Inverse Problems

Data-driven inverse design enables efficient generation of nanophotonic structures with prescribed optical responses, but spectrum-to-geometry mapping remains challenging due to non-uniqueness and fine geometric features. This work presents a two-stage deformable-convolutional framework for reconstructing metal--insulator--metal resonator geometries from 80-dimensional absorption spectra. The spectrum is projected to a $150\times4\times4$ latent representation and decoded into a $64\times64$ resonator mask. Training combines supervised reconstruction with least-squares adversarial refinement initialized from the best supervised checkpoint. A three-run ablation compares deformable convolution with plain convolution, involution, Dynamic Conv, and ODConv under the same architecture. The proposed model achieves $20.79\pm0.31$dB PSNR and $0.8501\pm0.0082$ SSIM, improving over plain convolution by 2.16dB and 0.0831, respectively. It further achieves Dice $0.9623\pm0.0027$, IoU $0.9342\pm0.0038$, and boundary F-score $0.9550\pm0.0027$. Spectral consistency evaluated using a frozen forward surrogate yields RMSE $0.0805\pm0.0013$ and $R^2=0.7923\pm0.0065$. Learned offsets show stronger adaptive sampling at coarse and intermediate decoder stages. Overall, deformable sampling with supervised initialization and adversarial refinement improves spectrum-conditioned geometry reconstruction.

Electromagnetic inverse scattering is a nonlinear and ill-posed computational imaging problem, where accurate reconstruction is challenging due to measurement limitations, noise, and high computational costs, especially for 3-D imaging. Although physics-driven neural networks (PDNNs) reduce the dependence on labeled training data, existing accelerated PDNN frameworks often rely on preliminary reconstruction-based region selection, which may introduce instability when the selected region is inaccurate. In this paper, a coordinate-residual physics-driven neural network (CRPDNN) is proposed for 3-D electromagnetic inverse scattering. CRPDNN represents the unknown complex contrast distribution using normalized spatial coordinates and a residual convolutional network, whose parameters are optimized by enforcing consistency between the measured and model-predicted scattered fields. Unlike existing subregion-accelerated PDNN approaches, CRPDNN does not require a preliminary reconstruction, thereby avoiding dependence on its accuracy. For the reported noise-free 3-D synthetic cases, CRPDNN achieves an average relative error of 2.10%, compared with 7.97% for CSI and 3.99% for $L_{2/3}$-FBE-WCIE, while providing approximately 5.5- and 12.1-fold speedups over the two baselines, respectively. Additional 2-D comparisons further demonstrate its stability and computational efficiency relative to existing PDNN frameworks. CRPDNN also maintains reliable reconstruction performance under noisy measurements, and the 3-D Fresnel experiments further indicate its potential for practical imaging applications.

Gravimetry images subsurface density contrasts associated with geological structures, geothermal systems, and intrusive bodies. Recovering a three-dimensional density model from gravity observations is highly ill-posed because of its non-uniqueness, limited data coverage, and the attenuation of the gravity field with depth. Classical inversion methods rely on explicit regularization and parameter tuning, whereas supervised deep-learning approaches require representative gravity--density pairs that are rarely available. This paper proposes an unsupervised depth-aware implicit neural representation for 3D gravity inversion. The density volume is represented by multiple coordinate-based neural networks assigned to overlapping depth slabs and optimized directly from the observed gravity measurements through the sensitivity matrix. Slab-specific Fourier features, physics-based depth gains, and scheduled regularization provide structural priors without requiring labeled density models. Experiments on four synthetic scenarios show that the proposed method provides better overall performance in terms of RMSE, PSNR, and SSIM than the evaluated conventional and neural baselines. It also recovers more compact and spatially coherent density bodies, improves the separation of nearby anomalies, preserves internal structures, and reconstructs their vertical extent better. These results indicate that the proposed depth-aware formulation helps to mitigate the depth ambiguity inherent in gravity inversion. In the field experiment, where no ground-truth density model was available, the method produced compact, separated, and vertically coherent anomalies consistent with the observed gravity pattern.

