Model-based deep learning methods such as loop unrolling (LU) and deep equilibrium model}(DEQ) extensions offer outstanding performance in solving inverse problems (IP). These methods unroll the optimization iterations into a sequence of neural networks that in effect learn a regularization function from data. While these architectures are currently state-of-the-art in numerous applications, their success heavily relies on the accuracy of the forward model. This assumption can be limiting in many physical applications due to model simplifications or uncertainties in the apparatus. To address forward model mismatch, we introduce an untrained forward model residual block within the model-based architecture to match the data consistency in the measurement domain for each instance. We propose two variants in well-known model-based architectures (LU and DEQ) and prove convergence under mild conditions. Our approach offers a unified solution that is less parameter-sensitive, requires no additional data, and enables simultaneous fitting of the forward model and reconstruction in a single pass, benefiting both linear and nonlinear inverse problems. The experiments show significant quality improvement in removing artifacts and preserving details across three distinct applications, encompassing both linear and nonlinear inverse problems. Moreover, we highlight reconstruction effectiveness in intermediate steps and showcase robustness to random initialization of the residual block and a higher number of iterations during evaluation. Code is available at \texttt{https://github.com/InvProbs/A-adaptive-model-based-methods}.
Fast Physics-Driven Untrained Network for Highly Nonlinear Inverse Scattering Problems
Department of Electronic Engineering, Northwestern Polytechnical University, Xi’an 710029, China（电子工程系，西北工业大学，西安710029，中国）；Department of Physics and Technology, UiT The Arctic University of Norway, 9037, Tromsø, Norway（物理与技术系，北极大学（挪威）UiT，9037，特罗姆瑟，挪威）；Department of Computer Science, Al-Farabi Kazakh National University, Almaty 050040, Kazakhstan（计算机科学系，阿利法比国立大学（哈萨克斯坦），阿拉木图050040，哈萨克斯坦）
Phase Retrieval with Holography and Untrained Priors: Tackling the Challenges of Low-Photon Nanoscale Imaging
Massachusetts Institute of Technology（麻省理工学院）；Center for Computational Mathematics, Flatiron Institute（弗拉特龙研究所计算数学中心）；Yale University（耶鲁大学）；New York University（纽约大学）
Theoretical Perspectives on Deep Learning Methods in Inverse Problems
National University of Singapore（新加坡国立大学）；Technical University of Munich（慕尼黑工业大学）；University College London（伦敦大学学院）；Northeastern University（东北大学）；Weizmann Institute of Science（魏茨曼科学研究所）
Provably Convergent Algorithms for Solving Inverse Problems Using Generative Models
Iowa State University（爱荷华州立大学）；University of Illinois, Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；New York University（纽约大学）；University of California Riverside（加州大学河滨分校）
Bias Inheritance in Neural-Symbolic Discovery of Constitutive Closures Under Function-Class Mismatch
Nanophotonics and Biophotonics Key Laboratory of Jilin Province, School of Physics, Changchun University of Science and Technology（吉林省纳米光子学与生物光子学重点实验室，物理学院，长春理工大学）
Modeling and Inverse Identification of Interfacial Heat Conduction in Finite Layer and Semi-Infinite Substrate Systems via a Physics-Guided Neural Framework
Reducing the Representation Error of GAN Image Priors Using the Deep Decoder
Department of Mathematics and Khoury College of Computer Sciences, Northeastern University（数学系和Khoury计算机科学学院，东北大学）；Electrical Engineering and Information Technology, Technical University of Munich（电子工程与信息科技，慕尼黑技术大学）
