Inverse Problems Young Academy (IPYA) Inverse Problems Seminar - Frontiers in Inverse Problems: Theory, Algorithms, and Applications

Tip

For proper equation rendering, please view this documentation in day mode instead of night mode.

Upcoming talk. Tianjiao Wang @ June 25, 13:00 GMT (click to view title and abstract)

Title. Probabilistic stability for the inverse random scattering problem
Abstract. In this talk, we concern an inverse random potential scattering problem for the random Schrödinger equation. The random potential is assumed to be a generalized Gaussian random function, whose covariance operator is a classical pseudo-differential operator. We focus on the inverse problem of recovering the principal symbol of this classical pseudo-differential operator. We derive a probabilistic stability estimate for determining the principal symbol of the covariance operator from the far-field data. The stability result provides an estimate of the probability for an event when the principal symbol can be quantitatively determined by a single realization of the multi-frequency far-field pattern. The stability analysis employs the scattering theory, ergodicity theory and quantitative analytic continuation principle. This work is based on joint research with Prof. Xiang Xu and Prof. Yue Zhao.

The Zoom link will be sent to all members of the seminar mailing list prior to each talk. To request inclusion on the list, please contact the IPYA secretary, Pu-Zhao Kow, on behalf of the organizing committee.

Kindly note that a Zoom license is required only for the host. All speakers and participants may join directly using the emailed link.

Organizers. Pu-Zhao Kow, Ping Liu, Suman Kumar Sahoo, Yaohua Zang

Note

1. The participants will be muted upon entry.
2. If you would like to ask a question, please unmute yourself and pose the question, then please switch the microphone back off.
3. The participants are kindly asked to log in with the video off, so as to avoid problems with the bandwidth. You are very welcome to turn the video on when asking questions.
4. Once the talk is over and there are no more questions, the participants are very welcome to stay around a bit and chat with your colleagues.

About the seminar (click to view)

Inverse problems play a central role across diverse fields, including medical imaging (CT, MRI), geophysical exploration, financial modeling, and machine learning. The fundamental challenge, recovering hidden causes from observed data, is inherently ill-posed and demands advanced mathematical techniques to ensure stability and interpretability of solutions.

This seminar aims to provide a cutting-edge survey of current developments in inverse problems, highlighting the interplay between rigorous theory, algorithmic innovation, and real-world applications. Participants will gain both conceptual insights and practical knowledge of state-of-the-art approaches. Topics will include:

1. Theoretical analysis of inverse problems
2. Regularization theory and optimization
3. Bayesian and statistical frameworks
4. Machine learning-based methods

To foster engagement and discussion, the seminar will follow this structure:

1. Frequency. Bi-weekly sessions (30-60 minutes)
2. Structure. Main presentation followed by 5-10 minutes of open discussion
3. Mode. Online

