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.

Jul 13Week of Sep 28

Latest papers 161

May 8, 2026cs.LG

P-Flow: Proxy-gradient Flows for Linear Inverse Problems

Generative models based on flow matching have emerged as a powerful paradigm for inverse problems, offering straighter trajectories and faster sampling compared to diffusion models. However, existing approaches often necessitate differentiating through unrolled paths, leading to numerical instability and prohibitive computational overhead. To address this, we propose P-Flow, a framework that stabilizes the reconstruction process by leveraging a proxy gradient to update the source point. This approach effectively circumvents the numerical instability and memory overhead of long-chain differentiation. To ensure consistency with the prior distribution, we employ a Gaussian spherical projection motivated by the concentration of measure phenomenon in high-dimensional spaces. We further provide a theoretical analysis for P-Flow based on Bayesian theory and Lipschitz continuity. Experiments across diverse restoration tasks demonstrate that P-Flow delivers competitive performance, especially under extreme degradations such as severely ill-posed conditions and high measurement noise.

Zehua Jiang, Fenghao Zhu, Xinquan Wang +2

University of Notre Dame Indiana, USA

Flow Matching Inverse Problems Image Inverse Problems

May 7, 2026cs.LG

PyCC.id: A package for hypothesis-driven equation discovery with structural identifiability

Data-driven equation discovery is fundamentally an inverse problem that seeks to infer the governing differential equations of a system directly from time-series measurements. A known issue is the ill-conditioned nature of the inverse problem, which frequently produces multiple mathematical models that fit the data similarly well. One path to address this issue is by incorporating known hypotheses and constraints into the training phase beforehand. While this approach effectively reduces the search space, it still results in multiple candidate models, forcing practitioners to rely on post-hoc manual filtering based on their own domain expertise. A recent approach incorporates structural `skeletons' inspired by characteristic curves (CCs), defining a hypothesis-driven methodology. In this methodology, practitioners define a skeleton, which is associated with a family of ordinary differential equations (ODEs), and then add their hypotheses and priors based on their domain knowledge to refine the obtained model iteratively. An important advantage of this approach is that some skeletons have demonstrable structural identifiability properties, which are useful for checking whether the skeleton is correct or should be discarded. Furthermore, this formalism enables the use of multiple equation discovery paradigms due to its modularity (such as neural networks, symbolic regression, and sparse regression). In this work, we present the Python library PyCC, which condenses these efforts into a flexible tool that allows researchers and engineers to seamlessly define their skeletons and hypotheses to discover ODEs from time-dependent data.

Federico J. Gonzalez

Physics Institute of Rosario (IFIR), CONICET-UNR, Blvd. 27 de Febrero 210 Bis, Rosario, S2000EZP, Argentina.

Autonomous Scientific Discovery Inverse Problems ODE Discovery

May 6, 2026cs.LG

Conditional Diffusion Under Linear Constraints: Langevin Mixing and Information-Theoretic Guarantees

We study zero-shot conditional sampling with pretrained diffusion models for linear inverse problems, including inpainting and super-resolution. In these problems, the observation determines only part of the unknown signal. The remaining degrees of freedom must be sampled according to the correct conditional data distribution. Existing projection-based samplers enforce measurement consistency by correcting the observed component during reverse diffusion. However, measurement consistency alone does not determine how probability mass should be distributed along the feasible set, and this can lead to biased conditional samples. We analyze this issue through a normal--tangent decomposition of the score function. For Gaussian noising, the observed-direction score is exactly determined by the measurement; only the tangent conditional score is unknown. We prove that the error from replacing this score by the unconditional tangent score is upper bounded by a dimension-free conditional mutual information between observed and unobserved components. This gives an information-theoretic decomposition into initialization and pathwise score-mismatch errors. Motivated by the theory, we propose a projected-Langevin initialization followed by guided reverse denoising, which outperforms a strong projection-based baseline in inpainting and super-resolution experiments.

Ahmad Aghapour, Erhan Bayraktar, Asaf Cohen

Department of Mathematics University of Michigan Ann Arbor, MI 48109, USA

Diffusion Models for Image Restoration Langevin Dynamics Bayesian Inverse Problems Diffusion-Based Inverse Problems Diffusion Posterior Sampling Inverse Problems

May 6, 2026cs.LG

DualTCN: A Physics-Constrained Temporal Convolutional Network for 2 Time-Domain Marine CSEM Inversion

DualTCN is the first deep-learning framework for inverting time-domain marine controlled-source electromagnetic (MCSEM) transient data. Moving away from traditional subsurface discretization, the framework regresses four earth-model parameters --

σ_1

,

σ_2

,

d_1

,

d_2

-- and reconstructs conductivity-depth profiles using a differentiable soft-step decoder. The optimized architecture (379K parameters) features a Temporal Convolutional Network (TCN) encoder paired with a late-time branch and an auxiliary seafloor-depth head. This design achieves a 25.3% loss reduction over baseline models, with high predictive accuracy (

R^2 = 0.898

for

σ_2

) and an inversion speed of 3.5~ms per sample on an A100 GPU. The framework demonstrates high robustness to noise through curriculum-based amplitude augmentation, maintaining a mean

\bar{R}^2

of 0.858 at

\pm2\%

random amplitude error, compared to

0.363

without augmentation. DualTCN generalizes effectively to three-layer extensions (seawater/resistive layer/basement), accurately resolving basement conductivity (

R^2 \approx 0.88

), though thin-layer resolution remains a physical limitation (

R^2 \approx 0.23

). In comparative benchmarks, DualTCN significantly outperforms traditional local optimization methods like Levenberg-Marquardt and L-BFGS-B, yielding a mean

\bar{R}^2 = 0.877

versus 0.129-0.439 for multi-start baselines, while operating at up to 21,000

\times

lower computational cost. Finally, the framework incorporates uncertainty quantification via Monte Carlo (MC) Dropout. While well-calibrated for

σ_1

(PICP90 = 0.944), inherent signal limitations at short offsets (200m) lead to under-coverage for

d_2

(PICP90 = 0.572), which can be mitigated through post-hoc temperature scaling or split conformal prediction.