Divertor heat-flux analysis is essential for understanding plasma-wall interactions and protecting plasma-facing components in magnetic-confinement fusion devices, while conventional infrared-based inversion is usually performed after discharge and requires heat-conduction modeling with device-specific material properties, divertor geometry, and boundary conditions. Rather than accelerating this conventional infrared-based inversion paradigm, we introduce a new online-oriented signal-based reconstruction paradigm that directly reconstructs time-resolved radial heat-flux profiles from multi-source macroscopic plasma-state signals available during discharge. To enable systematic study of this task, we construct \textbf{DivMPS2HF}, a multi-source discharge dataset that provides the data foundation and benchmark for signal-based divertor heat-flux reconstruction. We further propose \textbf{SafeDivertor}, a task-driven framework designed to address the key challenges of signal-based heat-flux reconstruction. It employs physical prior-aware initialization to provide radial-distribution guidance for target channels, input perturbation to reduce over-reliance on specific heterogeneous signals, spectral-aware reconstruction optimization to exploit time-frequency priors and preserve transient dynamics, and progressive training to stabilize the optimization of these complementary objectives. Experiments on DivMPS2HF demonstrate that SafeDivertor achieves the best overall performance among the evaluated time-series baselines across all five metrics, establishing a new performance benchmark for signal-based divertor heat-flux reconstruction. The source code will be released on https://github.com/Event-AHU/OpenFusion

Interpretability methods for large language models (LLMs) describe internal state but do not directly test whether that state is causally sufficient to produce the observed behavior. In earlier work, we lesioned LLMs to produce error profiles in picture naming, a central task for assessing aphasia, and found that specific lesions produced errors resembling those of individual stroke survivors. Here we ask the inverse question: given an error profile, can the lesion parameters that produced it be recovered, and what does this inverse problem reveal about transformer computation? Lesions in LLaVA-Vicuna 13B were parameterized by layer index, modification percentage, and noise sigma across 4,840 configurations, and error profiles were characterized by a seven-category clinical taxonomy (correct, semantic, unrelated, formal, mixed, neologism, no-response). We trained a multi-task neural network to map error profiles back to perturbation parameters. The problem admitted a partial solution: across 10 independently trained inverse models, modification percentage and noise sigma were recoverable, whereas layer index was recoverable only within a neighborhood. In counterfactual validation, a fresh model instance perturbed with the recovered parameters reproduced the target behavior in 81.4% of cases. This dissociation between low layer recovery and high counterfactual fidelity is consistent with functional redundancy across transformer layers, a property not captured by standard interpretability methods. As an out-of-distribution test, we applied the trained model to picture-naming error profiles from 278 stroke survivors; recovered parameters were syndrome-discriminative, most strongly for perturbation intensity, indicating generalization beyond the training distribution. Counterfactual validation provides a general framework for LLM interpretability claims beyond inverse mapping.

In this work, we present a wildfire temperature retrieval framework for VSWIR imaging spectroscopy data, employed on data from NASA's Airborne Visible Infrared Imaging Spectrometer (AVIRIS-3). The retrieval framework utilizes a full-physics approach in which a forward model is employed to resolve both solar and emitted radiance derived from a temperature distribution and utilizes the full spectral range in the residual fit. To optimize the forward model retrieval, we use state-of-the-art nonlinear least squares methods implemented for fast convergence on the on-board GPU, allowing for estimation of effective fire temperature within flight cadence. We verify the forward model assumptions on simulated spectra with an injected thermal signature and find good agreement with an RMSE of $41.8$ Kelvin (K). We apply the retrieval over the full 2025 FireSense AVIRIS-3 campaign, totaling 168 overflights with probable active fire spectra, and demonstrate a residual radiance fit of $\leq 10\%$ across bands in the short-wave infrared (SWIR). Lastly, we verify the applicability of the retrieved posterior fire temperature parameters to generalize to space-borne imaging spectrometers such as EMIT, by retrieving at coarsened spatial resolution. We find that the posterior distribution exhibits good coverage of the underlying sub-pixel temperature range with an absolute error of $30$ K across quantiles and a mean absolute error of $27.16$ K between spatial resolutions.

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.

