-frequency accuracy ceiling set by model mismatch and a posterior uncertainty that is not yet calibrated. Calibrated uncertainty therefore emerges as the central next step for probabilistic wavefield inference in dissipative media.

High deployment cost, poor spatial coverage and susceptibility to storm conditions are all challenges faced by traditional in-situ methods. This paper presents a video-based and high performance computing (HPC) enabled deep learning framework for joint sensor free estimation of five coastal wave parameters, namely significant wave height (Hs), maximum wave height (Hmax), peak period (Tp), zero upcrossing period (Tz) and wave direction (theta) from monocular coastal video. The proposed architecture comprises of a V-JEPA (self supervised) ViT Small backbone for robust spatiotemporal feature extraction in visually challenging scenarios, a dual-stream SlowFast temporal encoder for broad bandwidth representation of wave motion in both hydrodynamic breaking and swell regimes, an optical flow stream based on Farneback optical flow algorithm for adding saliency information to the structure with emphasis on hydrodynamically active wavelength bands of waves, and a multi-task regression layer with dispersion constraints (Airy wave dispersion lambda_p = 0.1). The model was trained on an NVIDIA DGX A100 cluster and was early stopped at epoch 31 and achieved Pearson correlation coefficients of 0.451, 0.578, 0.643, 0.680 and 0.832 for Hs, Hmax, Tp, Tz and wave direction respectively, with generalization ability to geographically diverse held out test data sites. While operating in a data-limited regime (6 annotated training scenes), the framework demonstrates statistically significant temporal correlations (PCC of 0.451 to 0.832), confirming proof of concept feasibility; R2 values (max 0.246) indicate that variance capture will improve with larger annotated datasets.

Seismic wavefield simulation is fundamental to seismology, but conventional finite-difference (FD) methods remain limited by numerical dispersion and stability constraints, which often require dense spatial grids and small time steps and thereby severely limit the effectiveness of iterative inversion workflows. We introduce a conditional diffusion-based wavefield propagator that advances seismic wavefields recursively from one time step to the next. Instead of learning an unconditional data distribution of wavefield evolution, the model is conditioned by a short history of recent wavefield time steps (snapshots), the velocity model, and the wavefield time step index, allowing it to represent the conditional transition between adjacent physical states. By training the network to directly predict the clean next wavefield snapshot, this strong physical conditioning makes it possible to replace the iterative reverse diffusion process with a single network evaluation for each predicted snapshot. To improve stability over long recursive rollouts, we further introduce a causal time-weighted loss, in which adaptive weights, accumulated as exponential moving averages of per-snapshot training errors, emphasize training directions that are consistent with the forward propagation sequence and reduce the amplification of one-step prediction errors. Because the learned propagator is tied to the temporal spacing of the training snapshots rather than to the FD stability limit, it can advance the wavefield using a physical time step ten times larger than that required by the underlying solver. Experiments on the Overthrust, SEG/EAGE, and Marmousi models show that the proposed method accurately reproduces wavefield snapshots and shot gathers and achieves an end-to-end speedup of 2.17 x over a GPU-accelerated tenth-order staggered-grid FD implementation under matched hardware conditions.

Tactile sensing is central to how robotic systems interact with the real world, yet current solutions face a tradeoff between sensing area and system complexity. This work investigates metallic ultrasound waveguides as distributed tactile sensors fully interrogated from a single proximal transducer. Using cylindrical indenters, we characterized the acoustic response to single and multi-point contacts with varying forces and contact materials. For single point indentation, the applied force was well captured by a linear relationship with the ratio of the reflection to transmission coefficients (F = a * R/T) across all nine tested materials (R2 >= 0.95). The calibration slope, a, correlated strongly with the material's effective contact modulus (log--log Pearson r=-0.98). The reflected energy partition was found to be a load-independent parameter related to the contacting material's properties, enabling material classification independent of force. For the two-indenter experiment, both contact forces were recovered from the waveguide signal and were in close agreement with reference load cell measurements (contact 1, R2 = 0.97; contact 2, R2=0.95). The approach was extended to two-dimensional metallic sheets, confirming both contact localization and material-dependent effects. Overall, these results validate metallic waveguides as a robust platform for distributed tactile sensing, providing contact localization, force estimation, and material-class discrimination for the contacting body.