Khaled Ahmed, Ghada Omar

School of Computing, Southern Illinois University Carbondale, Carbondale, IL, 62901, USA · School of Mathematics and Statistics, Southern Illinois University Carbondale, Carbondale, IL, 62901, USA

Temporal Convolutional Networks Physics-Informed ML Inverse Problems

May 5, 2026cs.CV

Conditions for well-posed color recovery in scattering media

Recovering scene color from images captured in scattering media is a fundamental inverse problem in optical imaging. Yet the problem is intrinsically ill-posed as multiple solutions can explain the same observation, and prediction error cannot be controlled without understanding the space of candidate solutions. Here, we present sufficient conditions under which color recovery in a scattering medium becomes well-posed. Observing that ill-posedness stems from (i) projection of spectral signals onto pixel intensities, and (ii) unknown medium parameters, we demonstrate that sensor improvements alone cannot resolve medium-induced distortions without additional constraints. We identify recovery patterns, cross-pixel relationships that naturally occur in images, and prove, for an ideal hyperspectral camera, that they restrict the solution to a unique candidate. This opens the door to a new class of vision algorithms grounded in first principles, enabling quantitative analysis of images in scattering environments.

Grigory Solomatov, Derya Akkaynak

Hatter Department of Marine Technologies, University of Haifa, Haifa, Israel · Interuniversity Institute for Marine Sciences, Eilat, Israel

Image Restoration Inverse Problems Image Inverse Problems

May 5, 2026stat.ML

Tempered Guided Diffusion

Training-free conditional diffusion provides a flexible alternative to task-specific conditional model training, but existing samplers often allocate computation inefficiently: independent guided trajectories can vary widely in quality, and additional function evaluations along a single trajectory may not recover from poor early decisions. We propose Tempered Guided Diffusion (TGD), an annealed sequential Monte Carlo framework for training-free conditional sampling with diffusion priors. TGD targets tempered posterior distributions over the clean signal, using noisy diffusion states only as auxiliary variables for proposing reconstructions and propagating particles. Particles are reweighted by incremental likelihood ratios, resampled, and propagated across noise levels, concentrating computation on trajectories plausible under both the prior and observation. Under idealized exact-reconstruction assumptions, full TGD yields a consistent particle approximation to the posterior as the number of particles grows. For expensive reconstruction tasks, Accelerated TGD (A-TGD) retains early particle exploration but prunes to a single high-likelihood trajectory partway through sampling. Experiments on a controlled two-dimensional inverse problem and image inverse problems show improved posterior approximation and favorable wall-clock speed-quality tradeoffs over independent multi-trajectory baselines.

Andreas Makris, Paul Fearnhead, Chris Nemeth

Department of Mathematics and Statistics Lancaster University, UK · Department of Mathematics and Statistics2026 Lancaster University, UK

Diffusion Model Sampling Diffusion-Based Inverse Problems Diffusion Posterior Sampling Diffusion Model Inference Acceleration Inverse Problems

May 5, 2026cs.LG

Meta-Inverse Physics-Informed Neural Networks for High-Dimensional Ordinary Differential Equations

Solving inverse problems in dynamical systems governed by high-dimensional coupled ordinary differential equations (ODEs) is a ubiquitous challenge in scientific machine learning. In many real-world applications, researchers seek to uncover unknown parameters or model unknown dynamics even as the underlying physics is only partially characterized, and observations are sparse and limited to specific measurable channels. While physics-informed neural networks (PINNs) are ideal for inverse inference under partial observability, existing PINNs typically rely on task-specific joint optimization, which suffers from optimization difficulties and poor generalization. In this paper, we propose a meta-inverse physics-informed neural network (MI-PINN) that reformulates inverse modeling as a two-stage meta-learning problem. MI-PINN first learns a physics-aware representation across multiple tasks, and then performs inverse modeling by optimizing task-specific unknowns while keeping the learned representation fixed. This two-stage formulation significantly reduces the parameter search dimension, thereby improving sample efficiency and enabling accurate inference. To handle multi-scale dynamics common in these high-dimensional ODE systems, we further introduce an adaptive clustering-based multi-branch learning scheme. We demonstrate the effectiveness of MI-PINN on whole-body physiologically based pharmacokinetic (PBPK) models with up to 33 coupled ODEs, using paracetamol and theophylline under intravenous and oral dosing scenarios. Experimental results show that MI-PINN enables accurate recovery of masked kinetic parameters and reconstruction of missing mechanistic terms despite limited clinical observations.