The extraction of $β$-feeding distributions in Total Absorption $γ$-ray Spectroscopy constitutes a challenging inverse problem, particularly in nuclei with complex decay schemes involving a large number of excited states. In such cases, the measured spectrum arises from the superposition of many detector response functions, making the determination of the individual feedings intrinsically ill-posed and highly sensitive to the methodology employed. In this work, we present a systematic comparison between supervised Machine-Learning techniques and Response-Matrix methods using realistic Monte Carlo simulations of an experimental Total Absorption Spectrometer. Supervised Machine-Learning approaches construct a non-parametric estimator that infers level feedings from the measured spectrum after a training stage, whereas Response-Matrix methods determine the feeding distribution by directly minimizing the difference between measured and reconstructed spectra. Our results show that supervised Machine-Learning techniques achieve superior accuracy in the reconstruction of individual feeding intensities, whereas Response-Matrix methods provide robust and physically consistent initial solutions. These findings support a hybrid strategy in which a Response-Matrix method is first used to obtain an initial feeding estimate, which is then refined using a supervised Machine-Learning approach to achieve improved overall accuracy.

Accurate option prices do not imply accurate recovery of the latent risk-neutral density. We study this distinction with two complementary benchmarks. A controlled benchmark exposes simulator-truth densities for latent evaluation, while a chronological NIFTY benchmark tests only held-out market prices. A two-component lognormal mixture has the lowest aggregate price, $L^1$, Wasserstein, and fixed-tail errors on the synthetic benchmark. Learned operators retain narrower strengths: DeepONet reduces 1% quantile and variance error by 39.0% and 34.6% relative to the mixture, and a quote transformer reduces $L^1$ by 16.4% on the structurally misspecified Merton family. A numerical conditioning analysis explains why these rankings can differ: after enforcing mass and forward constraints, 95 of 126 pricing directions are numerically null, and two densities separated by $L^1 = 0.061$ produce identical prices on the covered strikes. On 524 held-out NIFTY calls, validation-selected test-time adaptation reduces DeepONet RMSE by 28.3%, but per-expiry mixture and SVI fits remain much more accurate. The evidence supports target-dependent inductive bias, not a universal winner.

Full-field reconstruction of air pollution is essential for evaluating pollution exposure and supporting public health decision-making. However, the complex interactions among pollutants, hard-to-predict weather patterns, and limited monitoring station coverage make this a complex task. We apply deep learning techniques to provide fast and accurate reconstructions from sparse observations of four key pollutants: NO2, O3, PM2.5 and PM10. Models are trained on full-field simulation data and evaluated on real-world observations collected from 9 to 28 monitoring stations in the city of Paris. We introduce a diffusion-based generative framework for multi-pollutant reconstruction and benchmark its performance against deterministic deep learning models. Despite noisy observations and strong spatial variability, the models achieve high structural similarity on simulated validation data and produce realistic spatial patterns on real-world observations, as indicated by power-spectrum analysis. We introduce data augmentation methods that enable transfer to real-world observations without retraining, allowing the models to generalise beyond the training period. These findings highlight the potential of ML models for reliable real-world deployment in air pollution reconstruction tasks.

Source apportionment from sparse urban air-quality sensors is an inverse problem limited by sensor placement, wind-driven transport, background variation, and noise. Known or proxy emission inventories make attribution meaningful by restricting the unknown source field to a finite set of candidate groups, but do not guarantee those groups are distinguishable from the observations. We represent time-varying source activity with a low-dimensional nonnegative temporal basis and formulate inventory-based apportionment as a wind-conditioned lagged inverse problem in which each source--basis coefficient produces a sensor-time fingerprint. After projecting out a separate low-dimensional background space, the relevant object is the projected lagged response matrix $\widetilde H_Φ$: exact identifiability at the chosen basis resolution requires its full column rank, while noise-robust attribution is controlled by its singular values, coefficient visibility, background absorption, pairwise coherence, and ray distance. We propose an identifiability-aware apportionment (IASA) framework that estimates nonnegative source--basis coefficients, reconstructs activity trajectories, and reports uncertainty and conservative grouping recommendations for indistinguishable sources. We instantiate it on a New Delhi platform built from government PM$_{2.5}$ and wind records, regulatory sensor locations, and four proxy source groups, and define controlled and observed evaluations of recovery, ambiguity, wind diversity, background stress, transport error, inventory robustness, and residual adequacy. IASA reports the attribution resolution defensible under the declared inventories, transport, background, lag, and noise rather than the most detailed possible vector.