We introduce a physics-constrained neural network for the rapid prediction of rigorous coupled-wave analysis outputs in the form of Jones matrices. Starting from energy conservation in lossless layered periodic structures, we use the fact that the scattering outputs lie on a Stiefel manifold. This energy constraint is enforced as a hard condition by projecting onto the manifold using differentiable symmetric orthogonalization. The resulting surrogate enforces energy conservation by construction while preserving differentiability for gradient-based inverse design. The performance and generality of the proposed approach are demonstrated through the inverse design of a diffractive waveguide combiner for augmented reality glasses.

Gradient-based inverse lithography technology~(ILT) for extreme ultraviolet~(EUV) masks is presented. A novel framework treats the differentiable waveguide method and the recently proposed waveguide neural operator~(WGNO) as end-to-end physics engines, recovering the permittivity of the absorber of the mask through automatic differentiation of the full forward diffraction model. Numerical experiments on realistic 2D and 3D absorbers of the mask (TaBN, La, U) at $λ{=}11.2$~nm show that the considered ILT methods make it possible to obtain a mask structure that achieves the desired field on the wafer.

Traditional time-domain prediction of vessel motions in irregular waves usually relies on superposing responses from many regular-wave components, which is computationally expensive for long-duration simulation and real-time applications. This issue is particularly relevant to unmanned surface vehicles (USVs), for which efficient and realistic motion prediction is needed for seakeeping assessment, simulation-based testing, and control-system development. This study applies an impulse response function (IRF)-based time-domain framework to predict vessel motions in short-crested irregular waves. Froude-Krylov, diffraction, and radiation loads are obtained from frequency-domain analysis and transformed into the time domain. Instantaneous responses are then evaluated directly through convolution-based force reconstruction, reducing the need for repeated regular-wave simulations. Weak nonlinear restoring effects are included by instantaneous wetted-surface pressure integration, and directional wave spectra are used to represent realistic sea states. The framework is validated against model-test measurements of an offshore supply vessel in long-crested beam irregular waves and full-scale measurements of a USV operating in real sea conditions. Predicted significant amplitudes, mean zero-crossing periods, standard deviations, and motion time histories agree well with measurements. The effect of directional-spectrum discretization is also examined. Results show that motion amplitudes are moderately sensitive to directional resolution, whereas motion periods are relatively insensitive. A 30 deg directional interval provides a practical balance between prediction accuracy and computational cost. The proposed framework offers an efficient tool for high-fidelity time-domain prediction of USV motions in realistic directional irregular seas.

We investigate a structure-first approach to dynamical learning in which the organization of stateful interactions is prescribed explicitly rather than left entirely to a generic recurrent parameterization. We introduce causal recurrent units built from an ordered sequence of local, state-modulated transformations. The construction is motivated by wave-based interaction models, but the units studied here do not impose scattering, passivity, or energy-balance constraints. Because fixed recurrent dynamics, designed reservoir topologies, readout-only learning, and recurrent depth are already well established, the empirical question is deliberately narrower: does the proposed interaction organization provide a useful inductive bias under controlled computational conditions? We compare a one-layer structured model, a two-layer structured model, and a generic echo-state network (ESN), all with 12 recurrent states and the same strictly linear ridge readout. Each model family receives the same random-search budget on calibration data that are disjoint from the final test data, after which the selected hyperparameters are frozen. On a custom nonlinear identification task, the one-layer structured model attains a mean validation NMSE of 2.76 x 10^{-4}, compared with 3.19 x 10^{-4} for the two-layer model and 3.94 x 10^{-4} for the ESN. On NARMA10 the ordering reverses: the ESN attains 0.312, compared with 0.348 and 0.357 for the one- and two-layer structured models. Thus, the proposed organization can be competitive and advantageous on one task, but it is not universally superior; moreover, recurrent depth does not provide a systematic benefit under matched state dimension. The results support a task-dependent interpretation of structural inductive bias and position the present architecture as a controlled precursor to stronger wave- and system-theoretic constructions.

