Inverse Problems

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20 papers in the last four weeks, up 186% on the four weeks before. 0.2% of all new papers.

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Latest papers 161

Oct 7, 2026cs.LG

Edge Accuracy Is Not Enough: Why Dynamics-Learned Structure Fails to Transfer to Inverse Problems

A natural strategy for inverse problems with scarce labelled data is to transfer relational structure learned from abundant forward-simulation data. We show this strategy fails systematically, even when it satisfies the standard theoretical justification for why structure should help. We prove that approximate structure provides estimation-error benefits whenever the edge error satisfies

Δ< n^2 - kn

, reducing sample complexity from

O(n^2)

to

O(kn+Δ)

. Structure learned via Neural Relational Inference (NRI) from dynamics prediction satisfies this condition, yet on a source-localisation task across 180 CFD-simulated hydrogen-leak scenarios and 180 acoustic scenarios, it degrades performance by 116% and 201% relative to a flexible, task-optimised attention baseline, while a physics-based prior (Green's function) degrades by only 69-72%. Four independent lines of evidence show this is not a tuning failure: NRI improves only 0.5% when given 18x more training data (versus 16.6% for the task-optimised baseline,

p<0.001

); performance is insensitive to the NRI edge threshold across a wide range; the dynamics-learned graph overlaps the task-optimal graph on only 6% of edges; and two further dynamics-derived structure estimators (correlation- and mutual-information-based) show no measurable benefit over a structure-free baseline, with the correlation-based estimator performing markedly worse. We formalise this gap as a statement about approximation error that the edge-accuracy condition cannot control, and we provide a lightweight transferability test (Jaccard similarity against a partially-observed target-task graph) that separates successful from failed transfer in all four domain/structure pairs we evaluate, using under an hour of computation and 15-20% of target-domain data; we present this as a heuristic calibrated on few cases, not a validated general threshold.

Nicholas Tan Jerome, Fangnian Wang

Institute for Data Processing and Electronics (IPE) Karlsruhe Institute of Technology (KIT) Karlsruhe, Germany · Institute for Thermal Energy Technology and Safety (ITES) Karlsruhe Institute of Technology (KIT) Karlsruhe, Germany

Inverse Problems Graph Structure Learning Task Transferability Estimation

Oct 7, 2026hep-th

Fast holographic inversion of superconducting domes

A holographic superconductor whose scalar mass depends on the gauge field strength,

M(\Fsq)

, reproduces a superconducting dome for a suitable

M

, and recovering that

M

from a given dome has so far taken days for a single training run. We propose a new way of training this model, with which an inversion takes from about ten minutes to an hour. Training needs the gradient of the condition that fixes the critical temperature, which the earlier method obtains by finite differences, repeating the bulk integrations for every training parameter. Here that condition is obtained, without any fit, from two integrations started at the horizon and at the boundary, and its derivative with respect to

M

is an integral over the same two solutions, so the gradient needs no integration of its own. We use the speed to study the part of

M

that a dome cannot determine, on the interval between the value

\Fsq

takes at the horizon for the lowest doping and

\Fsq=0

, at which

M

is the scalar mass

M(0)

that fixes the dimension of the dual operator. We hold the scalar mass at several values, which we call pinned masses, retrain everything else at each, and find that the reconstructions agree wherever the horizons of the dome reach, including the minima of

M

, and differ only on that interval. A rule that keeps the reconstruction with the simplest closed form recovers both the scalar mass and the mass function of a test dome. On Gaussian and double-Gaussian domes and on the measured phase diagrams of YBa

_{2}

Cu

_{3}

O

_{y}

and 2M-WS

_{2}

, however, the pinned mass it keeps rests on ties or on narrow margins, so for these targets the scalar mass is left open. The dome thus constrains

M

where its horizons reach, and fixing the dimension of the dual operator needs a second observable.

Sejin Kim

Center for AI and Natural Sciences, Korea Institute for Advanced Study, Seoul 02455, Korea

Inverse Problems Quantum Many-Body Physics

Oct 7, 2026cs.LG

Self-attention summary networks for subsurface velocity-model building from common-image gathers

Common-image gathers (CIGs) contain physically meaningful information about velocity-model errors through reflector focusing and residual moveout, but in conventional imaging workflows they are typically used only as diagnostic tools. In this work, we propose a multiscale self-attention summary network that maps high-dimensional 3D CIG volumes into compact conditioning embeddings for probabilistic subsurface velocity inversion. These learned embeddings preserve offset-dependent kinematic structure and spatial coherence while reducing variability caused by background-velocity mismatch. Conditioned on these summary embeddings, a flow-matching model learns a transport from a Gaussian source distribution to the posterior distribution of plausible velocity fields. Numerical experiments show that, compared with direct conditioning on raw CIGs, the proposed summary network improves posterior velocity inference. In particular, the multiscale attention design provides greater robustness to background-model mismatch, yielding more accurate posterior reconstructions and lower predictive uncertainty.