The boundary and divertor plasma govern how a tokamak exhausts power and particles, setting heat fluxes, target conditions, and the onset of detachment. Predicting these quantities is essential for operating current and future devices, but edge simulations that resolve them are too slow for parameter scans, optimization, or real-time control. Machine-learning surrogates offer a fast alternative, yet most are forward-only: they cannot recover input parameters from observations or assess the reliability of their predictions. We introduce a cycle-consistent neural surrogate for edge plasmas, combining a conditional U-Net forward model with an optimization-based inverse method built on the frozen forward network. The forward model maps five control parameters to two-dimensional plasma-state fields on the SOLPS-ITER mesh; the inverse method enforces consistency between forward and inverse predictions, a self-supervised quality check needing no ground-truth labels at inference. An ensemble of multilayer perceptrons also predicts electron temperature and density profiles at the outboard midplane and divertor targets, with uncertainty estimates that flag where more simulations are needed. The forward model achieves normalized root-mean-square errors below 2.6% and Pearson correlations above 0.95 for all fields. Cycle-consistency regularization raises the average cyclical $R^2$ from 0.59 to 0.99 without degrading forward accuracy and enables recovery of the core fueling rate; all five control parameters are recovered with Pearson $r\ge0.97$. A $k$-d tree warm start yields a database completion rate above 95%, versus roughly 30% outright failures when cold-started. With about $4\times10^6$ parameters, the model produces full 2D predictions in milliseconds, five to six orders of magnitude faster than SOLPS-ITER, enabling real-time control, parameter scans, uncertainty analysis, and digital twins.

Acoustic impedance imaging is a fundamental yet severely ill-posed problem in subsurface analysis: the seismic wavelet is unknown, observations are band-limited, and labeled well-log samples are extremely scarce (typically <1% of all traces). Existing semi-supervised deep learning methods mitigate few-shot problem by incorporating forward modeling, yet they either rely on inaccurate prior wavelet assumptions or introduce auxiliary networks, leading to unstable optimization and degraded performance. We propose RD-SCL, a novel framework that integrates regularized deconvolution with semi-supervised cross-learning. At its core lies a differentiable, closed-form first-order Tikhonov deconvolution operator that dynamically estimates the latent wavelet in the frequency domain during training, providing stable physics-guided feedback without explicit auxiliary networks and fixed wavelet priors. Building on this operator, we design a symmetric cross-learning that enforces consistency between predictions on labeled and unlabeled data, thereby effectively exploiting abundant unlabeled traces. Extensive experiments on the SEAM and Marmousi 2 benchmarks demonstrate that RD-SCL consistently outperforms state-of-the-art supervised and semi-supervised methods, achieving substantial gains with lower computational cost. With only 56.5k learnable parameters and competitive runtime, RD-SCL offers a practical, physically consistent, and efficient solution for acoustic impedance imaging.

Diffusion-based methods have achieved remarkable empirical success in solving inverse problems. However, many existing posterior samplers either lack rigorous theoretical guarantees or incur substantial computational overhead. We propose a simple and efficient algorithm, called \pddim, for solving linear inverse problems with diffusion priors via a DDIM-type sampler. Our method requires only lightweight, coordinate-wise modifications to the standard DDIM update, while explicitly incorporating the measurement model. The key idea is to perform posterior sampling separately along each singular direction of the measurement operator: for each direction, the sampler follows the learned diffusion prior when the observation signal-to-noise ratio (SNR) is below the corresponding diffusion SNR, and switches to a calibrated measurement-based predictor otherwise. We prove that the proposed sampler converges to the Bayesian posterior conditioned on the measurements. Empirical results show that the proposed sampler performs favorably against existing diffusion-based posterior samplers across a range of image restoration tasks, achieving the best performance on the majority of evaluation metrics considered. Overall, our results convert posterior sampling for noisy linear inverse problems to simple coordinate-wise DDIM updates, yielding an efficient, easy-to-implement algorithm with provable posterior consistency.