Artificial dynamic tactile sensing requires sensitivity, robustness, and compliance, yet existing technologies face trade-offs when scaling to large-area arrays, compounded by wiring complexity and cost. Here, we report a passive distributed paradigm using deep sub-wavelength acoustic waveguides that decouples performance from structural flexibility. Elastic-membrane-capped Helmholtz resonators interconnected by spring-reinforced microtubes form an enclosed network with invariant acoustic transmission under macroscopic bending. By sparsely embedding microphones, the system achieves real-time localization (4 mm highest spatial resolution; >99% accuracy in a 4 microphones 64-node sensing array) and waveform reconstruction of low-frequency signals (<100 Hz). Fast Continuous Wavelet Transform and a lightweight neural network enable inference within 5.5 ms. We demonstrate conformable prototypes-fingertip arrays, a tactile glove, and large-area skins-detecting stimuli from single-hair contact to 5-mg particle impacts, arterial pulse waves, feather touches, and finger contact. This establishes a scalable, flexible, low-cost paradigm for next-generation human-machine interfaces.

Acoustic metamaterial (AMM) inverse design is particularly challenging for broadband target responses due to acoustic dispersion: a structure that matches the desired response at one frequency may deviate at others, and modifying geometry to improve one sub-band often perturbs neighboring sub-bands. Yet existing broadband inverse-design approaches are either constrained by predefined templates, or rely on image representations that fail to preserve the geometric precision and structural connectivity required by acoustic structures. We present MetaSeq, a physics-guided, sequence-based generative framework for acoustic metamaterial inverse design. At its core, MetaSeq introduces a language that represents each AMM as a structured sequence, rather than as a pixel grid or fixed template. This representation preserves precise geometry, explicitly encodes connectivity, and casts inverse design as a sequence-to-sequence task from target response to structure sequence. MetaSeq further constructs a balanced, high-fidelity dataset with efficient calibration and complexity-based sampling. To address the one-to-many nature of inverse design, MetaSeq combines supervised pretraining with reinforcement learning fine-tuning guided by a physics-based solver and validity checker. Extensive evaluations against COMSOL and five baselines show that MetaSeq reduces response error by 45% over the best baseline.

Metasurfaces enable precise manipulation of electromagnetic waves for applications such as beam steering, sensing, and stealth technology. However, inverse design of metasurfaces with targeted EM responses remains challenging due to the computational expense of iterative full wave simulation driven optimization and the limited conditioning fidelity and diversity of existing generative approaches. To address these challenges, this paper presents a generative inverse design framework for controllable and physically consistent metasurface synthesis under continuous spectral constraints. The proposed approach employs a progressively growing Wasserstein generative adversarial network with gradient penalty integrated with feature wise linear modulation based conditioning for stable propagation of continuous spectral and fabrication constraints. EM consistency is embedded directly into the generative learning process through a surrogate assisted spectral alignment loss, enabling physics constrained generation during training. Further, a determinantal point process based diversity regularization strategy is incorporated to generate geometrically diverse yet spectrally consistent realizations for the same target response. The effectiveness of the proposed framework is demonstrated through the generation of practically realizable metasurface absorbers exhibiting diverse reflection characteristics in the frequency range of 2 to 18 GHz. EM simulations validate that the generated designs meet the target specifications with high accuracy. The final proposed framework achieved an average mean squared error of 0.0052, diversity score of 0.8730, band alignment accuracy of 0.8533, and a valid EM design generation percentage of 89.57, clearly demonstrating its capability to generate highly accurate, diverse, electromagnetically consistent and fabrication realizable metasurface configurations.

We address the challenge of engineering distributed haptic displays capable of reproducing multiple localized, independently addressable vibrations -- representing virtual tactile pixels -- at arbitrary locations on a surface. Our technique is based on the focusing of mechanical waves in a flexural plate using a sparse set of actuators. At tactile frequencies, wave diffraction prevents the formation of localized virtual tactile pixels at spatial scales relevant for multi-digit touch interactions. We overcome this limitation by augmenting the plate with a lattice of mechanical resonators, forming a locally resonant metamaterial plate. Coupling between the plate's dynamic modes and those of the resonators alters the dispersion relation governing wave transmission, introducing a slow-wave branch that enables focusing beyond the diffraction limit imposed by the unmodified plate. We use numerical simulations to engineer the dispersion relation of the metamaterial system for high-resolution focusing at tactile frequencies. We then fabricate a metamaterial tactile display and experimentally demonstrate virtual pixels that are far more localized than those generated on an otherwise identical plate without resonators, resulting in a tenfold reduction in virtual-pixel area. In behavioral experiments, we show that this system can deliver perceptually localized single- and multi-point tactile feedback and moving tactile sources while maintaining independent control over temporal waveforms at multiple display locations. The methods reported here can enable high-resolution haptic displays for widespread applications using a small number of actuated degrees of freedom.