Shiqin Zeng, Yunlin Zeng, Abhinav Prakash Gahlot +2

Georgia Institute of Technology

Inverse Problems Bayesian Inverse Problems Image Inverse Problems Multi-Scale Attention

Oct 7, 2026cs.LG

Twist Flow for Inverse Problems

In Bayesian inverse problems, posterior sampling requires generating samples that are consistent with given observations while capturing the range of plausible solutions. Direct conditional generative models introduce latent noise to model this ambiguity, but paired inverse-problem training can still encourage an almost deterministic map from the observation to the target. As a result, generated samples may be observation-consistent while under-representing posterior variability, especially when the posterior is multimodal, leading to undercoverage, mode distortion, or artificial transitions between distinct feasible solutions. We propose joint twist-flow, an augmented flow-matching formulation that learns a continuous transport from the augmented source state

(z_x, y)

to the augmented terminal state

(x, z_y)

. Here x is the target variable,

y

is the observation,

z_x

is the Gaussian reference coordinate for posterior sampling, and

z_y

is a Gaussian likelihood-side coordinate associated with the observation branch. Under a Gaussian observation model,

z_y

is motivated by the normalized observation residual associated with observation compatibility. Its role is not to replace uncertainty in

x

, but to couple generated samples of x to observation consistency, helping reduce likelihood-inconsistent variation while preserving variability in weakly constrained directions. We validate the method on low-dimensional inverse problems with reference posterior samples, where joint twist-flow better preserves multimodal posterior support than a direct conditional-flow baseline. We further evaluate the method on image restoration and seismic subsurface velocity-model inversion, showing increased posterior variability while maintaining observation consistency.

Shiqin Zeng, Zijun Deng, Felix J. Herrmann

Georgia Institute of Technology

Bayesian Inverse Problems Posterior Sampling Inverse Problems Flow Matching Image Inverse Problems

Oct 5, 2026cs.LG

Inferring physical fields in coupled systems with unknown parameters from incomplete observations using physics-constrained attentive neural operators

Given incomplete measurements of a single physical field in a coupled system with unknown parameters, can we infer its full physical state and identify the underlying parameters? This problem is challenging because multiple coupled fields must be reconstructed simultaneously from limited observations of only one, while the system parameters are unknown. In this work, we propose a machine learning framework for full-field reconstruction and parameter identification of unknown physical systems from sparse observations of a single physical field. Specifically, the cross-attention encoder propagates sparse sensor observations onto a regular grid to construct a sensor-conditioned latent representation, while a Fourier neural operator (FNO) decoder captures global spatial dependencies to reconstruct all coupled physical fields. The network parameters and unknown physical parameters are jointly optimized by minimizing observation losses, governing equation residuals, and boundary/initial condition constraints. The proposed approach is validated on two- and three-dimensional lid-driven cavity flows, a two-dimensional cylinder wake, and a two-dimensional non-ideal magnetohydrodynamics problem, demonstrating the recovery performance of unobserved fields and physical parameters from incomplete observations.

Shilun Wei, Xiaoqiang Sun, Wei Li +1

School of Mathematics, Sun Yat-sen University, Guangzhou, China · School of Sciences, Great Bay University, Dongguan, China · John Hopcroft Center for Computer Science, School of Computer Science, Shanghai Jiao Tong University, Shanghai, China

Parameter Identifiability Physics-Informed Neural Operators PDE Inverse Problems Inverse Problems

Oct 4, 2026cs.LG

Robust Ensemble Guidance for Scientific Inverse Problems

Ensemble guidance combines pretrained diffusion priors with black-box forward models to solve inverse problems without differentiating through the physical simulator. However, observation coordinates with large predictive spread or extreme residuals can dominate the ensemble correction, degrading reconstruction accuracy. We show that two simple modifications, weighting and clipping, substantially improve this correction. Our method, Robust Ensemble Guidance (REG), uses ensemble predictive spread to balance observation scales and adaptively clips standardized residuals to limit the influence of extreme discrepancies. Both operations reuse existing particles and forward predictions, requiring no additional denoiser or forward-model evaluations. Under a local linear Gaussian model, we derive conditions for reduced one-step estimation risk, bound the influence of individual observation coordinates, and characterize when these benefits persist with finite ensembles. Experiments on Navier-Stokes inversion, black-hole imaging, and acoustic full-waveform inversion demonstrate improved reconstruction over the underlying ensemble solver. In particular, REG increases black-hole reconstruction PSNR by 6.2-8.2 dB across three observation regimes and reduces Navier-Stokes reconstruction error by 26.4% in a matched-budget comparison. These findings highlight the importance of observation heterogeneity and residual influence in designing reliable generative solvers for scientific inverse problems.

Zixiang Li, Wei Wang, Yunchao Wei +2

Beijing Jiaotong University · Tsinghua University

Diffusion Model Guidance Diffusion-Based Inverse Problems PDE Inverse Problems Inverse Problems Robust Estimation

Oct 4, 2026cs.AI

R1A-PC: Physics-Guided Electromagnetic Inversion of Three-Dimensional Human Point Clouds in Complex Static Environments

Recovering three-dimensional human geometry from electromagnetic measure?ments in a complex static environment is difficult because strong multipath responses from walls, floors, and other objects obscure the weak target per?turbation. We propose R1A-PC, a physics-guided method that reconstructs a 2048-point human cloud from paired complex fields measured with and without the target. Complex background subtraction emphasizes target-induced ampli?tude and phase changes, while the background field remains available as an environmental condition. A frequency-balanced discrete Born adjoint produces a three-dimensional spatial knowledge map. At each of two bounded deformation stages, the decoder combines complex measurement features, background fea?tures, and multiscale physical features queried at the current point coordinates; the second stage queries again after the first coordinate update. We analyze the residual of paired subtraction, the weighted normal-operator structure of the raw adjoint, and the feasible set of the predicted cloud. In a held-out background generated by full-wave simulation under a fixed acquisition geometry, R1A-PC obtains a squared Chamfer distance of 0.001434 m2 and an F-score of 0.963080 at 0.05 m. Compared with TopNet, the Chamfer distance decreases by 70.28%. Removing physical guidance or background subtraction increases the Chamfer distance by 242.06% or 241.18%, respectively. Experiments across background layouts and poses support the complementary roles of paired subtraction and position-dependent adjoint features.