Estimating spatially heterogeneous elastic properties from low-resolution displacement measurements is a severely ill-posed inverse elasticity problem because low resolution obscures spatial details needed to distinguish heterogeneous property variations, and small measurement perturbations or fitting errors are amplified through inverse estimation. Existing inverse methods often rely on high-fidelity observations and manually prespecified loss weights, limiting their adaptability and making them sensitive to noise and resolution degradation. We propose a Probabilistic Inverse Elasticity Physics-Informed Neural Network (PIE-PINN) framework for robust estimation of Young's modulus and Poisson's ratio from noisy, low-resolution displacement data. PIE-PINN models displacement observation, strain-discrepancy, and equilibrium residuals using Laplace distributions within a unified probabilistic model. To improve robustness, the framework combines a B-spline-guided displacement network with a hierarchical half-Cauchy model for displacement residual scales. The B-spline provides a smooth global representation of the displacement field, while the neural network correction captures local variations. The hierarchical scale model adaptively downweights severe displacement fitting errors, enabling more robust recovery of the latent mean displacement field. An alternating maximum-likelihood training strategy updates the mean through weighted residual minimization and updates the scales to adjust the loss weights. Systematic case studies across varying noise levels and observation resolutions demonstrate the robustness of PIE-PINN.

Recovering a latent potential from observed flow on a directed graph (a discrete Poisson problem with Dirichlet boundaries) is ill-posed, and the standard fix backfires: ridge regularization shrinks toward a gauge-meaningless origin, collapsing and reversing the recovered ordering ($+0.81\to-0.42$ rank correlation against a planted ground truth). The gauge-invariant graph Dirichlet energy removes the hazard and delivers parameter-insensitivity: the estimate is stable across four orders of magnitude in $λ$, whereas ridge inverts the ordering for every $λ>0$. We prove the reduced solve is SPD and preserves dynamic range exactly where ridge collapses it, and localize absorbing boundaries from flow alone via a Poisson residual. The $H^1$ seminorm is classical; what is new is the gauge diagnosis, the parameter-insensitivity it buys, and an ablation showing the result is robust to the extraction method. On three public clickstream corpora the gauge-invariant estimate retains $28$--$41\%$ of the interior dynamic range while ridge collapses to as little as $0.2\%$. The same gauge invariance carries into graph neural networks -- neutralizing the constant mode per layer prevents the oversmoothing that collapses a deep directed GCN -- linking this classical inverse problem to a central question in graph learning.

Generative models often represent signals as dense grids of amplitudes, blurring sharp transients that are crucial for the correctness of physical signals. We introduce Singularity Space, a generative framework that represents signals through complex-plane singularities, rooted in the classical pole-residue representation of meromorphic functions. We learn a latent space of physically constrained, per-signal singularity configurations to solve an inverse problem from degraded or partial observations. The framework has three key properties: interpretability, in which each generated singularity configuration corresponds to a set of physical parameters; structural stability, which mitigates Gibbs artifacts at discontinuities; and resolution-free output reconstruction on arbitrary grids without retraining or interpolation. Our framework employs a transformer-based diffusion model that directly predicts samples at complex-plane singularity coordinates, subject to geometric constraints during sampling. As a controlled test case for sharp-feature recovery, we evaluate our framework on 1D Burgers shocks, where each shock is represented by 32 predicted singularities (an $8\times$ reduction versus a 1024-point grid signal). Our framework preserves signal structure ($\text{TV ratio} \approx 1$) under unseen test-time observation noise, achieves a $4.2\times$ lower reconstruction error in zero-shot sub-resolution generalization than a grid-based baseline, and recovers physical parameters to $10^{-4}$ absolute error in-distribution. These results suggest that singularity-based representations may provide a practical foundation for other transient-dominated signals such as speech and biomedical signals, with potential extension to higher-dimensional domains.

This work studies the inverse problem of recovering the relative magnitudes of the tension, bending, and bearing loads acting on a crack from its stress-intensity-factor profile along the crack front, using the public SIFBench finite-element data. The central claim is not forensic load recovery on field cases, but a rigorous characterization of when the combined load is identifiable at all, together with an estimator that returns calibrated uncertainty precisely in the regimes where it is not. For a known geometry the forward map from loads to profile is exactly linear, and identifiability reduces to a single geometric question: whether the three elementary load profiles are linearly independent as functions along the front. When they are nearly dependent, many different load combinations produce almost the same profile and the inverse problem is illposed; the analysis shows that the degree of ill-posedness is controlled by an intrinsic stability margin, not by the conditioning number alone. A single crack-front operator serves both as a structured forward surrogate and as the differentiable map required by a simplex-constrained, set-valued inverse estimator. On the SIFBench corner-crack scenario the empirical behaviour matches the theory: the typical geometry is well posed while a sizable minority is genuinely ill-posed, so a point estimate is reliable on the majority and provably uninformative on the rest. Validation is on controlled synthetic noise; no real fracture cases are used or claimed.

