Inverse Problems

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Inverse problems work backward from observations to estimate the hidden image, physical state, or system parameters that produced them, often when measurements are sparse, noisy, or ambiguous. Methods range from classical regularization and optimization to physics-informed neural networks, learned operators, and generative priors such as diffusion and flow models; Bayesian methods can also represent multiple plausible solutions and their uncertainty. Applications include medical and computational imaging, seismic exploration, spectroscopy, and identifying material or dynamical properties from sensor data. A central challenge is balancing measurement consistency with useful prior information: learned priors can recover detail but may invent unsupported structure, especially when the forward model or data differs from training, so identifiability, stability, and calibrated uncertainty remain important.

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246 papers30 papers in the last four weeks, up 36% on the four weeks before. 0.2% of all new papers.

Inverse Reconstruction of Shock Time Series from Shock Response Spectrum Curves using Machine Learning
Mar 3, 2026Adam Watts, Andrew Jeon, Destry Newton +1Inverse Problems
Los Alamos National Laboratory · University of Rochester
Infinite dimensional generative sensing
Mar 3, 2026Paolo Angella, Vito Paolo Pastore, Matteo SantacesariaCompressed Sensing Inverse Problems
Neural Electromagnetic Fields for High-Resolution Material Parameter Reconstruction
Mar 3, 2026Zhe Chen, Peilin Zheng, Wenshuo Chen +3Materials Property Prediction Inverse Problems
Xidian University · The Hong Kong University of Science and Technology
Constrained Particle Seeking: Solving Diffusion Inverse Problems with Just Forward Passes
Mar 2, 2026Hongkun Dou, Zike Chen, Zeyu Li +3Diffusion-Based Inverse Problems Inverse Problems
Beihang University · Beijing Zhongguancun Academy
FAST-DIPS: Adjoint-Free Analytic Steps and Hard-Constrained Likelihood Correction for Diffusion-Prior Inverse Problems
Mar 2, 2026Minwoo Kim, Seunghyeok Shin, Hongki LimDiffusion-Based Inverse Problems Inverse Problems
Department of Electrical and Computer Engineering, Inha University Incheon, 22212, South Korea
PhysFormer: A Physics-Embedded Generative Model for Physically Self-Consistent Spectral Synthesis
Mar 2, 2026Siqi Wang, Mengmeng Zhang, Yude Bu +1Radiative Transfer Physics-Informed Generative Modeling
School of Mathematics and Statistics, Shandong University, Weihai, 264209, Shandong, China · Weihai Institute for Interdisciplinary Research, Shandong University, Weihai 264209, Shandong, China
Dual-space posterior sampling for Bayesian inference in constrained inverse problems
Feb 28, 2026Ali Siahkoohi, Kamal Aghazade, Ali GholamiBayesian Inverse Problems Inverse Problems
Department of Computer Science, University of Central Florida, Orlando, FL, USA · Institute of Geophysics, Polish Academy of Sciences, Warsaw, Poland
DiffSOS: Acoustic Conditional Diffusion Model for Speed-of-Sound Reconstruction in Ultrasound Computed Tomography
Feb 27, 2026Yujia Wu, Shuoqi Chen, Shiru Wang +3Ultrasound Imaging Inverse Problems
Thayer School of Engineering, Dartmouth College, Hanover, NH, USA · NVIDIA Corp
Improving Full Waveform Inversion in Large Model Era
Feb 27, 2026Yinan Feng, Peng Jin, Yuzhe Guo +2Inverse Problems OOD Generalization
School of Data Science and Society University of North Carolina at Chapel Hill Chapel Hill, NC, USA · The Pennsylvania State University State College, PA, USA · Google DeepMind
Advancing accelerator virtual beam diagnostics through latent evolution modeling: an integrated solution to forward, inverse, tuning, and UQ problems
Feb 26, 2026Mahindra Rautela, Alexander ScheinkerLatent Dynamics Modeling Inverse Problems
Los Alamos National Laboratory, Los Alamos, NM, US
Learning to reconstruct from saturated data: audio declipping and high-dynamic range imaging
Feb 25, 2026Victor Sechaud, Laurent Jacques, Patrice Abry +1Inverse Problems Self-Supervised Learning
CNRS and ENS de Lyon, Laboratoire de physique, Lyon, France · UCLouvain, ICTEAM, Louvain-la-Neuve, Belgium · CIFAR Fellow
GSNR: Graph Smooth Null-Space Representation for Inverse Problems
Feb 23, 2026Romario Gualdrón-Hurtado, Roman Jacome, Rafael S. Suarez +1Inverse Problems Image Inverse Problems
Universidad Industrial de Santander, Colombia, 680002
Separating Oblivious and Adaptive Models of Variable Selection
Feb 18, 2026Ziyun Chen, Jerry Li, Kevin Tian +1Sparse Recovery Feature Selection
University of Washington · University of Texas at Austin
Guided Diffusion by Optimized Loss Functions on Relaxed Parameters for Inverse Material Design
Feb 17, 2026Jens U. Kreber, Christian Weißenfels, Joerg StuecklerInverse Design Inverse Problems
Intelligent Perception in Technical Systems Group, University of Augsburg, Germany · Faculty of Mathematics, Natural Science and Engineering, University of Augsburg, Germany · Centre for Advanced Analytics and Predictive Sciences, University of Augsburg, Germany