Zhao Wei, Kenneth Hor Cheng Koh, Sheng Yuan Chin +3

Centre for Frontier AI Research (CFAR) and the Institute of High Performance Computing (IHPC), Agency for Science, Technology and Research (A*STAR), 1 Fusionopolis Way, #16-16 Connexis, Singapore 138632, Singapore · Singapore Institute of Food and Biotechnology Innovation (SIFBI), Agency for Science, Technology and Research (A*STAR), 31 Biopolis Way, Nanos, Singapore 138669, Singapore · A*STAR Skin Research Labs (A*SRL), Agency for Science, Technology and Research (A*STAR), 8A Biomedical Grove, Immunos, Singapore 138648, Singapore +1

Meta-Learning Physics-Informed ML Inverse Problems

May 5, 2026eess.SP

Neural Posterior Estimation of Terrain Parameters from Radar Sounder Data

Radar sounders are electromagnetic instruments that can probe deep into the subsurface of Earth and other planetary bodies by processing the echo of transmitted radar waves. Conventional approaches for analyzing such data rely on approximate assumptions and often produce point estimates that ignore parameter correlations as well as galactic and measurement noise. We propose a simulation-based inference approach to terrain parameter inversion from radar sounder data, where synthetic observations from a GPU-based simulator are used to train a neural network-based density estimator for neural posterior estimation (NPE). By explicitly conditioning on reference surface assumptions, the proposed framework allows systematic evaluation of posterior robustness to reference surface variability. We demonstrate that our NPE model is well calibrated on simulated data and transferable to real Mars radar profiles, where we analyze terrain parameters using literature-informed reference values.

Jordy Dal Corso, Annalena Kofler, Marco Cortellazzi +2

University of Trento, Trento, Italy · Max Planck Institute for Intelligent Systems, Tübingen, Germany · Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Potsdam, Germany +1

Simulation-Based Inference Parameter Estimation Neural Posterior Estimation Remote Sensing Inverse Problems

Apr 29, 2026cs.CV

Hearing the Room Through the Shape of the Drum: Modal-Guided Sound Recovery from Multi-Point Surface Vibrations

Optical vibration sensing enables recovering the scene sound directly from the surface vibration of nearby objects, turning everyday objects into ``visual microphones''. However, most prior methods had focused on capturing the vibrations of specific objects with highly favorable vibration responses. These include objects where the surface vibrations are generated by the object itself (e.g., speaker membrane or guitar body) or objects consisting of a thin membrane which is highly reactive to sound (e.g., a chip bag or the leaf of a plant). In this paper, we tackle sound recovery for a more challenging class of solid objects whose vibration responses are poor or highly resonant. We simultaneously capture vibrations for multiple surface points on the object using a speckle-based vibrometry imaging system. Then, we derive a novel physics-guided vibration formation model that relates the scene sound source to the captured multi-point multi-axis vibrations via the object's vibrational modes. The model is then used to reverse the resonant transfer function of the vibrating object, fusing multiple vibration signals to estimate the original sound source in the scene. We evaluate our approach by recovering sound from a variety of everyday objects, demonstrating that it significantly outperforms traditional single-point speckle vibrometry in challenging scenarios and other signal-processing-based methods for multi-signal fusing.

Shai Bagon, Matan Kichler, Mark Sheinin

Weizmann Institute of Science, Israel

Inverse Problems

Apr 28, 2026cs.AI

Distill-Belief: Closed-Loop Inverse Source Localization and Characterization in Physical Fields

{Closed-loop inverse source localization and characterization (ISLC) requires a mobile agent to select measurements that localize sources and infer latent field parameters under strict time constraints.} {The core challenge lies in the belief-space objective: valid uncertainty estimation requires expensive Bayesian inference, whereas using fast learned belief model leads to reward hacking, in which the policy exploits approximation errors rather than actually reducing uncertainty.} {We propose \textbf{Distill-Belief}, a teacher--student framework that decouples correctness from efficiency. A Bayes-correct particle-filter teacher maintains the posterior and supplies a dense information-gain signal, while a compact student distills the posterior into belief statistics for control and an uncertainty certificate for stopping. At deployment, only the student is used, yielding constant per-step cost.} {Experiments on seven field modalities and two stress tests show that Distill-Belief consistently reduces sensing cost and improves success, posterior contraction, and estimation accuracy over baselines, while mitigating reward hacking.}

Yiwei Shi, Zixing Song, Mengyue Yang +2

SEMT, University of Bristol, Bristol, UK · LUCAS, Loughborough University, Loughborough, UK

Belief-Space Planning Reward Hacking Active Sensing Inverse Problems

Apr 28, 2026physics.acc-ph

Adaptable phase retrieval for coherent transition radiation spectroscopy based on differentiable physics information

Coherent transition radiation (CTR) spectroscopy is a critical diagnostic for characterizing the longitudinal structure of relativistic electron bunches in laser-plasma and conventional accelerators. In practice, recovering the bunch profile from a measured CTR spectrum is an ill-posed phase-retrieval problem. Traditionally, this is addressed using Gerchberg-Saxton (GS)-type iterative algorithms. However, these implementations often rely on explicit inverse propagators, making them difficult to adapt to sophisticated experimental forward models. In this work, we introduce a flexible gradient-based framework for CTR phase retrieval. By leveraging a differentiable forward model, we propose a phase-only gradient descent (GD-Phase) approach that enforces the measured spectral amplitude as a hard constraint while optimizing the Fourier phase under physical real-space priors. Using synthetic CTR spectra spanning multi-peaked and strongly modulated profiles, we benchmark GD-Phase against traditional GS and a real-space amplitude-parametrized gradient descent (GD-Amp) algorithm. Unlike traditional methods, this formulation allows for the seamless inclusion of arbitrary differentiable experimental effects into the reconstruction loop. We demonstrate that this physics-informed approach not only reproduces the fidelity of GS methods but also establishes a robust baseline for incorporating multi-diagnostic constraints and uncertainty quantification. This enables the systematic extension to higher-dimensional, multimodal, and uncertainty-aware diagnostics, facilitating fast and scalable phase retrieval in realistic experimental settings.