Xudong Yuan, Ruyun Xu, Jingtai Yang +1

School of Mathematics and Statistics, Changchun University of Science and Technology, Changchun, China.

3D Reconstruction Point Cloud Surface Reconstruction 3D Human Reconstruction Physics-Informed ML Inverse Problems

Oct 4, 2026physics.comp-ph

A Contrast-Source Inversion Scheme Based on Stochastic Optimization and Plug-and-Play Regularization

An electromagnetic inversion scheme that integrates stochastic optimization (STO) and plug-and-play (PNP) regularization into contrast-source inversion (CSI), termed STO-PNP-CSI, is developed. Standard CSI solves for the contrast source vector of every transmitter at each iteration, which is expensive in a multi-transmitter configuration. STO instead solves for only one randomly selected contrast source vector per iteration, which reduces the per-iteration cost and can help the inversion escape poor local minima and saddle points. The resulting loss of information, however, increases the ill-posedness of the inversion. To counter this, the Swin-Conv-UNet (SCUNet) denoiser is plugged into the CSI scheme as an implicit regularizer, supplying a learned prior that is stronger than conventional hand-crafted ones and stabilizes the reconstruction. The proposed STO-PNP-CSI is applied to both synthetic and experimental data. The results show that it yields accurate reconstructions at substantially lower computational cost than CSI, including under strong nonlinearity and measurement noise.

Lingqi Gao, Hakan Bagci

Electrical and Computer Engineering (ECE) Program Computer, Electrical, and Mathematical Science and Engineering (CEMSE) Division King Abdullah University of Science and Technology (KAUST) Thuwal, 23955-6900, Saudi Arabia

Inverse Problems

Oct 1, 2026math.OC

Initial condition recovery in nonlinear damped viscous photoacoustic tomography using a convolutional neural network-guided gradient-free optimization framework

Photoacoustic tomography (PAT) is a hybrid imaging modality that combines high optical contrast with high ultrasonic resolution for biomedical imaging applications. In this work, we investigate the inverse problem of recovering the initial pressure distribution from boundary measurements in the presence of nonlinear acoustic propagation and viscous attenuation effects. To model these phenomena more accurately, we consider a nonlinear damped viscoelastic wave equation incorporating spatially varying sound speed, temporal attenuation, and nonlinear propagation mechanisms. We first establish the well-posedness of the corresponding forward problem using a Galerkin approximation combined with energy estimates and a fixed-point argument. For the inverse problem, we derive existence, uniqueness, and local uniqueness results under suitable assumptions through a harmonic extension reduction, spectral Laplace transform techniques, and observability estimates. To numerically reconstruct the initial pressure field, we develop a hybrid reconstruction framework that combines a convolutional neural network (CNN) with a gradient-free optimization strategy based on the sequential quadratic Hamiltonian (SQH) method derived from Pontryagin's maximum principle. The CNN is used to generate an informative initial guess, while the SQH framework enforces the governing PDE dynamics during the reconstruction process. Numerical experiments demonstrate that the proposed hybrid strategy significantly improves reconstruction quality, contrast, and robustness compared to standalone time-reversal and CNN-based approaches.

Madhu Gupta, Anwesa Dey, Prapti Tala +1

Department of Mathematics, Indian Institute of Technology, Gandhinagar, Gujarat, India. · Department of Mathematics, University of Utah, Salt Lake City, Utah, UT, USA. · Department of Mathematics, The University of Texas at Arlington, Arlington, TX, USA.

Medical Imaging PDE Inverse Problems Inverse Problems

Sep 29, 2026cs.CV

DynamicHOI: Coupled Dynamics for Physics-aware HOI Reconstruction

We study hand-object interaction (HOI) reconstruction from monocular RGB videos, where partial observations can produce visually plausible yet mechanically inconsistent trajectories. Existing methods mainly enforce visual and geometric agreement, leaving the underlying interaction dynamics insufficiently constrained. We propose DynamicHOI, a physics-aware HOI reconstruction framework combining geometry-grounded diffusion refinement with coupled hand-object dynamics. Geometry spatially grounds visual evidence for trajectory refinement, while articulated inverse dynamics and Newton-Euler dynamics derive hand generalized forces and object wrenches for dynamics-level supervision. We further couple hand and object dynamics through contact-force transfer and recover active hand actuation as an interaction-level physical quantity. We formulate its empirical magnitude distribution into a probabilistic prior that penalizes unlikely actuation and suppresses mechanically implausible reconstructed motion. Experiments on three HOI datasets show consistent improvements in both hand and object reconstruction. The reconstructed trajectories further benefit downstream applications including hand world-model generation and robotic manipulation learning, demonstrating the value of physics-aware HOI modeling beyond reconstruction.

Wenliang Guo, Zhanbo Huang, Yu Kong

Michigan State University

3D Reconstruction Monocular 3D Reconstruction Inverse Problems Human-Object Interaction

Sep 28, 2026cs.LG

Livin' on a Prior: Likelihood Score Approximation for Inverse Problems

Generative models have found great success as data-driven methods of solving inverse problems. Two popular approaches work either by combining a pretrained generative prior with a known degradation model, or by training a conditional generative model directly from paired data. We target a setting that spans both regimes: unknown degradations can be learned from few paired examples, while known degradations can be learned from self-generated samples. We introduce Likelihood Score Approximation (LSA), a generative framework that keeps a pretrained unconditional model fixed and learns an observation-conditioned model that approximates the likelihood score from paired samples. Within a conditional stochastic-interpolant framework, LSA can be trained in either score or velocity coordinates, independently of the unconditional model's native parameterization, and supports both deterministic and stochastic sampling. We further show empirically that the prior model can be swapped post-training while keeping the same LSA model. Across speech and image inverse problems, LSA operates effectively even at roughly 0.01% of the full training dataset. On the ImageNet-256 benchmark it achieves competitive or better restoration quality than strong posterior-sampling baselines while requiring up to several orders of magnitude fewer network evaluations.