date and time	Speaker
Jun 25, 2026 13:00 GMT	Tianjiao Wang (click to view title and abstract) Title. Probabilistic stability for the inverse random scattering problem Abstract. In this talk, we concern an inverse random potential scattering problem for the random Schrödinger equation. The random potential is assumed to be a generalized Gaussian random function, whose covariance operator is a classical pseudo-differential operator. We focus on the inverse problem of recovering the principal symbol of this classical pseudo-differential operator. We derive a probabilistic stability estimate for determining the principal symbol of the covariance operator from the far-field data. The stability result provides an estimate of the probability for an event when the principal symbol can be quantitatively determined by a single realization of the multi-frequency far-field pattern. The stability analysis employs the scattering theory, ergodicity theory and quantitative analytic continuation principle. This work is based on joint research with Prof. Xiang Xu and Prof. Yue Zhao.
Jun 11, 2026 13:00 GMT	Yiwen Lin (click to view title and abstract) Title. Frequency-Explicit A Priori Bounds and Multi-Frequency MCCUQ Reconstructions for Random Surface Scattering Abstract. This talk investigates direct and inverse acoustic scattering from random scatterers. We first derive frequency-explicit a priori stability bounds for random surface scattering using variable transformation, Pettis measurability theorem and Bochner's Theorem. For inverse scattering with randomness, we propose an MCCUQ (Monte Carlo Continuation Uncertainty Quantification) reconstruction method for periodic random surface scattering with multi-frequency data. This method integrates Monte Carlo sampling over the probability space, wavenumber-based continuation, and Karhunen–Loève expansion of random structures to reconstruct statistical features of unknown periodic surfaces from boundary measurements of the scattered fields away from the structure. Numerical results will demonstrate the reliability and efficiency of the proposed method. This work is based on joint research with Gang Bao and Xiang Xu.
May 28, 2026 13:00 GMT	Anamika Purohit (click to view title and abstract) Title. An Inverse problem for a fourth order nonlinear Schrödinger equation (NLS) Abstract. In this talk, we study an inverse problem for the time-dependent nonlinear fourth-order Schrödinger equation on compact Euclidean domains. This model arises in nonlinear fiber optics and the theory of optical solitons in gyrotropic media. Our main objective is the identification of unknown coefficients from the associated source-to-solution map, which assigns to each source term , supported in , the corresponding solution restricted to the same set, where is a neighborhood of . We prove that the zeroth-order term, the second-order coefficient, and the nonlinear coefficient are uniquely determined by this map. Moreover, the recovery of the symmetric second-order tensor reduces to the inversion of a divergent beam transform. If time permits, we will also discuss related inverse problems for time-dependent nonlinear fourth-order Schrödinger equations on compact Riemannian manifolds. This work is based on joint research with Rohit Kumar Mishra and Suman Kumar Sahoo.
Apr 30, 2026 13:00 GMT	Pu-Zhao Kow (click to view title and abstract) Title. Frequency dependent contraction rates for the Bayesian method to the inverse source problem Abstract. We study an inverse source problem for acoustic waves over a range of frequencies from two complementary perspectives. First, although the problem is severely ill-posed (exhibiting only logarithmic stability), we show, through a detailed analysis of the singular values of the forward operator, that enlarging the frequency range enhances stability. This phenomenon is commonly referred to as increasing resolution/stability. Second, motivated by this singular value behavior, we establish a consistency result within a nonparametric Bayesian framework. Despite the ill-posedness, the posterior distribution contracts around the true source at a rate involving both polynomial and logarithmic terms, with explicit dependence on the frequency range. This captures the increasing resolution/stability phenomenon from a Bayesian viewpoint. Our results also offer practical insights into how to balance the quantity, quality, and cost of measurements. This talk is based on joint work with Jenn-Nan Wang.
Apr 2, 2026 13:00 GMT	Akari Ishida (click to view title and abstract) Title. Convergence of the Levenberg-Marquardt method under Hölder stability Abstract. In this talk, we study the convergence of the nonlinear Levenberg-Marquardt method for inverse problems in Hilbert spaces under Hölder stability assumptions. We establish local convergence results together with convergence rate estimates for both exact and noisy data. Furthermore, based on these results, we develop iterative reconstruction algorithms for inverse problems with finite measurements. This work is based on joint research with Sei Nagayasu (University of Hyogo) and Gen Nakamura (Hokkaido University).
Mar 19, 2026 13:00 GMT	Yaohua Zang (click to view title and abstract) Title. A unified physics-informed generative operator framework for general inverse problems Abstract. Inverse problems governed by partial differential equations (PDEs) are fundamental across science and engineering, yet remain challenging when measurements are sparse or noisy, and when unknown coefficients are high-dimensional or discontinuous. We introduce IGNO, a physics-informed generative neural operator framework that encodes complex coefficient fields into a low-dimensional latent space and reconstructs both coefficients and PDE solutions through neural operator decoders. The framework is trained purely through physical constraints, without paired input–output data, and unifies solution-based and operator-based measurements within a single architecture. Inversion is performed via efficient gradient-based optimization in the latent space, further accelerated by an a priori normalizing flow model. We demonstrate the effectiveness of IGNO on challenging inverse problems, including recovery of discontinuous coefficients and electrical impedance tomography (EIT), where it achieves accurate and stable reconstructions under severe noise, consistently outperforms state-of-the-art methods, and generalizes well to out-of-distribution targets, establishing IGNO as a unified and scalable approach for PDE-based inverse problems. This work was carried out in collaboration with Prof. Gang Bao (Zhejiang University).
Jan 15, 2026 13:00 GMT	Rommel R. Real (click to view title and abstract) Title. The Hanke-Raus rule for regularization of inverse problems Abstract. We consider the Hanke-Raus heuristic parameter choice rule to the Landweber iteration and Tikhonov regularization for solving ill-posed problems. This rule does not require the noise level, which may be inaccessible and prone to improper estimation in many instances. A famous veto states that convergence in the worst-case scenario cannot be expected in general. However, by imposing certain conditions on the noisy data, we can establish convergence. Convergence under this rule also extends with a penalty functional penalty, such as L1 and TV-penalty terms, which are used to recover solutions with special features, such as sparsity and piecewise constancy. We discuss some recent progress in this heuristic rule, which also involves Newton-type methods.
Dec 11, 2025 13:00 GMT	Antti Kykkänen (click to view title and abstract) Title. Geometrization of Elasticity and Ray Tomography Problems Abstract. This talk has two parts. The first part discusses geometrization of elasticity for purposes of inverse problems. I will introduce and discuss analytic and algebraic tools for studying elastic geometry. The second part of the talk is dedicated to the study of inverse problems for a class of integral ray transforms arising from the linearization of elastic travel time data.
Nov 27, 2025 13:00 GMT	Janne Nurminen (click to view title and abstract) Title. An inverse problem for the prescribed mean curvature equation Abstract. In this talk I will formulate an inverse source problem for the prescribed mean curvature equation (PMC) The question is if from boundary measurements one can determine the mean curvature . The talk is based on joint work with Tony Liimatainen (arXiv:2509.22078) and we show that it is indeed possible to recover . I will discuss the outline and main ideas behind the proof.
Nov 13, 2025 13:00 GMT	Giovanni Covi (click to view title and abstract) Title. Nonlocality in Inverse problems Abstract. We will discuss the use of nonlocality in inverse problems for partial differential equations. In particular, we will see the example of the fractional Calderón problem, which can be solved in any dimension and with partial data by making use of the unique continuation property of the fractional Laplacian. We will also discuss recent developments in this direction.