PDE Inverse Problems

PDE: Partial Differential Equation

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14 papers in the last four weeks, against 2 the four weeks before. 0.1% of all new papers.

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Geological text descriptions in ill-posed inverse problems: insights from learned hydraulic-conductivity inversion
Jun 23, 2026Taiga Saito, Yu Otake, Daijiro Mizutani +1PDE Inverse Problems Inverse Problems
Department of Civil and Environmental Engineering, Tohoku University, 6-6-06 Aramaki Aoba, Aoba-ku, Sendai, Miyagi, 980-8579, Japan
Flow Annealing Posterior Sampling for Function-Space Regression and Inverse Problems
Jun 21, 2026Yaozhong Shi, Zachary E. Ross, Yisong YueBayesian Inverse Problems Posterior Sampling
California Institute of Technology
Starter-Iterator Neural Operator: A Unified Architecture for High-Fidelity Forward and Inverse PDE Problems
Jun 16, 2026Kuilin Qin, Lianfang Wang, Xu Sun +4PDE Surrogate Modeling PDE Operator Learning
Decoupled Latent Optimization of Diffusion Models for Full Waveform Inversion
Jun 12, 2026Chen Min, Zheng MaDiffusion-Based Inverse Problems PDE Inverse Problems
School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai, China · CMA-Shanghai, Shanghai Jiao Tong University, Shanghai, China
Physics-Informed Neural Networks and Radial Basis Functions for PDEs with Dirac Delta Sources
Jun 10, 2026Manuel Reyna, Alexandre TartakovskyPDE Solving Physics-Informed ML
Department of Civil and Environmental Engineering, University of Illinois Urbana-Champaign, 205 North Mathews Avenue, Urbana, 61801, IL, USA
Adjoint Method versus Physics-Informed Neural Networks in PDE-Constrained Inverse Problems
Jun 10, 2026Zhen Zhang, Alessandro Alla, George Em KarniadakisConstrained Optimization Physics-Informed ML
Division of Applied Mathematic, Brown University, Providence, RI, USA · Department of Mathematics, Sapienza Università di Roma, Rome, Italy
Loss Landscape Diagnosis for Gradient-Based Gray-Scott System Inversion: Disentangling the Roles of PINN Components
Jun 9, 2026Yan YangDynamical Systems Parameter Estimation
Independent Researcher.
No-Harm Physics-Informed Inverse Learning with Residual-Calibrated Uncertainty
Jun 5, 2026Ronald KatendeUncertainty Quantification Physics-Informed ML
Department of Mathematics Kabale University Kikungiri Hill, Katuna Road, Kabale, Uganda
Wall Shear Stress Reconstruction from Concentration: Differentiable Physics and Physics-Informed Neural Networks
Jun 4, 2026Mahmoud Elhadidy, Siva Viknesh, Roshan M. D'Souza +1Differentiable Physics Physics-Informed ML
Department of Mechanical Engineering, University of Utah, Salt Lake City, UT, USA · Scientific Computing and Imaging Institute, University of Utah, Salt Lake City, UT, USA · Department of Mechanical Engineering, University of Wisconsin–Milwaukee, Milwaukee, WI, USA +1
The Right Measure for Physics-Constrained Generation: A Co-Area Correction for Posterior-Consistent PDE Inverse Problems
Jun 3, 2026Jian Xu, Yanning Wu, Delu Zeng +2Constrained Generative Modeling Physics-Informed Generative Modeling
1RIKEN iTHEMS · 2RIKEN AIP · 3South China University of Technology +1
Critical evaluation of PINN for FWD inverse analysis and differentiable FEM as an alternative
Jun 2, 2026Yongjin Choi, Hyeonbin Moon, Seunghwa RyuDifferentiable Physics Physics-Informed ML
KAIST InnoCORE PRISM-AI Center, Korea Advanced Institute of Science and Technology (KAIST), Daejeon, 34141, Republic of Korea · Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology (KAIST), Daejeon, 34141, Republic of Korea · School of Civil and Environmental Engineering, Georgia Institute of Technology, Atlanta, 30332, GA, USA
Physics-Aware Linearized ADMM and Its Unrolling
Jun 1, 2026Satoshi Takabe, Shunta Arai, Tadashi WadayamaAlternating Direction Method of Multipliers Algorithm Unrolling