Rostislav Makarov, Tal Peer, Danilo de Oliveira +1

Signal Processing University of Hamburg Hamburg, Germany

Conditional Generative Modeling Inverse Problems Image Inverse Problems

Sep 28, 2026cs.CV

SNaP: One-Step Posterior Sampling for Noisy Inverse Problems

Diffusion and flow-matching models can produce high-quality posterior samples for inverse problems, but typically require tens to thousands of network evaluations per draw. MeanFlow enables one-step generation, yet applying it to inverse problems leaves no intermediate steps at which to enforce measurement consistency. We introduce SNaP, a one-step MeanFlow posterior sampler for linear inverse problems with Gaussian noise. Its central innovation is a measurement-adapted source: a Gaussian distribution whose mean and anisotropic covariance are determined by the measurement operator, observation, and noise level. The source anchors well-measured directions while preserving variation where the measurements are weak or uninformative. We show that the exact conditional flow transports this source to the true posterior. Across natural-image restoration and multi-coil MRI, SNaP produces diverse, high-quality samples with one network evaluation per draw, 30 to 2250

\times

faster than iterative samplers.

Shirin Shoushtari, Edward P. Chandler, Xiao Shi +1

WashU · UW-Madison

Flow Matching MeanFlow Posterior Sampling Accelerated MRI Reconstruction Flow-Based Generative Modeling Diffusion Posterior Sampling+1

Sep 24, 2026cs.LG

FB-GDM: Fully-Bayesian Guided Diffusion Models for High-Dimensional Linear Inverse Problems via Unsupervised Variational Inference

Diffusion models are powerful priors for linear inverse problems, but the reference guidance methods, Diffusion Posterior Sampling (DPS) and Pseudoinverse-Guided Diffusion Models (

Π

GDM), rely on scalar hyperparameters tuned per task, usually against the ground truth. We introduce FB-GDM, a fully-Bayesian guided diffusion method that removes this calibration step. Starting from the Gaussian approximation of

Π

GDM, we derive a closed-form conditional score that depends on two precision parameters (inverse variances), one associated with the denoising approximation and one with the observation likelihood, and treat them as latent variables inferred by variational inference at each reverse step. A separable factorization makes each update scale linearly with the number of pixels, so the inference stays tractable at full image resolution, at a cost comparable to one

Π

GDM run. FB-GDM requires neither the noise level nor the ground truth: its only inputs are the observation and the forward operator. Experiments on CelebA-HQ inverse problems establish two results. (i) The precision parameters, inferred from the observation alone, allow FB-GDM to outperform

Π

GDM at its nominal setting, even when the latter is given the true noise level, by up to 14 dB depending on the operator, and to match the ground-truth-calibrated

Π

GDM oracle within 0.1 dB. (ii) FB-GDM is robust when the forward operator, the noise level, or the image distribution changes: it stays close to a per-problem

Π

GDM oracle throughout and does not exhibit the hallucinations observed with DPS, whereas DPS substantially degrades at a fixed scale and

Π

GDM stays competitive only if it is re-tuned against the ground truth for each new problem. When the prior is applied to images outside its training set, this re-balancing between data and prior keeps FB-GDM faithful where a fixed face-prior guidance can otherwise hallucinate.

Gatien Séguy, Thomas Rodet

SATIE · SATIE Laboratory, ENS Paris-Saclay, CNRS, Universit´e Paris-Saclay, 91190 Gif-sur-Yvette, France

Diffusion Model Guidance Bayesian Inverse Problems Diffusion-Based Inverse Problems Inverse Problems

Sep 23, 2026cs.CV

NeuralSRNF: Neural Square Root Normal Fields for the Statistical Shape Analysis and Generation of Nonrigid 3D and 4D Objects

We introduce NeuralSRNF, a novel framework for the statistical shape analysis and generation of genus-zero 3D and 4D objects that undergo nonrigid deformations. Traditional methods rely on complex and computationally expensive nonlinear elastic metrics that measure bending and stretching. Recent advances in elastic shape analysis achieve computational efficiency by mapping input 3D shapes to the space of Square Root Normal Fields (SRNFs) where the L2 metric approximates the partial elastic metric, significantly facilitating the process of computing geodesics and summary statistics. SRNFs, however, are not invertible, and the numerical algorithms used to map SRNFs back to the original space of surfaces remain computationally very expensive and often lead to approximate results. This paper addresses this fundamental SRNF inversion problem using a novel neural representation, termed NeuralSRNF. Unlike the commonly used numerical SRNF, NeuralSRNF is (1) continuous, and thus resolution-agnostic, enabling full functional shape analysis, (2) more accurate, and (3) computationally more efficient as it can compute inverse SRNF maps along a geodesic path in less than 3 s compared to over 10 min for the numerical SRNF. We demonstrate, using various datasets, the utility and efficiency of the proposed NeuralSRNF in multiple elastic 3D and 4D shape analysis tasks such as geodesic computation, deformation transfer, statistical summaries computation, and 3D shape generation. We show that it outperforms competing methods on most evaluated datasets and metrics by a wide margin in both accuracy and computational efficiency. The source code and additional results are available at https://awaisnizamani16.github.io/awais/NeuralSRNF/.