Ritz Ann Aguilar, Maxwell LaBerge, Andreas Doepp +6

Institute of Radiation Physics, Helmholtz-Zentrum Dresden-Rossendorf, Dresden, Germany · Centre for Advanced Laser Applications, Ludwig-Maximilians-Universität München, Garching, Germany · Center for Advanced Systems Understanding, Görlitz, Germany +2

Differentiable Physics Physics-Informed ML Inverse Problems

Apr 28, 2026cs.CV

When Less Is More: Simplicity Beats Complexity for Physics-Constrained InSAR Phase Unwrapping

Operational phase unwrapping is the primary computational bottleneck in InSAR-based volcanic and seismic monitoring. We challenge the industry trend of adopting high-complexity computer vision architectures, such as attention mechanisms, without validating their suitability for physics-constrained geophysical regression. We present the first large-scale architectural ablation study on a global LiCSAR benchmark (20 frames, 39,724 patches, 651M pixels). Our results reveal a significant "complexity penalty": a vanilla U-Net (7.76M parameters) achieves

R^2=0.834

and RMSE

= 1.01

cm, outperforming 11.37M-parameter attention-based models by 34% in

R^2

and 51% in RMSE. Power Spectral Density (PSD) analysis provides the physical justification: while attention excels at capturing sharp semantic edges in natural images, it injects unphysical high-frequency artifacts (

>0.3

cycles/pixel) into geophysical fields, violating the fundamental smoothness constraints of elastic surface deformation. With a 2.92ms inference latency (a

2.5\times

speedup), the vanilla U-Net is the only candidate to comfortably meet the sub-100ms requirement for operational early-warning systems. This work bridges the "publication-to-practice" gap by proving that convolutional locality outperforms modern complexity for smooth-field regression, advocating for physics-informed simplicity in ML4RS. Code available at https://github.com/prabhjotschugh/When-Less-is-More-InSAR-Phase-Unwrapping

Prabhjot Singh, Manmeet Singh

The University of Texas at Austin, USA · RediMinds Inc., USA · Western Kentucky University, USA

U-Net Remote Sensing Physics-Informed ML Convolutional Neural Networks Synthetic Aperture Radar Inverse Problems

Apr 26, 2026cs.LG

Learning Interpretable PDE Representations for Generative Reconstructions with Structured Sparsity

Scientific measurements are often bottlenecked by suboptimal conditions, whether that be noise, incomplete spatial coverage, or limited resolution, rendering accurate field reconstruction a difficult task. We introduce LatentPDE, a latent diffusion framework designed to simultaneously resolve sparse-observation reconstruction and super-resolution. While existing physics-guided diffusion models typically rely on soft loss penalties or uninterpretable representations, our approach enforces physical compliance by constructing an inherently interpretable latent space. Specifically, we parameterize the latent variables directly as the coefficients and source terms of an assumed governing PDE. In doing so, LatentPDE is able to reliably reconstruct dynamics across highly disparate and structured data gaps. Empirical results on diverse configurations demonstrate that our model achieves high-fidelity recovery at any desired resolution while also tracking the underlying predictive uncertainty.

Valerie Tsao, Nathaniel Chaney, Manolis Veveakis

Department of Civil & Environmental Engineering, Duke University, NC, USA.

Physics-Informed Diffusion Models Sparse Recovery Latent Diffusion Models Physics-Informed ML Diffusion-Based Inverse Problems PDE Inverse Problems+1

Apr 24, 2026cs.AI

On the Existence of an Inverse Solution for Preference-Based Reductions in Argumentation

Preference-based argumentation frameworks (PAFs) extend Dung's approach to abstract argumentation (AAFs) by encoding preferences over arguments. Such preferences control the transformation of attacks into defeats, and different approaches to doing so result in different reductions from a PAF to an AAF. In this paper we consider a PAF inverse problem which takes an argumentation graph, a labelling and a semantics as an input, and outputs a yes" or no" as to whether there is a preference relation between the arguments which can yield the desired labelling. This inverse problem has applications in areas including preference elicitation and explainability. We consider this problem in the context of the four most widely-used preference based reductions under the complete semantics. We show that in most cases, the problem can be answered in polynomial time.

Alessio Zaninotto, Bruno Yun, Nir Oren +1

1CRIL - Université d’Artois, CNRS · 2Universite Claude Bernard Lyon 1, CNRS, Ecole Centrale de Lyon, INSA Lyon, Université Lumière Lyon 2, LIRIS, UMR5205, 69622 Villeurbanne, France · University of Aberdeen

Computational Argumentation Inverse Problems

Apr 24, 2026eess.IV

Multimodal Diffusion to Mutually Enhance Polarized Light and Low Resolution EBSD Data

In spite of the utility of 3-D electron back-scattered diffraction (EBSD) microscopy, the data collection process can be time-consuming with serial-sectioning. Hence, it is natural to look at other modalities, such as polarized light (PL) data, to accelerate EBSD data collection, supplemented with shared information. Complementarily, features in chaotic PL data could even be enriched with a handful of EBSD measurements. To inherently learn the complex dynamics between EBSD and PL to solve these inverse problems, we use an unconditional multimodal diffusion model, motivated by progress in diffusion models for inverse problems. Although trained solely on synthetic data once, our model has strong generalizable capabilities on real data which can be low-resolution, noisy, corrupted, and misregistered. With inference-time scaling, we show gains in performance on a variety of objectives including grain boundary prediction, super-resolution, and denoising. With our model, we demonstrate that there is little difference from full resolution performance with only 25% (1/4 the resolution) of EBSD data and corrupted PL data.