Here, we present a platform built on our inverted Graph Transformer Network, IMPRESSION-G2, which can accurately and rapidly reconstruct molecular bonding directly from experimental nuclear magnetic resonance (NMR) spectroscopic information. It comprises three interconnected stages: a one-shot model that predicts bond connectivity between atoms; a structure-correction stage that corrects the predicted structures by removing uncertain bonds and iteratively reassigning them; noise-augmented multi-shot prediction, generating an ensemble of candidate structures, which are ranked to identify the best-fit structure. By integrating a range of $^{1}$H and $^{13}$C NMR data, including two-dimensional (2D) experiments such as COSY, HSQC, and HMBC, the inverse-IMPRESSION platform correctly identifies the structures of 77.8% of molecules with up to 30 heavy atoms (H, C, N, O and F) using simulated NMR data, and 10 of 19 (53%) molecules using experimental NMR data. The experimental structures solved have molecular weights of up to 480 Da and are representative of the complex structures in synthetic and natural products that routinely challenge chemists. The inverse-IMPRESSION framework thus provides the first effective approach for automated molecular structure elucidation using graph-based machine learning on experimental data.

Inferring latent physical properties from sensory observations is a fundamental challenge in machine perception. Among available sensing modalities, thermal imaging is particularly promising because temperature evolution is directly governed by heat-transfer physics and therefore encodes information about underlying thermophysical properties of a scene. Recovering spatially resolved thermophysical properties from thermal observations could transform applications ranging from digital twins and infrastructure monitoring to robotics and scientific imaging. However, existing thermal scene reconstruction methods can recover temperature fields in complex 3D environments without identifying the thermophyiscal properties that govern thermal evolution, whereas inverse methods provide physically interpretable parameter estimation but typically rely on simplified geometries and controlled experimental conditions. Here we introduce ThermoField, a framework that unifies thermal scene reconstruction and thermophysical parameter estimation through differentiable heat-transfer simulation. The proposed framework represents these quantities as spatially varying neural fields and constrains them through scene geometry, governing heat-transfer physics, and temporal thermal observations. We demonstrate that ThermoField jointly reconstructs geometry, estimates spatially varying thermal diffusivity, and predicts thermal evolution under previously unseen environmental conditions. By integrating neural scene representations with differentiable heat-transfer solver, the framework enables physically interpretable parameter inference in complex 3D scenes. Our results establish a bridge between thermal scene reconstruction and inverse heat-transfer analysis, providing a unified approach for geometry reconstruction, thermophysical property estimation, and predictive thermal simulation from thermal observations.

Vision-language models (VLMs) and agentic AI have shown strong performance on semantic visual tasks, but it remains unclear whether they can handle the physics and inverse problems that underlie computational imaging. We present ImagingBench, a benchmark of 20 computational imaging tasks spanning five categories: ray and wave optics, image signal processing, inverse reconstruction, computational sensing, and calibration. ImagingBench evaluates three complementary settings: Expert, fixed expert-guided inverse reconstruction; Planner, planner-guided inverse reconstruction; and Forward, forward-system simulation for consistency checking. We benchmark leading proprietary and open-source image-centric multimodal systems, including Gemini, GPT, and Qwen, and compare them with representative task-specific non-agentic baselines. Across tasks, agentic models remain consistently weaker than specialized methods, especially on computational sensing problems such as lensless imaging, event-based reconstruction, time-of-flight imaging, and holography. Planner guidance provides only modest and inconsistent gains over the fixed-prompt Expert baseline. Although the models often generate visually plausible outputs, their reference-based fidelity remains poor, revealing a substantial gap between semantic visual competence and physically grounded imaging performance. ImagingBench provides a unified testbed for measuring this gap and tracking progress in agentic AI for computational imaging.