Awais Nizamani, Hamid Laga, Guanjin Wang +3

Murdoch University, Perth, Australia · The University of Western Australia, Perth, Australia · The Johns Hopkins University, Maryland, US

Neural Representation Geometry Statistical Shape Modeling 3D Shape Generation Inverse Problems

Sep 20, 2026cs.LG

GenVoid: Uncertainty-Aware Learning of Subsurface Material Defects with an Experimentally Validated Physics-Informed Generative Model

Internal voids are ubiquitous defects in manufactured structures, yet their characterization remains challenging because their geometry is hidden and can only be inferred indirectly from accessible measurements. Here we introduce \textit{GenVoid}, a physics-informed generative model-based framework for identifying internal voids in complex two- and three-dimensional solids from surface displacement measurements alone. By incorporating the governing mechanics into a generative inference framework, \textit{GenVoid} enables void identification across linear elastic, hyperelastic and plastic material behaviours and accommodates complex two- and three-dimensional structural geometries. Importantly, the framework explicitly accounts for uncertainty and noise in displacement measurements, producing probabilistic reconstructions of internal void geometry rather than a single deterministic estimate. We demonstrate the approach using high-fidelity synthetic datasets and experimentally measured displacement fields obtained from in-situ mechanical experiments, establishing its ability to infer hidden voids from realistic displacement measurements. To quantify the fundamental limits of such inference, we further introduce an observability measure that characterizes the sensitivity of boundary measurements to localized stiffness perturbations within the interior under an ensemble of applied loads. This framework provides a direct connection between defect location, sensor configuration and reconstruction fidelity, enabling systematic assessment of how the number and spatial distribution of boundary measurements govern void-identification accuracy. To this end, these results establish a physics-informed and uncertainty-aware approach for non-invasive characterization of hidden defects and provide a quantitative basis for designing measurement strategies for inverse problems in solid mechanics.

Trishit Mondal, Prajwal Bharadwaj, Nikhil Karanjgaokar +1

Aerospace Engineering Department, Worcester Polytechnic Institute, Worcester, MA 01609, USA.

Physics-Informed Generative Modeling Structural Mechanics Inverse Problems

Sep 17, 2026cs.LG

Ranking Competing geologic interpretations via foundation-model-assisted generative hydrologic inversion

High-consequence subsurface decisions often rely on sparse data that permit competing geological interpretations. Determining consistency of these interpretations with the available observations remains challenging. We present a workflow that addresses this challenge by translating competing geologic interpretations into alternative priors and ranking them according to their consistency with hydraulic-head observations. A key step in this workflow is exploiting the broad knowledge of image-generation foundation models to transform nuanced geologic interpretations into data ready for computer modeling. For each interpretation, a text-to-image foundation model generates an ensemble of geologic images, and a separately trained variational autoencoder learns an interpretation-specific latent representation. A supervised inverse network maps head observations into this latent space, and the frozen decoder reconstructs an image that is mapped to a log-conductivity field. Steady-state flow simulations predict heads, and the aggregate normalized head error determines the ranking. We evaluate the framework using a synthetic benchmark based on the Johansen Formation with three interpretations of decreasing consistency with the reference geology. Across 595 test cases, the Precise & Accurate interpretation produces lower normalized errors than Accurate in 58.5% of cases and Mismatched in 82.5% of cases. Accurate outperforms Mismatched in 65.5% of cases. We then compare spatial representations of two published conceptual models of the Culebra Dolomite Member at the Waste Isolation Pilot Plant. The revised representation yields an aggregate normalized error of 7.598, compared with 8.595 for the original, consistent with the documented conceptual-model revision. The framework enables quantitative comparison of competing geological interpretations using available hydraulic observations.

Harun Ur Rashid, Daniel O'Malley

Earth and Environmental Sciences Division, Los Alamos National Laboratory, Los Alamos, NM, USA

Inverse Problems

Sep 17, 2026cs.LG

Learning-Based Reconstruction of Optical Properties in Bilayered Media from Single-distance Time-Resolved Reflectance Measurements

The inverse problem of reconstructing optical properties, specifically absorption and scattering coefficients, in layered biological media from time-domain reflectance measurements remains a significant challenge for traditional analytical models. Inverse solvers based on the diffusion equation often struggle with structural heterogeneity, frequently yielding poor accuracy for superficial absorption and deep-layers scattering. In this work, we propose a machine learning framework as an alternative approach to reconstruct the optical properties of a bilayered medium, benchmarking its efficiency and accuracy against model-based algorithms. To overcome the intrinsic approximations of diffusion theory and inverse reconstruction, we generated a robust synthetic dataset of forward DTOF using exact Monte Carlo simulations at multiple source-detector distances. A machine learning pipeline was then trained on this dataset and validated against state-of-the-art model-based reconstruction methods. Besides the significant reconstruction speed-up, the machine learning approach achieves higher accuracy than model-based inverse solvers, further providing an estimate of the parameter space dimensionality without requiring any a priori information about the number of layers in the investigated geometry. Further enhancements in the reconstruction accuracy can be expected in future extensions of this work, by training the pipeline over multiple DTOF curves from the same medium, in a joint multi-distance reconstruction approach.

Caterina Amendola, Giulia Maffeis, Lorenzo Buffoni +8

Department of Physics, Politecnico di Milano, Milan, 20133, Italy

Inverse Problems Image Inverse Problems

Sep 16, 2026hep-th

Deep learning emergent spacetime from fermionic spectral functions in holography

We present a physics-informed machine learning framework based on Neural Ordinary Differential Equations that solves the holographic inverse problem: reconstructing the bulk spacetime and gauge field of a charged AdS black hole directly from boundary fermionic spectral functions. Encoding the UV asymptotics, horizon regularity, and zero temperature extremality as hard constraints in the neural network architecture, our framework reliably reconstructs the extremal Reissner-Nordström AdS geometry across three quantum critical regimes set by the

U(1)

probe charge---non-Fermi liquid, marginal Fermi liquid (strange metal), and Fermi-liquid-like states---and can jointly infer the probe charge itself to sub-percent accuracy. Relaxing the near-AdS boundary constraint uncovers a geometrical degeneracy: bulk profiles that differ throughout the radial direction but share the same near-horizon

AdS_2 \times \mathbb{R}^2

data reproduce identical spectral functions near the Fermi surface. This isospectral non-uniqueness is precisely the bulk degeneracy expected on general holographic grounds at zero temperature, and its spontaneous emergence across independent training runs shows that the network isolates the IR CFT universality rather than overfitting a single UV completion.