Department of Computer Science Institute of Science Tokyo Tokyo, Japan · Center for Advanced Intelligence Project RIKEN Tokyo, Japan · Department of Engineering Nagoya Institute of Technology Nagoya, Japan
(HB-ARFM) History-Bootstrapped Flow Matching for Inverse Boiling Reconstruction
May 29, 2026Xianwei Zou, Sheikh Md Shakeel Hassan, Arthur Feeney +1Flow Matching PDE Inverse Problems
Department of Electrical Engineering and Computer Science, University of California Irvine, USA.
Oscillatory State-Space Models as Inductive Biases for Physics-Informed Neural PDE Solvers
May 29, 2026Abhishek Chandra, Taniya KapoorNeural PDE Solvers Physics-Informed ML
KTH Royal Institute of Technology Stockholm, Sweden · Wageningen University & Research Wageningen, The Netherlands
Scalable Bayesian Inference for Nonlinear Conservation Laws
May 29, 2026Tim Weiland, Philipp HennigUncertainty Quantification Bayesian Inverse Problems
T"{u}bingen AI Center, University of T"{u}bingen, T"{u}bingen, Germany
Deep Adaptive Dimension Reduction for Bayesian Inference in Inverse Problems
May 28, 2026Yueyang Wang, Xili Wang, Kejun Tang +3Bayesian Inverse Problems Dimensionality Reduction
School of Mathematical Sciences, Peking University · School of Sciences, Great Bay University · Department of Mathematics, Louisiana State University +1
Guided Flow Matching for Forward and Inverse PDE Problems with Sparse Observations: Algorithm and Theory
May 25, 2026Xifeng Zhang, Jin ZhaoFlow Matching PDE Solving
School of Mathematical Science Capital Normal University Beijing, 100048, China · Academy for Multidisciplinary Studies Capital Normal University2026 Beijing, 100048, China
PDEInvBench: A Comprehensive Dataset and Design Space Exploration of Neural Networks for PDE Inverse Problems
May 25, 2026Divyam Goel, Nithin Chalapathi, Sanjeev Raja +1Neural Network Optimization Synthetic Benchmark Generation
Department of Computer Science, UC Berkeley · Departments of Computer Science and Chemical EngineeringMay UC Berkeley; LBNL
Physics-Informed Generative Solver: Bridging Data-Driven Priors and Conservation Laws for Stable Spatiotemporal Field Reconstruction
May 21, 2026Ziyuan Zhu, Keyu Hu, Zhifei Chen +10Physics-Informed Generative Modeling Physics-Informed ML
School of Advanced Manufacturing Engineering, Nanjing University, Suzhou, 215163, China. · National Laboratory of Solid State Microstructures, Nanjing University, Nanjing, 210093, China. · Suzhou Acoustics Industry Technology Research Institute Co., Ltd., Suzhou, 215513, China. +8
Diffusion Graph Posterior Sampling for Nonlinear Inverse Problems with Application to Electrical Impedance Tomography
May 19, 2026Giovanni S. Alberti, Damiana Lazzaro, Serena Morigi +2Image Reconstruction Diffusion-Based Inverse Problems
MaLGa Center, Department of Mathematics, University of Genova, Italy · Department of Mathematics, University of Bologna, Bologna, Italy · Department of Mathematics, Harbin Institute of Technology, China
An End-to-End PyTorch Interface for Differentiable PDE Solvers: A RANS Model-Correction Study
May 19, 2026Luca Saverio, Michele Alessandro Bucci, Gianmarco Farro +2PDE Solving Differentiable Optimization
MONHADE · Digital Sciences & Technologies Department, Safran Tech, Magny-Les-Hameaux, 78114, France. · DAAA, ONERA, Institut Polytechnique de Paris, Meudon, 92190, France. +1
Harnessing AI for Inverse Partial Differential Equation Problems: Past, Present, and Prospects
May 16, 2026Zhentao Tan, Yuze Hao, Boyi Zou +3Inverse Design PDE Inverse Problems
Collaborative Innovation Center of Artificial Intelligence (CCAI), Zhejiang University, China · School of Mathematical Sciences, Zhejiang University, China · Tsinghua University, China +1
Amortized Energy-Based Bayesian Inference
May 14, 2026Hojjat Kaveh, Ricardo Baptista, Andrew M. StuartAmortized Inference Bayesian Inverse Problems