Neural field surrogates can accelerate photonic design loops, but a surrogate that looks accurate in global field error can still mis-rank candidate devices when the final decision depends on localized output-port readouts. This risk is acute in propagation-dominated MMI splitters and couplers, where port power, splitting, phase, and coupling are determined by accumulated modal interference and output-window aggregation rather than by average field similarity alone. We study this field-to-design mismatch through a Field/Mediator/Readout view that separates dense complex-field error from propagation-profile and output-window errors before port aggregation. To align the surrogate with this chain, we propose PaNO, a propagation-aligned neural operator that keeps the full-field prediction interface while organizing latent states around local boundary structure, transverse modal content, axial propagation, and cross-mode interaction. We also evaluate PaNO-R2, an output-aware feedback variant for residual field components near the port region. On a 15-wavelength tunable $3{\times}3$ MMI benchmark with 4608 held-out fields, PaNO lowers NeurOLight's port-power error from 0.2018 to 0.0739 despite slightly higher cMAE, showing that global field accuracy alone is not sufficient for design-relevant readout fidelity. PaNO-R2 attains the best cMAE, propagation-profile error, output-profile error, and port-power error, reducing NeurOLight's port-power and output-profile errors by 72.7% and 72.5%.

Full waveform inversion (FWI) reconstructs heterogeneous material properties from receiver data but remains computationally demanding. Physics-informed neural networks (PINNs) and their domain-decomposed variants (FBPINNs) offer a mesh-free alternative but face convergence challenges when representing complex velocity fields. We present a hybrid quantum-classical FBPINN for acoustic FWI, bringing together quantum computing and classical machine learning, in which the decomposed wavefield network and the global velocity network are implemented as classical-to-quantum pipelines terminating in parameterized quantum circuits (PQCs). The PQCs are realized as differentiable JAX statevector simulators, enabling end-to-end automatic differentiation through the classical PINN, the quantum circuit, and the physics-informed loss. On a geophysical anomaly benchmark, the quantum hybrid reaches a lower L1 velocity error than the primary classical FBPINN baseline in approximately 8x fewer training iterations, despite using approximately 33% fewer trainable parameters, and it outperforms all 15 classical hyperparameter variants tested. A second benchmark (checkerboard) demonstrates the generality of the inversion pipeline, confirming that the quantum hybrid architecture can recover structured spatial variations beyond the localized anomaly benchmark. Our framework is broadly applicable to wave-based inverse problems beyond geophysics, including medical ultrasound tomography and non-destructive evaluation.

We study cross-subject emotion recognition from EEG, a practically important yet challenging problem in brain-computer interfaces. Unlike tasks with clear waveform signatures, emotion-related EEG signals are primarily encoded in spectral power and are weak, noisy, and highly variable across subjects. Existing approaches rely either on large pretrained EEG foundation models, which require massive data yet still struggle with cross-subject variability, or frequency-domain encoders, which better reflect spectral structure but suffer from mismatched representations, drift-dominated tokenization, and lack of band-specific spatial modeling. In this article, we propose the Morlet Spectral Transformer (MST), built around three key components and integrated with a spatiotemporal Transformer backbone. First, Morlet wavelet tokenization provides a time-frequency representation that matches the multi-scale structure of brain rhythms, and extends classical differential entropy features to a form suitable for Transformers. Second, long-context baseline removal acts as a simple temporal normalization that removes subject-specific drift and redundancy across nearby windows. Third, frequency-specific spatial projection learns a separate channel mixer for each frequency band, capturing interpretable band-specific patterns and reducing cross-channel mixing. We show that, even without pretraining, MST consistently outperforms both large pretrained EEG foundation models and frequency-based methods across all SEED-family datasets. These results suggest that careful representation design can yield an accurate, cost-effective, and interpretable alternative to large-scale pretraining.