Harry Dong, Timofey Efimov, Megna Shah +4

Department of Electrical and Computer Engineering, Carnegie Mellon University, USA · Materials and Manufacturing Directorate, Air Force Research Laboratory, USA · Department of Materials Science and Engineering, Carnegie Mellon University, USA +1

Diffusion Models for Image Restoration Materials Science Microscopy Image Analysis Inverse Problems Multimodal Diffusion Models

Apr 20, 2026q-bio.BM

Boltzmann Machine Learning with a Parallel, Persistent Markov chain Monte Carlo method for Estimating Evolutionary Fields and Couplings from a Protein Multiple Sequence Alignment

The inverse Potts problem for estimating evolutionary single-site fields and pairwise couplings in homologous protein sequences from their single-site and pairwise amino acid frequencies observed in their multiple sequence alignment would be still one of useful methods in the studies of protein structure and evolution. Since the reproducibility of fields and couplings are the most important, the Boltzmann machine method is employed here, although it is computationally intensive. In order to reduce computational time required for the Boltzmann machine, parallel, persistent Markov chain Monte Carlo method is employed to estimate the single-site and pairwise marginal distributions in each learning step. Also, stochastic gradient descent methods are used to reduce computational time for each learning. Another problem is how to adjust the values of hyperparameters; there are two regularization parameters for evolutionary fields and couplings. The precision of contact residue pair prediction is often used to adjust the hyperparameters. However, it is not sensitive to these regularization parameters. Here, they are adjusted for the fields and couplings to satisfy a specific condition that is appropriate for protein conformations. This method has been applied to eight protein families.

Sanzo Miyazawa

Sequence Modeling Inverse Problems

Apr 17, 2026cs.CV

Self-Supervised Angular Deblurring in Photoacoustic Reconstruction via Noisier2Inverse

Photoacoustic tomography (PAT) is an emerging imaging modality that combines the complementary strengths of optical contrast and ultrasonic resolution. A central task is image reconstruction, where measured acoustic signals are used to recover the initial pressure distribution. For ideal point-like or line-like detectors, several efficient and fast reconstruction algorithms exist, including Fourier methods, filtered backprojection, and time reversal. However, when applied to data acquired with finite-size detectors, these methods yield systematically blurred images. Although sharper images can be obtained by compensating for finite-detector effects, supervised learning approaches typically require ground-truth images that may not be available in practice. We propose a self-supervised reconstruction method based on Noisier2Inverse that addresses finite-size detector effects without requiring ground-truth data. Our approach operates directly on noisy measurements and learns to recover high-quality PAT images in a ground-truth-free manner. Its key components are: (i) PAT-specific modeling that recasts the problem as angular deblurring; (ii) a Noisier2Inverse formulation in the polar domain that leverages the known angular point-spread function; and (iii) a novel, statistically grounded early-stopping rule. In experiments, the proposed method consistently outperforms alternative approaches that do not use supervised data and achieves performance close to supervised benchmarks, while remaining practical for real acquisitions with finite-size detectors.

Markus Haltmeier, Nadja Gruber, Gyeongha Hwang

Department of Mathematics, University of Innsbruck Technikerstrasse 13, 6020 Innsbruck, Austria · Department of Computer Science, University of Innsbruck Technikerstrasse 21a, 6020 Innsbruck, Austria · Department of Mathematics, Yeungnam University 280 Daehak-Ro, Gyeongsan, Gyeongbuk 38541, South Korea

Medical Imaging Image Deblurring Image Reconstruction Inverse Problems

Apr 17, 2026cs.CV

SPLIT: Self-supervised Partitioning for Learned Inversion in Nonlinear Tomography

Machine learning has achieved impressive performance in tomographic reconstruction, but supervised training requires paired measurements and ground-truth images that are often unavailable. This has motivated self-supervised approaches, which have primarily addressed denoising and, more recently, linear inverse problems. We address nonlinear inverse problems and introduce SPLIT (Self-supervised Partitioning for Learned Inversion in Nonlinear Tomography), a self-supervised machine-learning framework for reconstructing images from nonlinear, incomplete, and noisy projection data without any samples of ground-truth images. SPLIT enforces cross-partition consistency and measurement-domain fidelity while exploiting complementary information across multiple partitions. Our main theoretical result shows that, under mild conditions, the proposed self-supervised objective is equivalent to its supervised counterpart in expectation. We regularize training with an automatic stopping rule that halts optimization when a no-reference image-quality surrogate saturates. As a concrete application, we derive SPLIT variants for multispectral computed tomography. Experiments on sparse-view acquisitions demonstrate high reconstruction quality and robustness to noise, surpassing classical iterative reconstruction and recent self-supervised baselines.