California Institute of Technology · University of Toronto
Di-BiLPS: Denoising induced Bidirectional Latent-PDE-Solver under Sparse Observations
May 13, 2026Zhonghao Li, Chaoyu Liu, Qian ZhangNeural PDE Solvers Latent Diffusion Models
School of Science, Harbin Institute of Technology, Shenzhen, China · Department of Theoretical Physics and Applied Mathematics, University of Cambridge, Cambridge, United Kingdom
Local Inverse Geometry Can Be Amortized
May 13, 2026Aaditya L. KachhadiyaNeural Surrogate Modeling Inference-Time Optimization
Independent Researcher Surat, India
Total Generalized Variation regularization closes the gap between neural-eld and classical methods in seismic travel-time tomography
May 11, 2026Isao KurosawaSeismology PDE Inverse Problems
IVXA, Japan.
Functional-prior-based approaches to Bayesian PDE-constrained inversion using physics-informed neural networks
May 8, 2026Ryoichiro Agata, Tomohisa OkazakiBayesian Inverse Problems Physics-Informed ML
Japan Agency for Marine-Earth Science and Technology, Japan · Disaster Prevention Research Institute, Kyoto University, Japan · RIKEN Center for Advanced Intelligence Project, Japan
PerFlow: Physics-Embedded Rectified Flow for Efficient Reconstruction and Uncertainty Quantification of Spatiotemporal Dynamics
May 5, 2026Hao Zhou, Rui Zhang, Han Wan +1Physics-Informed Generative Modeling Uncertainty Quantification
Gaoling School of Artificial Intelligence, Renmin University of China
Learning Interpretable PDE Representations for Generative Reconstructions with Structured Sparsity
Apr 26, 2026Valerie Tsao, Nathaniel Chaney, Manolis VeveakisPhysics-Informed Diffusion Models Sparse Recovery
Department of Civil & Environmental Engineering, Duke University, NC, USA.
Uncertainty Quantification in PINNs for Turbulent Flows: Bayesian Inference and Repulsive Ensembles
Apr 18, 2026Khemraj Shukla, Zongren Zou, Theo Kaeufer +2Uncertainty Quantification Deep Ensembles
Division of Applied Mathematics, Brown University, Providence, RI, USA · Department of Computing and Mathematical Sciences, California Institute of Technology, Pasadena, CA, USA · Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA

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Geological text descriptions in ill-posed inverse problems: insights from learned hydraulic-conductivity inversion

Taiga Saito, Yu Otake, Daijiro Mizutani, Sopheakpolin Mom

Department of Civil and Environmental Engineering, Tohoku University, 6-6-06 Aramaki Aoba, Aoba-ku, Sendai, Miyagi, 980-8579, Japan

PDE Inverse Problems Inverse Problems

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Hydraulic-conductivity inversion is ill posed: even complete head observations can leave structural ambiguity. Geological text descriptions can supply additional information about subsurface structure to constrain reconstruction. However, it remains unclear when descriptions improve reconstruction and how solvers use their stated content. We examine these questions in learned inversion using a synthetic Darcy-flow benchmark with idealised descriptions, varying observation density and flow direction. After sparse-observation training, descriptions can improve reconstruction over models trained without them when observations leave structural ambiguity, though gains vary across conditions and runs. Instance-specific content can improve reconstruction beyond field-type information. Editing this content shifts reconstructions toward the stated geometry of selected features, less strongly as observations become more informative about those features. We do not establish a reconstruction advantage of text over numerical inputs encoding the same geological information. Finally, we discuss how this complementarity could guide the joint design of measurements and geological knowledge acquisition.

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