Guided-wave structural health monitoring enables damage localization in composite plates using sparse networks of bonded piezoelectric transducers. However, supervised localization remains weakly constrained when measurements are available from only a limited set of damage locations. Because exhaustive spatial coverage is impractical, models trained at observed locations may generalize poorly to unseen regions. We propose WaveGraphNet, an inverse-forward graph-learning framework for guided-wave damage localization in carbon-fiber-reinforced polymer (CFRP) plates. The sensing network is represented as a graph, with transducers as nodes and measured pitch-catch paths as edges. The inverse branch uses order-invariant message passing and a geometry-constrained decoder to map path-wise energy deviations to a damage coordinate. An independently trained forward branch predicts the energy-deviation pattern associated with a candidate coordinate. At test time, gradients propagated through the forward branch update only the inverse-predicted coordinate to reduce the discrepancy between the measured and predicted response patterns. The framework is evaluated on the OGW-1 benchmark using three spatial hold-out splits in which complete damage regions are excluded from training. Comparisons include non-graph and graph-learning baselines together with the training-free Reconstruction Algorithm for Probabilistic Inspection of Damage (RAPID). Under the validation-selected settings, refined WaveGraphNet achieves the lowest reported test mean absolute error on all three splits. Refinement reduces the standalone localization error by 23.6 percent-67.9 percent, with an average relative reduction of 50.4 percent. These results demonstrate that learned forward-response consistency can improve guided-wave localization under limited spatial training coverage.

Inverse design of metasurfaces under continuous electromagnetic constraints requires generation of geometries that simultaneously satisfy stringent spectral specifications and remain manufacturable. Conventional approaches based on iterative full wave simulations are computationally prohibitive for large design spaces, while existing generative models often suffer from poor conditional controllability and limited fabrication awareness. In this regard, we propose a physics guided condition quality enhanced diffusion framework for the inverse design of metasurface based absorbers. Fabrication-aware constraints are incorporated to ensure practical realizability of the generated designs. The framework introduces a conditioning mechanism for continuous spectral specifications, wherein feature-wise linear modulation propagates the condition across the denoising hierarchy, enabling stable and accurate generation with improved spectral controllability. Further, to embed EM consistency directly into the generative learning process, a pre trained surrogate EM simulator is integrated within the diffusion training pipeline. The proposed framework generated physically realizable metasurface designs for diverse reflection characteristics in the frequency range of 2 to 18 GHz, achieving a very low average spectral mean squared error of 0.0006 and a high band alignment accuracy of 0.958. The framework also addresses the fundamentally non-unique nature of inverse EM design by enabling structured multimodal generation of geometrically distinct yet spectrally consistent metasurface designs for the same target response. The proposed model produces the suitable design in approximately 30 seconds, whereas the conventional approach can take several months under comparable computational resources. The efficiency of the model is also established via experimental measurements.

Full-waveform inversion (FWI) estimates unknown parameters in the wave equation from limited boundary measurements. Recent advances in neural reparameterized FWI (NeurFWI) demonstrate that representing the parameters using a neural network can reduce the reliance on the high-quality initial model and wavefield data, at the cost of slow high-resolution convergence. However, its underlying theoretical mechanism remains unclear. In this study, we establish the neural sensitivity kernel (NSK) and the wave tangent kernel (WTK) to analyze their convergence behavior from both model and data domains. These theoretical frameworks show that the neural tangent kernel (NTK) induced by neural representation adaptively modulates the original sensitivity and wave tangent kernels. This modulation leads to several key outcomes, i.e., the spectral filtering effect, the gradient wavenumber modulation, and the wave frequency bias, connecting the convergence behavior of NeurFWI with the eigen-structures of NSK and WTK. Building on these insights, we propose several enhanced NeurFWI methods with tailored eigen-structures in NSK and WTK to improve inversion performances and efficiency. We numerically validate these theoretical claims and the proposed methods in seismic exploration, and firstly extend their application to medical imaging.