Markus Haltmeier, Lukas Neumann, Nadja Gruber +1

Self-Supervised Learning Sparse-View CT Reconstruction Computed Tomography Inverse Problems Image Inverse Problems

Mar 17, 2026cs.CV

IRIS: A Real-World Benchmark for Inverse Recovery and Identification of Physical Dynamic Systems from Monocular Video

Unsupervised physical parameter estimation from video lacks a common benchmark: existing methods evaluate on non-overlapping synthetic data, the sole real-world dataset is restricted to single-body systems, and no established protocol addresses governing-equation identification. This work introduces IRIS, a high-fidelity benchmark comprising 240 real-world videos captured at 4K resolution and 60fps, spanning both single- and multi-body dynamics with independently measured ground-truth parameters and uncertainty estimates. Each dynamical system is recorded under controlled laboratory conditions and paired with its governing equations, enabling principled evaluation. A standardized evaluation protocol is defined encompassing parameter accuracy, identifiability, extrapolation, robustness, and governing-equation selection. Multiple baselines are evaluated, including a multi-step physics loss formulation and four complementary equation-identification strategies (VLM temporal reasoning, describe-then-classify prompting, CNN-based classification, and path-based labelling), establishing reference performance across all IRIS scenarios and exposing systematic failure modes that motivate future research. The dataset, annotations, evaluation toolkit, and all baseline implementations are publicly released.

Rasul Khanbayov, Mohamed Rayan Barhdadi, Erchin Serpedin +1

Hamad Bin Khalifa University · Texas A&M University

Parameter Identifiability System Identification Inverse Dynamics Inverse Problems

Mar 6, 2026cs.LG

Joint 3D Gravity and Magnetic Inversion via Rectified Flow and Ginzburg-Landau Guidance

Subsurface ore detection is of paramount importance given the rising depletion of shallow mineral resources in recent years. It is crucial to explore approaches that go beyond the limitations of traditional geological exploration methods. Due to readily available surface readings, joint magnetic and gravitational inversion is a promising new method - given magnetic and gravitational data on a surface, jointly reconstructing the underlying densities that generate them. However, this is ill-posed and has non-unique solutions. Deterministic methods often require handcrafted priors and converge to a single solution and do not capture the distribution, which is often of interest. We introduce a novel framework that reframes 3D gravity and magnetic joint inversion as a rectified flow on the Noddyverse dataset, the largest physics-based dataset for inversion. We introduce a Ginzburg-Landau (GL) regularizer, a generalized version of the Ising model that aids in ore identification, enabling physics-aware training. We also propose a guidance methodology based on GL theory that can be used as a plug-and-play module with existing unconditional denoisers. Lastly, we also train and release a VAE for the 3D densities, which facilitates downstream work in the field.

Dhruman Gupta, Yashas Shende, Aritra Das +2

Ashoka University · Department of Computer Science Ashoka University · Department of Physics Ashoka University

Physics-Informed ML Inverse Problems

Mar 3, 2026cs.LG

Inverse Reconstruction of Shock Time Series from Shock Response Spectrum Curves using Machine Learning

The shock response spectrum (SRS) is widely used to characterize the response of single-degree-of-freedom (SDOF) systems to transient accelerations. Because the mapping from acceleration time history to SRS is nonlinear and many-to-one, reconstructing time-domain signals from a target spectrum is inherently ill-posed. Conventional approaches address this problem through iterative optimization, typically representing signals as sums of exponentially decayed sinusoids, but these methods are computationally expensive and constrained by predefined basis functions. We propose a conditional variational autoencoder (CVAE) that learns a data-driven inverse mapping from SRS to acceleration time series. Once trained, the model generates signals consistent with prescribed target spectra without requiring iterative optimization. Experiments demonstrate improved spectral fidelity relative to classical techniques, strong generalization to unseen spectra, and inference speeds three to six orders of magnitude faster. These results establish deep generative modeling as a scalable and efficient approach for inverse SRS reconstruction.

Adam Watts, Andrew Jeon, Destry Newton +1

Los Alamos National Laboratory · University of Rochester

Inverse Problems

Feb 18, 2026math.ST

Separating Oblivious and Adaptive Models of Variable Selection

Sparse recovery is among the most well-studied problems in learning theory and high-dimensional statistics. In this work, we investigate the statistical and computational landscapes of sparse recovery with

\ell_\infty

error guarantees. This variant of the problem is motivated by \emph{variable selection} tasks, where the goal is to estimate the support of a

k

-sparse signal in

\mathbb{R}^d

. Our main contribution is a provable separation between the \emph{oblivious} (for each'') and \emph{adaptive} (for all'') models of

\ell_\infty

sparse recovery. We show that under an oblivious model, the optimal

\ell_\infty

error is attainable in near-linear time with

\approx k\log d

samples, whereas in an adaptive model,

\gtrsim k^2

samples are necessary for any algorithm to achieve this bound. This establishes a surprising contrast with the standard

\ell_2

setting, where

\approx k \log d

samples suffice even for adaptive sparse recovery. We conclude with a preliminary examination of a \emph{partially-adaptive} model, where we show nontrivial variable selection guarantees are possible with

\approx k\log d

measurements.

Ziyun Chen, Jerry Li, Kevin Tian +1

University of Washington · University of Texas at Austin

Sparse Recovery Feature Selection Statistical Learning Theory Inverse Problems

Feb 10, 2026cs.CV

Stability and Concentration in Nonlinear Inverse Problems with Block-Structured Parameters: Lipschitz Geometry, Identifiability, and an Application to Gaussian Splatting

We develop an operator-theoretic framework for stability and statistical concentration in nonlinear inverse problems with block-structured parameters. Under a unified set of assumptions combining blockwise Lipschitz geometry, local identifiability, and sub-Gaussian noise, we establish deterministic stability inequalities, global Lipschitz bounds for least-squares misfit functionals, and nonasymptotic concentration estimates. These results yield high-probability parameter error bounds that are intrinsic to the forward operator and independent of any specific reconstruction algorithm. As a concrete instantiation, we verify that the Gaussian Splatting rendering operator satisfies the proposed assumptions and derive explicit constants governing its Lipschitz continuity and resolution-dependent observability. This leads to a fundamental stability--resolution tradeoff, showing that estimation error is inherently constrained by the ratio between image resolution and model complexity. Overall, the analysis characterizes operator-level limits for a broad class of high-dimensional nonlinear inverse problems arising in modern imaging and differentiable rendering.