Koji Hashimoto, Hyun-Sik Jeong, Keun-Young Kim +2

Department of Physics, Kyoto University, Kyoto 606-8502, Japan · Asia Pacific Center for Theoretical Physics, Pohang 37673, Korea · Department of Physics, Pohang University of Science and Technology, Pohang 37673, Korea +3

High-Energy Physics Physics-Informed ML Inverse Problems

Sep 16, 2026astro-ph.SR

Physics-Informed Neural Networks for Fast Multilayer Spectral Inversion of Hα 6562.8 A and Ca II 8542.1 A Spectra

Strong chromospheric absorption lines such as H

α

6562.8 A and Ca II 8542.1 A provide vital diagnostics of plasma dynamics and thermal structure in the solar chromosphere. Multilayer spectral inversion (MLSI) offers a physically interpretable framework for modeling these lines using a finite number of radiative-transfer layers, but conventional MLSI relies on pixel-by-pixel nonlinear least-squares fitting, making it computationally expensive for large imaging spectroscopic data sets. Here, we introduce a physics-informed neural-network (PINN) framework to accelerate MLSI while preserving its analytic radiative-transfer formulation. The network predicts MLSI parameters directly from observed line profiles and passes them through a differentiable MLSI forward model to synthesize spectra. Training follows a two-stage approach: an initial stage optimized solely via spectral reconstruction loss, followed by fine-tuning that combines spectral consistency with parameter-space supervision from conventional MLSI results on a single reference image. This strategy eliminates the need for large precomputed training sets while maintaining physical interpretability. Applied to Fast Imaging Solar Spectrograph (FISS) observations from the Goode Solar Telescope (GST) targeting both quiet-Sun and active-region regions, MLSI-PINN parameter maps reproduce the primary spatial structures of direct inversions, achieving an arithmetic mean pixel-wise Pearson correlation coefficient of 0.933 across all evaluated parameters. The reconstructed spectra closely match both observed profiles and conventional MLSI fits. Post-training, MLSI-PINN processes a raster in approximately 5-15 seconds compared to 3-5 minutes for conventional MLSI, delivering an inference speedup of about 12-60 times without substantial loss in reconstruction quality, enabling efficient MLSI analysis on large chromospheric data sets.

Ziyang Zhang, Qin Li, Vasyl B. Yurchyshyn +4

Department of Mechanical and Industrial Engineering, New Jersey Institute of Technology, Newark, NJ, USA · Department of Physics, New Jersey Institute of Technology, Newark, NJ, USA · Big Bear Solar Observatory, New Jersey Institute of Technology, Big Bear City, CA, USA +1

Efficient Neural Network Inference Physics-Informed ML Inverse Problems

Sep 14, 2026cs.LG

Physical-State-Guided Diffusion Sampling for Full-Waveform Inversion

Full waveform inversion (FWI) estimates subsurface velocity from seismic recordings, but its ill-posedness and nonlinearity make accurate reconstruction strongly dependent on initialization and prior information. Diffusion posterior sampling provides a learned geological prior, yet directly coupling its denoiser to the nonlinear wave solver can yield unreliable physical guidance. We propose Physical-State-Guided Diffusion Sampling (PSG), which couples a persistent physical velocity to the diffusion prior through a Gaussian bridge. The physical state is refined by waveform fitting regularized by the denoised velocity, and in turn guides the reverse diffusion process. This formulation separates the wave-equation and denoiser gradients while preserving conventional FWI initialization and accumulated optimization history. On four OpenFWI families, PSG's terminal denoised estimates outperform classical and diffusion-based baselines under clean and missing-trace acquisitions and maintain strong structural recovery under measurement noise. Repeated stochastic runs preserve the dominant geological structures, with ensemble variability concentrated near geological interfaces and positively associated with local inversion error. A frozen OpenFWI-trained prior further supports inversion of the larger Marmousi, Overthrust, and BP2004 Salt models, recovering complex geological structures without retraining.

Chen Min, Haowen Jiang, Zheng Ma +1

School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai, China · CMA-Shanghai, Shanghai Jiao Tong University, Shanghai, China · School of Mathematics and Statistics, Lanzhou University, Lanzhou, China

Physics-Informed Diffusion Models Diffusion-Based Inverse Problems Diffusion Posterior Sampling PDE Inverse Problems Inverse Problems Image Inverse Problems

Sep 14, 2026physics.optics

Proximal-Only Transmission Matrix Recovery of an Arbitrarily Deformed Graded-Index Multimode Fiber

The multimode fiber is among the thinnest imaging conduits available, carrying hundreds to thousands of spatial modes through a cross-section comparable to a human hair, but its endoscopic capabilities are currently limited by the sensitivity of the transmission matrix to the fiber's deformed state. Proximal-only recovery of the fiber's transmission matrix is an appealing approach for enabling general use multimode fiber endoscopy, and within the last decade, machine learning techniques have been applied to both single-ended and double-ended transmission matrix recovery tasks. We present a new approach to this interdisciplinary problem and show that neural networks can generalize to recover transmission matrices of an arbitrarily deformed graded-index multimode fiber from proximal measurements alone.