In this paper, we discuss a novel continuum robot design that enables the online tuning of the magnetic response at its tip. The proposed method allows for the change of both effective magnetic direction and intensity, introducing steering DOF without the need to control the external fields. This is unattainable with classical designs, which rely on fixed internal magnetic content and steer solely under the effect of a controllable magnetic field. The proposed robot design can be used in both controllable and fixed magnetic fields, potentially widening the clinical applicability of these robots. We experimentally show a max tip deflection of 33.8 mm from the resting state (23 % of the length of the robot). We discuss a model based on modified beam theory that captures the mechanical behavior of the continuum robot, with a mean absolute tip tracking error of 1.86 mm (1.2 % of the length) and maximum errors of less than 4.8 mm (3.2 % of the length) for all experimental points.

Performance of deep learning models is strongly governed by architectural capacity, with width and depth as primary controls. However, in physical-science applications, models are often compared at a single fixed size or by separating accuracy and computational cost, which can be misleading since architectures exhibit different accuracy-cost scaling as width and depth vary. This issue is particularly relevant for U-Net-type encoder-decoder models, widely used for multi-scale gas, fluid, and plasma dynamics due to their ability to represent features across spatial scales. A U-Net constructs a multi-resolution representation via an encoder that progressively reduces spatial resolution, followed by a decoder that restores it for prediction. Skip connections link corresponding encoder and decoder features, preserving fine-scale information and improving optimization. In practice, U-Net width is routinely tuned, while depth is typically kept fixed (a set number of down/up-sampling stages with few convolutions per stage), limiting systematic exploration of depth for improving the accuracy-cost trade-off. We address this limitation by increasing effective depth through stacking multiple encoder-decoder "waves" in series, with skip connections both within and across waves to enable progressive cross-scale refinement. We call this architecture a Deep Wave Network (DW-Net). Training data, optimization, and schedules are kept identical across models. Instead of evaluating single configurations, we train multiple width variants of each architecture and compare accuracy vs. GPU time Pareto fronts. Across several 2D and 3D flow benchmarks, DW-Net models consistently improve the Pareto frontier over single-wave U-Nets, achieving higher accuracy at matched cost or similar accuracy at reduced cost, and reaching low-error regimes with up to 3x less training time under identical training settings.

Spatio-temporal signals arising from event-driven biological processes, such as surface electromyography (sEMG), exhibit asynchronous and highly structured activation patterns that are challenging to model using conventional discrete or purely real-valued representations. In this work, we propose a continuous temporal modeling framework based on interference-based wave representations. The approach maps event-like input signals into a complex-valued latent wave field, where temporal structure is encoded through phase modulation and interactions between latent components. By projecting the resulting wave field onto an energy domain, the model induces structured activation patterns that capture both temporal localization and relational dependencies within finite observation windows, without relying on explicit recurrence or causal state propagation. The proposed formulation is particularly suited for event-driven biosignals, where continuous representations enable efficient gradient-based optimization and robust feature extraction. In particular, the method is designed to support learning from sEMG data for downstream control tasks in biomechanical systems, such as prosthetic devices and exoskeletons. Experimental results demonstrate that the proposed interference-based wave model provides improved representation quality compared to purely real-valued representations, while maintaining computational efficiency suitable for practical deployment.

We solve the time-dependent Schrödinger equation by learning the score function, the gradient of the log-probability density, on Bohmian trajectories. In Bohm's formulation of quantum mechanics, particles follow deterministic paths under the classical potential supplemented by a quantum potential depending on the score function of the evolving density. These non-crossing Bohmian trajectories form a continuous normalizing flow governed by the score. We parametrize the score with a neural network and minimize a self-consistent Fisher divergence between the network and the score of the resulting density. We prove that the zero-loss minimizer of this self-consistent objective recovers Schrödinger dynamics for nodeless wave functions, a condition naturally met in quantum vibrations of atoms. We demonstrate the approach on wavepacket splitting in a double-well potential and anharmonic vibrations of a Morse chain. By recasting real-time quantum dynamics as a self-consistent score-driven normalizing flow, this framework opens the time-dependent Schrödinger equation to the rapidly advancing toolkit of modern generative modeling.

We establish a mathematical correspondence between state space models, a state-of-the-art architecture for capturing long-range dependencies in data, and an exactly solvable nonlinear oscillator network. As a specific example of this general correspondence, we analyze the diagonal linear time-invariant implementation of the Structured State Space Sequence model (S4). The correspondence embeds S4D, a specific implementation of S4, into a ring network topology, in which recent inputs are encoded, as waves of activity traveling over the one-dimensional spatial layout of the network. We then derive an exact operator expression for the full forward pass of S4D, yielding an analytical characterization of its complete input-output map. This expression reveals that the nonlinear decoder in the system induces interactions between these information-carrying waves that enable classifying real-world sequences. These results generalize across modern SSM architectures, and show that they admit an exact mathematical description with a clear physical interpretation. These insights enable a new level of interpretability for these systems in terms of nonlinear oscillator networks.