Joe-Mei Feng, Hsin-Hsiung Kao

Computer Science and Information Engineering, Tamkang University, New Taipei City, Taiwan (R.O.C.) · Department of Information Management, Central Police University, Taoyuan, Taiwan

Inverse Rendering Parameter Identifiability Gaussian Splatting Inverse Problems

Feb 9, 2026eess.IV

Trajectory Stitching for Solving Inverse Problems with Flow-Based Models

Flow-based generative models have emerged as powerful priors for solving inverse problems. One option is to directly optimize the initial latent code (noise), such that the flow output solves the inverse problem. However, this requires backpropagating through the entire generative trajectory, incurring high memory costs and numerical instability. We propose MS-Flow, which represents the trajectory as a sequence of intermediate latent states rather than a single initial code. By enforcing the flow dynamics locally and coupling segments through trajectory-matching penalties, MS-Flow alternates between updating intermediate latent states and enforcing consistency with observed data. This reduces memory consumption while improving reconstruction quality. We demonstrate the effectiveness of MS-Flow over existing methods on image recovery and inverse problems, including inpainting, super-resolution, and computed tomography.

Alexander Denker, Zeljko Kereta, Carola-Bibiane Schönlieb +1

Department of Computer Science, University College London · Department of Applied Mathematics and Theoretical Physics, University of Cambridge.

Generative Flow Networks Flow-Based Generative Modeling Inverse Problems Image Inverse Problems

Feb 3, 2026cs.LG

Variational Sparse Paired Autoencoders (vsPAIR) for Inverse Problems and Uncertainty Quantification

Inverse problems are fundamental to many scientific and engineering disciplines; they arise when one seeks to reconstruct hidden, underlying quantities from noisy measurements. Many applications demand not just point estimates but interpretable uncertainty. Providing fast inference alongside uncertainty estimates remains challenging yet desirable in numerous applications. We propose the Variational Sparse Paired Autoencoder (vsPAIR) to address this challenge. The architecture pairs a standard VAE encoding observations with a sparse VAE encoding quantities of interest (QoI), connected through a learned latent mapping. The variational structure enables uncertainty estimation, the paired architecture encourages interpretability by anchoring QoI representations to clean data, and sparse encodings provide structure by concentrating information into identifiable factors rather than diffusing across all dimensions. To validate the effectiveness of our proposed architecture, we conduct experiments on blind inpainting, computed tomography (CT), and initial-condition inference for the heat equation, demonstrating that vsPAIR is a capable inverse problem solver that can provide interpretable and structured uncertainty estimates.

Jack Michael Solomon, Rishi Leburu, Matthias Chung

Emory University Department of Mathematics

Variational Autoencoders Uncertainty Quantification Autoencoders Sparse Autoencoders Inverse Problems

Jan 29, 2026cs.LG

Inverse Problems Conditioned on Observation Ensembles: Applications and Methods

We introduce a new multivariate statistical problem that we refer to as the Ensemble-conditioned Inverse Problem (EIP). The aim of EIP is to invert for an ensemble that is distributed according to the pushforward of a prior under a forward process. In high energy physics (HEP), this is related to a widely known problem called unfolding, which aims to reconstruct the true physics distribution from observations that are distorted by detector effects. The EIP also arises in full waveform inversion (FWI) and inverse imaging with unknown priors. We propose non-iterative inference-time methods that construct posterior samplers based on a new class of conditional generative models, which we call ensemble inverse generative models. For the posterior modeling, these models additionally use the ensemble information contained in the observation set on top of single observations. Unlike existing methods, our proposed methods avoid explicit and iterative use of the forward model at inference time via training across several sets of truth-observation pairs that are consistent with the same forward model, but originate from a wide range of priors. We empirically demonstrate that this training procedure can implicitly encode the likelihood model, enabling direct posterior inference for unseen priors to some degree. We benchmark the proposed method on several synthetic and real datasets in inverse imaging, HEP, and FWI. Our code is available at https://github.com/ZhengyanHuan/EIP.

Zhengyan Huan, Camila Pazos, Martin Klassen +3

Department of Electrical and Computer Engineering, Tufts University, Medford, Massachusetts · The NSF AI Institute for Artificial Intelligence and Fundamental Interactions · Department of Physics and Astronomy, Tufts University, Medford, Massachusetts +1

Posterior Sampling Inverse Problems Image Inverse Problems

Jan 12, 2026cs.CV

Fundamental Recovery Bounds for SPAD Signals under Stationary Flux

Single-photon avalanche diodes (SPADs) record light as a discrete stream of individual detections. The signal is stochastic. Its statistical structure depends on the sensor's operation mode: binary detection in fixed bins, timestamped detection in fixed bins, or free-running timestamped detection. We derive the likelihood score function for each of these three passive modes. From this single object, stem both fundamental limits of recovery (Cramer-Rao bounds) and practical recovery algorithms based on diffusion posterior sampling. The paper further generalizes fundamental limits to Bayesian Cramer-Rao lower bounds. This generalization makes use of a learned approximation of the score function of signal priors. In prior art, analyses and diffusion-based reconstruction for SPAD data have treated individual modes in isolation. Our unified treatment shows a qualitative high-flux gap between modes: binary counts saturate exponentially, while timestamped modes degrade only linearly. We further extend diffusion posterior sampling, previously restricted to binary SPAD data, to a full timestamped case using the suitable score function. We demonstrate experimentally that matching the score to the operation mode is beneficial for high-fidelity reconstruction. By tying the recovery bounds and diffusion to the score function, this work aims to establish a common foundation for both asking what is recoverable in single-photon sensing, and building methods that approach the bound.