Pulsar timing arrays (PTAs) provide a unique window into nanohertz gravitational waves (GWs), but extracting astrophysical parameters from noisy, long-baseline timing residuals remains computationally challenging with traditional Bayesian techniques due to the high dimensionality of the parameter space, complex and correlated noise models, and the cost of repeated likelihood evaluations. We introduce a Transformer with a physics-informed positional-encoding framework for the efficient inference of eccentric binary black holes in relativistic orbits from PTA data. Our approach embeds analytical GW phase evolution directly into the model through structured positional encodings, enabling the network to learn physically meaningful representations from raw PTA timing residuals. We then use generative models, including discrete and continuous conditional normalizing flows, to infer posterior distributions within a simulation-based inference framework. Across a range of signal-to-noise ratios, the proposed method achieves improved accuracy, sharper posteriors, and faster inference compared to physics-agnostic baselines. While presented for deterministic white-noise signals, the modular framework readily generalizes to realistic PTA analyses incorporating red noise and additional components. This work highlights the potential of physics-aware deep learning models as scalable alternatives to conventional inference pipelines for next-generation PTA datasets.

This paper presents a machine learning framework for data-driven inverse design of V-beam thermal sensors. The goal is to determine the optimal sensor geometry: beam inclination angle, beam length and beam width that achieves a target displacement under a given temperature. The design should also provide the geometry with minimum structure volume and minimum mechanical stress the sensor must support. This problem is ill-posed as for a given displacement there are multiple possible geometric configurations, causing direct regression methods to fail. We document a series of five exploratory trials that progressively revealed the nature of the problem culminating in a two-phase solution: a neural network forward model trained to map geometry and material constants to sensor responses, a gradient-descent inverse optimization over the frozen forward model, minimizing stress and volume simultaneously. The proposed pipeline utilizes a 3000-sample dataset and achieves a MAPE of 4.76% for predicting the displacement, more than 70% of predictions having MAPE of under 5%.

While diffusion models have revolutionized image synthesis, their application to real-world inverse problems is often hampered by the need for massive datasets and the difficulty of imposing strict physical constraints. In this work, we introduce \textbf{SE-UNet} (Singular Equivariant UNet), a framework designed to solve ill-posed imaging tasks without extensive pre-training. By treating generation as an optimization problem constrained by geometric equivariance ($D_4$ group) and singular value gating, SE-UNet effectively standardizes the solution space. We demonstrate that these strong inductive biases allow for state-of-the-art zero-shot inpainting results (80% missing pixels) on CIFAR-10. Our method surpasses Deep Image Prior (DIP) baselines by over 4 dB in PSNR and exhibits a characteristic "singular snap" convergence -- rapidly locking into the signal manifold. SE-UNet thus offers a data-efficient pathway for constrained generation, aligning with the ReALM-GEN goal of bridging theoretical priors with practical deployment.

We demonstrate the application of Flow Matching, a technique originating from generative Artificial Intelligence, to probabilistic inversion in geophysical settings, such as seismic Full-Waveform inversion. We adapt the well-established mathematical theory of Flow Matching from generative Artificial Intelligence to the context of probabilistic inversion. We evaluate the approach with two case studies: a simple 2D velocity model to illustrate the general features of the method, and the OpenFWI dataset to show its capabilities for probabilistic inversion of more complex seismic velocity models.

Reconstructing physics-based 3D assets -- geometry, materials, and illumination -- from multi-view images is a core problem in computer graphics and vision, and a prerequisite for realistic relighting and editing. Physics-based inverse rendering offers an accurate image-formation model, but is severely underconstrained: without strong priors, illumination is baked into materials, and reconstructions generalize poorly to novel views and lighting. Data-driven diffusion models, in contrast, predict visually plausible materials, yet their predictions rarely satisfy the rendering equation and are not directly usable for physics-based rendering. We bridge these two paradigms rather than replacing either. Our key idea is to treat the predictions of a state-of-the-art diffusion model not as target material values but as a similarity kernel for optimization: we introduce a regularization loss that penalizes deviations in the optimized material over surface regions where the diffusion predictions are near-constant, while leaving the optimization free to match the input images. Built on this regularizer, our end-to-end pipeline jointly reconstructs geometry, materials, and illumination, yielding high-quality assets that drop into standard rendering pipelines and relight faithfully. On the Synthetic4Relight, Stanford-ORB, and DTC-Synthetic datasets, our method significantly outperforms state-of-the-art baselines in both reconstruction accuracy and relighting quality.