Meta-optics promises compact, high-performance imaging and color routing. However, designing high-performance structures is a high-dimensional optimization problem: mapping a desired optical output back to a physical 3D structure requires solving computationally expensive Maxwell's equations iteratively. Even with adjoint optimization, broadband design can require thousands of Maxwell solves, making industrial-scale optimization slow and costly. To overcome this challenge, we propose the Neural Adjoint Method, a solver-supervised surrogate that predicts 3D adjoint gradient fields from a voxelized permittivity volume using a Fourier Neural Operator (FNO). By learning the dense, per-voxel sensitivity field that drives gradient-based updates, our method can replace per-iteration adjoint solves with fast predictions, greatly reducing the computational cost of full-wave simulations required during iterative refinement. To better preserve sensitivity peaks, we introduce a stage-wise FNO that progressively refines residual errors with increasing emphasis on higher-frequency components. We curate a meta-optics dataset from paired forward/adjoint FDTD simulations and evaluate it across three tasks: spectral sorting (color routers), achromatic focusing (metalenses), and waveguide mode conversion. Our method reduces design time from hours to seconds. These results suggest a practical route toward fast, large-scale volumetric meta-optical design enabled by AI-accelerated scientific computing.

Parallel simulation of robotic systems requires partitioning the dynamics into coupled subsystems. Finite-iteration coupling across the partition boundary can inject spurious energy, even when each subsystem is passive. We propose an early-terminable, energy-safe coupling interface for port-Hamiltonian subsystems based on Douglas--Rachford splitting in wave (scattering) coordinates. The wave-domain formulation reduces passivity to norm inequalities and coupling to orthogonality. Within this setting, the deep correspondence between monotone operator theory and discrete passivity can be exploited to construct a Douglas--Rachford inner iteration whose Fejér monotonicity provides algorithmic dissipation. Under passivity of the subsystem integrators and an impedance-tuning condition, the proposed method guarantees discrete passivity of the augmented storage for any finite inner-iteration budget and converges to the monolithic discretization as the budget increases. Experiments on a linear--Duffing coupled-oscillator benchmark support the finite-iteration energy inequality at numerical roundoff (1e-14 in double precision), with state-error metrics decreasing over the tested inner-iteration budgets.

We present a novel machine-learning (ML) approach (EM-GANSim) for real-time electromagnetic (EM) propagation that is used for wireless communication simulation in 3D indoor environments. Our approach uses a modified conditional Generative Adversarial Network (GAN) that incorporates encoded geometry and transmitter location while adhering to the electromagnetic propagation theory. The overall physically-inspired learning is able to predict the power distribution in 3D scenes, which is represented using heatmaps. We evaluated our method on 15 complex 3D indoor environments, with 4 additional scenarios later included in the results, showcasing the generalizability of the model across diverse conditions. Our overall accuracy is comparable to ray tracing-based EM simulation, as evidenced by lower mean squared error values. Furthermore, our GAN-based method drastically reduces the computation time, achieving a 5X speedup on complex benchmarks. In practice, it can compute the signal strength in a few milliseconds on any location in 3D indoor environments. We also present a large dataset of 3D models and EM ray tracing-simulated heatmaps. To the best of our knowledge, EM-GANSim is the first real-time algorithm for EM simulation in complex 3D indoor environments. We plan to release the code and the dataset.

This paper studies experimental designs for estimation and inference on policies with spillover effects. Units are organized into a finite number of large clusters and interact in unknown ways within each cluster. First, we introduce a single-wave experiment that, by varying the randomization across cluster pairs, estimates the marginal effect of a change in treatment probabilities, taking spillover effects into account. Using the marginal effect, we propose a test for policy optimality. Second, we design a multiple-wave experiment to estimate welfare-maximizing treatment rules. We provide strong theoretical guarantees and an implementation in a large-scale field experiment.