Lior Dvir, Nadav Torem, Mohit Gupta +1

Viterbi Faculty of Electrical and Computer Engineering, Technion-Israel Institute of Technology, Haifa 3200003, Israel · Department of Computer Sciences, University of Wisconsin-Madison, Madison, WI 53706, USA

Bayesian Inverse Problems Diffusion Posterior Sampling Inverse Problems

Dec 5, 2025cs.CV

InverseCrafter: Efficient Video ReCapture as a Latent Domain Inverse Problem

Recent approaches in controllable novel view video generation often rely on fine-tuning pre-trained Video Diffusion Models (VDMs). This dominant paradigm is computationally expensive and frequently suffers from catastrophic forgetting of the model's original generative priors. To address this challenge, here we propose InverseCrafter, a VDM training-free framework that reformulates novel view video generation as an inpainting-based inverse problem in the latent space, eliminating the need for any annotated 4D training data. The core of our method is to establish operator equivalence by employing a lightweight latent mask encoder to define a latent-domain masking operation via a continuous, multi-channel representation. This principled representation faithfully models the forward process in the latent domain, enabling efficient, backpropagation-free solvers while bypassing the costly bottleneck of repeated VAE operations. InverseCrafter achieves high-fidelity, spatio-temporally coherent novel view synthesis with near-zero additional inference overhead and excels at general-purpose video inpainting and editing by fully preserving the pre-trained VDM's generative capabilities.

Yeobin Hong, Suhyeon Lee, Hyungjin Chung +1

Graduate School of AI, KAIST, South Korea · EverEx, South Korea · Korea University, South Korea

Camera-Controlled Video Generation Video Diffusion Models Dynamic Novel View Synthesis Inverse Problems

Dec 2, 2025gr-qc

Flexible Gravitational-Wave Parameter Estimation with Transformers

Gravitational-wave data analysis relies on accurate and efficient methods to extract physical information from noisy detector signals, yet the increasing rate and complexity of observations represent a growing challenge. Deep learning provides a powerful alternative to traditional inference, but existing neural models typically lack the flexibility to handle variations in data analysis settings. Such variations accommodate imperfect observations or are required for specialized tests, and could include changes in detector configurations, overall frequency ranges, or localized cuts. We introduce a flexible transformer-based architecture paired with a training strategy that enables adaptation to diverse analysis settings at inference time. Applied to parameter estimation, we demonstrate that a single flexible model, called Dingo-T1, can (i) analyze 48 gravitational-wave events from the third LIGO-Virgo-KAGRA Observing Run under a wide range of analysis configurations, (ii) enable systematic studies of how detector and frequency configurations impact inferred posteriors, and (iii) perform inspiral-merger-ringdown consistency tests probing general relativity. Dingo-T1 also improves median sample efficiency on real events from a baseline of 1.4% to 4.2%. Our approach thus demonstrates flexible and scalable inference with a principled framework for handling missing or incomplete data, key capabilities for current and next-generation observatories.

Annalena Kofler, Maximilian Dax, Stephen R. Green +6

Max Planck Institute for Intelligent Systems, Max-Planck-Ring 4, 72076 Tübingen, Germany · ELLIS Institute Tübingen, Maria-von-Linden-Straße 2, 72076 Tübingen, Germany · Tübingen AI Center, Maria-von-Linden-Straße 1, 72076 Tübingen, Germany +4

Transformer Inference Gravitational-Wave Astronomy Bayesian Inference Inverse Problems

Nov 1, 2025cs.SD

Physics-Informed Neural Networks for Speech Production

The analysis of speech production based on physical models of the vocal folds and vocal tract is essential for studies on vocal-fold behavior and linguistic research. This paper proposes a speech production analysis method using physics-informed neural networks (PINNs). The networks are trained directly on the governing equations of vocal-fold vibration and vocal-tract acoustics. Vocal-fold collisions introduce nondifferentiability and vanishing gradients, challenging phenomena for PINNs. We demonstrate, however, that introducing a differentiable approximation function enables the analysis of vocal-fold vibrations within the PINN framework. The period of self-excited vocal-fold vibration is generally unknown. We show that by treating the period as a learnable network parameter, a periodic solution can be obtained. Furthermore, by implementing the coupling between glottal flow and vocal-tract acoustics as a hard constraint, glottis-tract interaction is achieved without additional loss terms. We confirmed the method's validity through forward and inverse analyses, demonstrating that the glottal flow rate, vocal-fold vibratory state, and subglottal pressure can be simultaneously estimated from speech signals. Notably, the same network architecture can be applied to both forward and inverse analyses, highlighting the versatility of this approach. The proposed method inherits the advantages of PINNs, including mesh-free computation and the natural incorporation of nonlinearities, and thus holds promise for a wide range of applications.

Kazuya Yokota, Ryosuke Harakawa, Masaaki Baba +1

Department of Mechanical Engineering, Nagaoka University of Technology, 1603-1, Kamitomioka, Nagaoka, Niigata, Japan · Department of Electrical, Electronics and Information Engineering, Nagaoka University of Technology

Speech Processing Physics-Informed ML Inverse Problems