Cole Reynolds

Weyl Labs

Endoscopy Inverse Problems

Sep 11, 2026cs.CV

FIRM: Flow-based Imaging via Regularized Minimization

Flow matching methods for imaging inverse problems typically incorporate measurements through network conditioning or guidance during sampling. Neither approach explicitly applies the forward operator within the learned conditional velocity field. We develop a principled measurement-conditional velocity parameterization that does. For a linear interpolation path, we express the optimal velocity through the posterior mean

E[x_1|x_t, y]

and show that this mean is the unique minimizer of a variational objective with an explicit data-consistency term. The velocity defined by this minimizer provably transports the source distribution to the measurement-conditioned posterior. This result leads to a forward operator-aware velocity field that is trained end-to-end and requires no separate guidance during sampling. Across five imaging tasks, our method achieves leading reconstruction quality with up to

50\times

fewer network evaluations than competitive flow-based methods. Varying the number of sampling steps also controls the distortion-perception trade-off without retraining.

Shirin Shoushtari, Edward P. Chandler, Xiao Shi +1

WashU · UW-Madison

Conditional Flow Matching Image Reconstruction Inverse Problems Image Inverse Problems

Sep 9, 2026cs.CV

Advanced Brain Tissue Imaging with Data-Consistent Diffusion Priors in Laminographic X-Ray Nanoimaging

Nanoscale imaging of mammalian brains is critical for connectomics. X-ray laminography enables high-throughput imaging of extended, plate-like biological specimens. However, the tilted acquisition geometry leads to incomplete Fourier-space coverage, giving rise to a missing-cone of information. Conventional reconstruction methods cannot recover unmeasured information within the cone, resulting in artifacts that distort fine brain structures. While resolving these requires modeling 3D structure, direct 3D deep learning approaches are limited by data scarcity and computational cost. Here we introduce LUCID (Laminography with Unified Consistent Diffusion), a framework that combines multi-view diffusion priors with projection-domain data consistency. LUCID integrates complementary 3D structural information while enforcing strict alignment with the laminography forward model. On simulated datasets, LUCID substantially improves spatial fidelity and restores missing Fourier components, outperforming baseline methods. Applied to experimental laminography data, LUCID generalizes robustly despite being trained exclusively on fully sampled tomographic volumes, and effectively recovers unmeasured Fourier information.

Wenxuan Fang, Abraham L. Levitan, Ana Diaz +10

Ecole Polytechnique F´ed´erale de Lausanne, Lausanne, Switzerland. · Paul Scherrer Institute, Villigen, Switzerland. · Sensory Circuits and Neurotechnology Lab, The Francis Crick Institute, 1 Midland Road, London, NW1 1AT, UK. +2

3D Reconstruction Image Reconstruction Diffusion-Based Inverse Problems Neuroimaging Inverse Problems

Sep 9, 2026stat.ML

Why Learning Rediscovers the Closed-Form Diagonal Regularizer

We identify a diagonal saturation principle in modal inverse problems: when truncation noise is isotropic, the Bayes-optimal Tikhonov shape is a closed-form power law Gamma_k proportional to lambda_k^|s| set by the prior alone, independent of the domain. Berry's random-wave conjecture decorrelates the truncation noise across modes, and Weyl's eigenvalue counting law supplies enough modes for the conclusion to survive empirical Berry violations. Together they predict an approximately flat loss landscape across the per-mode family, leaving narrow scope for a diagonal regularizer to robustly beat the closed form. On FEM-simulated acoustic rooms, the closed form is near-optimal relative to per-room oracle tuning across observation windows, and three diagonal architectures trained on the same data match its reconstruction error within 1 pp despite learning qualitatively different spectra. The framework extends to heat diffusion via a known exponential Green's function correction with no new free parameters. Saturation is restricted to the diagonal family: Learned Iterative Ridge crosses the boundary by exploiting cross-mode coupling, locating where learning starts to help.

Jeahn Han, Pyojin Kim

GIST

Spectral Regularization PDE Inverse Problems Inverse Problems

Sep 8, 2026cs.LG

Multi-Level-Set-Based Physics-Driven Neural Network to Solve 3-D Inverse Scattering Problems

This paper proposes a level-set-based physics-driven neural network solver (LSPDNN) for 3-D electromagnetic inverse scattering. To mitigate boundary blurring and reconstruction artifacts in voxel-wise contrast reconstruction, the proposed solver exploits the piecewise homogeneity of practical scatterers by representing unknown targets with multiple coordinate-dependent neural level-set components. Specifically, a soft-union multi-material model is proposed to separately describe the object support and material distribution. The global support is formed by the union of multiple level-set components, while the local contrast is determined by normalized component weights and learnable complex permittivity candidates. In addition, a model-consistent total variation (TV) regularization is imposed on the material-region indicators, rather than directly on the reconstructed contrast, to suppress fragmented material assignments without excessively smoothing material interfaces. An adaptive loss balancing strategy is further introduced to reduce the dependence on manually selected regularization weights. For each measurement instance, the neural level-set parameters and material candidates are optimized by minimizing a physics-consistent objective function. Numerical and experimental results demonstrate that LSPDNN can reconstruct scatterers with clear boundaries, more uniform material regions, and substantially reduced background artifacts. The results highlight the advantage of the neural level-set parameterization in challenging 3-D inverse scattering cases involving irregular shapes, closely spaced objects, multiple materials, and measurement noise.