Rapid prototyping of algorithms is a critical step in modern machine learning. Most algorithms exploit linear algebra, creating a need for lightweight numerical routines which -- while potentially sub-optimal for the task at hand -- can be rapidly implemented. For the numerical solution of ill-conditioned linear systems of equations, the standard solution for prototyping is Tikhonov-regularised inversion using a nugget. However, selection of the size of nugget is often difficult, and the use of data-adaptive procedures precludes automatic differentiation, introducing instabilities into end-to-end training. Further, while data-adaptive procedures perform multiple linear solves to select the size of nugget, only the result of one such solve is returned, which we argue is wasteful. This paper aims to circumvent the above difficulties, presenting autonugget; a Python package for automatic and stable numerical solution of linear systems suitable for rapid prototyping, and fully compatible with automatic differentiation using JAX. autonugget combines multiple linear solves using Richardson extrapolation to determine the solution of the ill-conditioned system, improving in accuracy over approximations based on a single nugget.

Learned reconstruction operators for inverse problems are typically trained under a fixed noise model, and generalize poorly when the distribution during testing differs from the one assumed during training. Distributionally robust optimization (DRO) addresses this by optimizing against the worst-case distribution within a prescribed ambiguity set, but standard Wasserstein DRO perturbs the full joint distribution uniformly, which can be overly conservative and ignores the physics of the measurement process. We develop a structured DRO framework in which the ambiguity set is restricted to structured perturbations aligned with the data-acquisition process. This allows us to learn data-driven reconstruction operators that remain robust to distributional shifts. By constraining perturbations to subsets such as $P(Y|X)$, our framework models uncertainty in the forward operator and noise model more faithfully, accommodating any noise model expressible as a stochastic forward operator. We establish strong duality for this general formulation and derive explicit finite-dimensional dual representations for perturbations in the joint, marginal, and conditional distributions. A central result is an explicit worst-case risk bound that induces Tikhonov regularization on the Lipschitz constant of the reconstruction operator, and is less conservative relative to standard DRO for well-posed problems. Numerical experiments on deblurring and sinogram-to-CT reconstruction demonstrate improved robustness, stability, and interpretability over standard DRO and MSE baselines. In the linear setting, the learned operator becomes effectively low-rank, truncating at the intrinsic dimension of the data and recovering a data-driven analogue of truncated-SVD regularization.

We investigate the reconstruction of holographic duals for strongly coupled quantum field theories in regimes characterized by large hierarchies and the presence of false vacua. Within the gauge/gravity duality, these features translate into non-trivial thermodynamic behaviour and exotic renormalization group flows, including skipping flows between non-adjacent fixed points. Building on previous work based on Physics-Informed Neural Networks (PINNs), we extend the holographic inverse problem of reconstructing the bulk scalar potential from boundary thermodynamic data into this new regime. This setting presents a variety of conceptual and numerical challenges, such as near-degenerate states, large hierarchies of energy scales, and regions of the potential that are not directly probed by the input data. We develop a set of methodological advances that overcome these obstacles, thereby improving the established PINNs-based methodology and extending it to new physical regimes of interest that were previously out of reach. Applying the developed framework, we demonstrate accurate reconstruction of scalar potentials deep into the false vacuum regime, achieving robust agreement with the physical features of the underlying thermodynamics despite significant numerical stiffness. Our results extend the bridge between holography and machine learning, and suggest that data-driven approaches can provide new insights into the structure of strongly coupled systems.

Physics-informed neural networks (PINNs) have recently emerged as a promising framework for addressing the Calderón inverse problem from limited boundary data. In this work, we revisit neural Calderón inversion by introducing multiscale boundary excitations based on randomized wavelet functions and investigating the role of Fourier-feature encoding (FFE) for representing sharp conductivity variations. We propose a physics-informed reconstruction framework that represents the unknown conductivity and the associated family of electric potentials with separate neural networks conditioned on the applied boundary excitations. The governing elliptic PDE is enforced through physics-informed residuals, while finite Dirichlet-to-Neumann (DtN) data are incorporated through boundary losses. Using synthetic data from a finite-difference forward solver, we evaluate the method on conductivity fields with inclusions, sharp interfaces, smooth profiles, and heterogeneous media. Results show that the framework recovers dominant conductivity structures from finite boundary measurements with relative errors between $3\%-12\%$ approximately. We show that FFE improves the reconstruction of localized sharp features, particularly for inclusions and interfaces, but are not universally optimal, with raw-coordinate networks performing competitively for smoother fields. These results highlight coordinate representations and boundary excitation design as key factors in neural Calderón inversion.