Stability and Concentration in Nonlinear Inverse Problems with Block-Structured Parameters: Lipschitz Geometry, Identifiability, and an Application to Gaussian Splatting
Feb 10, 2026Joe-Mei Feng, Hsin-Hsiung KaoInverse Rendering Parameter Identifiability
Computer Science and Information Engineering, Tamkang University, New Taipei City, Taiwan (R.O.C.) · Department of Information Management, Central Police University, Taoyuan, Taiwan
Trajectory Stitching for Solving Inverse Problems with Flow-Based Models
Feb 9, 2026Alexander Denker, Zeljko Kereta, Carola-Bibiane Schönlieb +1Generative Flow Networks Flow-Based Generative Modeling
Department of Computer Science, University College London · Department of Applied Mathematics and Theoretical Physics, University of Cambridge.
Variational Sparse Paired Autoencoders (vsPAIR) for Inverse Problems and Uncertainty Quantification
Feb 3, 2026Jack Michael Solomon, Rishi Leburu, Matthias ChungVariational Autoencoders Uncertainty Quantification
Emory University Department of Mathematics
Inverse Problems Conditioned on Observation Ensembles: Applications and Methods
Jan 29, 2026Zhengyan Huan, Camila Pazos, Martin Klassen +3Posterior Sampling Inverse Problems
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
Fundamental Recovery Bounds for SPAD Signals under Stationary Flux
Jan 12, 2026Lior Dvir, Nadav Torem, Mohit Gupta +1Bayesian Inverse Problems Diffusion Posterior Sampling
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
Deep learning methods for inverse problems using connections between proximal operators and Hamilton-Jacobi equations
Dec 29, 2025Oluwatosin Akande, Gabriel P. Langlois, Akwum OnwuntaInverse Problems
Industrial and Systems Engineering, Lehigh University, 200 West Packer Avenue, Bethlehem, PA 18015, USA · Department of Mathematics, University of Illinois Urbana-Champaign, Chicago, IL, USA
InverseCrafter: Efficient Video ReCapture as a Latent Domain Inverse Problem
Dec 5, 2025Yeobin Hong, Suhyeon Lee, Hyungjin Chung +1Camera-Controlled Video Generation Video Diffusion Models
Graduate School of AI, KAIST, South Korea · EverEx, South Korea · Korea University, South Korea
Flexible Gravitational-Wave Parameter Estimation with Transformers
Dec 2, 2025Annalena Kofler, Maximilian Dax, Stephen R. Green +6Transformer Inference Gravitational-Wave Astronomy
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
Physics-Informed Neural Networks for Speech Production
Nov 1, 2025Kazuya Yokota, Ryosuke Harakawa, Masaaki Baba +1Speech Processing Physics-Informed ML
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
Robustness to Sparse Adversarial Corruption in Arbitrary Linear Measurements: Beyond Exact Recovery
Oct 28, 2025Vishal Halder, Alexandre Reiffers-Masson, Abdeldjalil Aïssa-El-Bey +1Sparse Recovery Adversarial Robustness
IMT Atlantique, Lab-STICC, CNRS UMR 6285, Brest, France · Department of Computer Science and Automation, Indian Institute of Science, Bengaluru, India
Inverse Mixed-Integer Programming: Learning Constraints then Objective Functions
Oct 6, 2025Akira KitaokaMixed-Integer Linear Programming Learning to Optimize
MACS: Measurement-Aware Consistency Sampling for Inverse Problems
Oct 2, 2025Amirreza Tanevardi, Pooria Abbas Rad Moghadam, Seyed Mohammad Eshtehardian +2Diffusion Model Sampling Inverse Problems
Department of Electrical Engineering Sharif University of Technology Tehran, Iran · Electronics Research Institute Sharif University of Technology Tehran, Iran
Patch Rebirth: Fast and Transferable Model Inversion of Vision Transformers
Sep 27, 2025Seongsoo Heo, Dong-Wan ChoiVision Transformer Inverse Problems
Inha University
A Gradient Flow Approach to Solving Inverse Problems with Latent Diffusion Models
Sep 23, 2025Tim Y. J. Wang, O. Deniz AkyildizWasserstein Gradient Flows Bayesian Inverse Problems
Department of Mathematics Imperial College London
NeuralDMD: Interpretable Neural Representation of Dynamics from Sparse and Noisy Measurements
Jul 3, 2025Ali SaraerToosi, Renbo Tu, Esther Y. H. Lin +2Spatiotemporal Forecasting Inverse Problems
University of Toronto, Toronto, ON, Canada · Vector Institute, Toronto, ON, Canada · NVIDIA Corporation, USA
Diff-SPORT: Diffusion-based Sensor Placement Optimization and Reconstruction of Turbulent flows in urban environments
May 30, 2025Abhijeet Vishwasrao, Sai Bharath Chandra Gutha, Andres Cremades +8Diffusion-Based Inverse Problems Inverse Problems
Department of Aerospace Engineering, University of Michigan, Ann Arbor, USA · FLOW, Engineering Mechanics, KTH Royal Institute of Technology, Stockholm, Sweden · Division of Robotics, Perception and Learning, School of EECS, KTH Royal Institute of Technology, Stockholm, Sweden +7

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

Adam Watts, Andrew Jeon, Destry Newton, Ryan Bowering

Los Alamos National Laboratory · University of Rochester

Inverse Problems

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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.