Yutong Du, Zicheng Liu, Bo Qi +2

Department of Electronic Engineering, School of Electronics and Information, Northwestern Polytechnical University, Xi’an 710029, China

Physics-Informed ML Inverse Problems

Sep 2, 2026cs.LG

Scalable Bayesian Optimization of Composite Functions for Image-Based Inverse Problems in Materials Characterization

Estimating physical parameters from scientific images is a common inverse problem in materials characterization that often relies on expensive physics-based simulations. In electron microscopy, specimen thickness and crystal mistilt are critical parameters that govern how electrons scatter through the sample, and therefore the accuracy of any atomic-scale structure recovered from it. They are commonly inferred by matching experimental position-averaged convergent-beam electron diffraction (PACBED) patterns to simulated ones, but grid searches scale poorly and neural-network methods require extensive pretraining that may not transfer to new conditions. Here, we propose scalable Bayesian optimization of composite functions (SBOCF), a simulation-efficient method that exploits the known composite structure of the image-matching objective and the intermediate information contained in simulated images. By representing PACBED images with patch-level summaries and two correction terms, SBOCF preserves the original pixel-wise objective while reducing the number of modeled outputs from 24,649 to 11. Under a budget of 50 simulator evaluations, SBOCF outperformed standard Bayesian optimization with expected improvement on synthetic SrTiO3 benchmarks with thick and thin specimens, reducing the median final SSE by up to 290x in the thick-sample case. On experimental data, SBOCF produced parameter estimates consistent with previously reported values without task-specific pretraining. For a simulated mistilted specimen, using the SBOCF estimates in a downstream ptychographic reconstruction recovered sharp atoms that were otherwise blurred. These results establish SBOCF as a promising approach for inverse problems involving expensive simulators and high-dimensional structured outputs.

Dasol Yoon, Poompol Buathong, Chia-Hao Lee +3

School of Applied and Engineering Physics, Cornell University, Ithaca, NY 14853, USA · Department of Materials Science and Engineering, Cornell University, Ithaca, NY 14853, USA · Center for Applied Mathematics, Cornell University, Ithaca, NY 14853, USA +2

Bayesian Optimization Inverse Problems Microscopy Image Analysis

Sep 1, 2026cs.CV

Diffusion Based Unpaired Data Learning for Inverse Problems

Data is important in many deep learning-based inverse problem solvers. However, obtaining sufficient paired data in many scenarios remains highly challenging, while unpaired data is cheap. To maximize data utilization, this paper proposes LUD-DIF, a diffusion-based approach for solving inverse problems with unpaired data. Starting from the evidence lower bound (ELBO) of the joint distribution, we decouple it into two independent diffusion processes under the weak-coupling assumption. The method provides theoretical support from a variational inference perspective, derives the loss function, quantitatively analyzes the error bound introduced by the assumption, and offers a theorem-motivated heuristic for hyperparameter selection. Experimental results demonstrate that LUD-DIF achieves outstanding performance on multiple image inverse problems, validating its effectiveness and generalization capability in unpaired inverse problem settings.

Chenglong Bao, Yiming Dang, Chenguang Duan +2

Yau Mathematical Sciences Center, Tsinghua University, Beijing, China · Department of Mathematical Sciences, Tsinghua University, Beijing, China · Institut für Geometrie und Praktische Mathematik, RWTH Aachen University, Aachen, Germany +2

Diffusion-Based Inverse Problems Inverse Problems Diffusion Models Image Inverse Problems

Sep 1, 2026cs.LG

iPINN for Broadband CARS Phase Retrieval: A Framework for Function Approximation and Inverse Modeling Problems in Nonlinear Spectroscopy

Phase retrieval in broadband coherent anti-Stokes Raman spectroscopy (BCARS) is an ill-posed inverse problem. The Raman-like signal is encoded in the imaginary part of the resonant susceptibility, which mixes coherently with a non-resonant background (NRB) that varies across acquisitions. We introduce an inverse physics-informed neural network (iPINN) that predicts Lorentzian peak parameters from raw BCARS spectra and reconstructs the resonant susceptibility through a differentiable analytical forward model. A transformer encoder assigns spectral features to 24 learnable peak slots, and a multi-view consistency loss enforces invariance across NRB pattern, NRB strength, and noise. Unlike direct spectral regression approaches, the method retains accuracy under varying acquisition conditions. On a public benchmark, iPINN achieves the lowest error among the tested baselines (MAE 0.016 vs. next-best 0.046). On 28 zero-shot test spectra acquired across seven solvents and four focal positions, accuracy is depth-invariant in five of seven solvents. These results show that inverse parametric prediction with a differentiable physical decoder supports robust phase retrieval across measurement conditions.

Ravi Teja Vulchi, Carl Messerschmidt, Mohammadsadegh Vafaeinezhad +4

Institute of Physical Chemistry (IPC) and Abbe Center of Photonics (ACP), Friedrich Schiller University Jena, Member of the Leibniz Centre for Photonics in Infection Research · Leibniz Institute of Photonic Technology, Member of Leibniz Health Technologies, Member of the Leibniz Centre for Photonics in Infection Research (LPI)

Physics-Informed ML Raman Spectroscopy Inverse Problems

Sep 1, 2026cs.LG

HarmoCore: Functional Latent Diffusion for Sparse Reconstruction of Oscillatory Wave Fields

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.

Lihao Chen, Xinyu Zhang, Panqi Chen +4

College of Information Science and Electronic Engineering, Zhejiang University

Sparse Recovery Latent Diffusion Models Inverse Problems

Aug 30, 2026cs.LG

Diffusion-Based Inverse Design of Dielectric Resonator Metasurfaces for Shaping Smart Electromagnetic Environments

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.

M. Tsukerman, K. Grotov, D. Vovchuk +1

Conditional Generative Modeling Inverse Design Inverse Problems Diffusion Models