Yiran Wang

Welcome! I am an Associate Professor in the Department of Mathematics at Emory University.

My research focuses on inverse problems, microlocal analysis, integral geometry, spectral and scattering theory. My research is driven by modern challenges in physics, medical imaging and deep learning. I completed my Ph.D. at Purdue University under the supervision of Prof. Antônio Sá Barreto.

I am a member of the Inverse Problems International Association (IPIA). I am on the Editorial Board of the journal Communications on Analysis and Computation. At Emory, I am a faculty representative of the College Senate and the Executive Council.

Here is my contact information:

  • E-mail: yiran.wang(at)emory.edu
  • Office: Mathematics & Science Center, E414.
  • Mailing address: Department of Mathematics, 400 Dowman Drive, Atlanta, GA 30322.



Teaching

2027 Spring semester: 2026 Fall semester: 2026 Spring semester: 2025 Spring semester:

Research

Manuscripts and preprints (available upon request):
  • Generalization in post-processing type deep learning methods for limited-angle tomography
    Abstract: Post-processing type deep learning methods are popular in limited angle tomography. Empirical evaluations have demonstrated generalization ability of these methods in removing artifacts, but the mechanism remains elusive. In this work, we formulate the learning problem as a nonlinear inverse problem, and analyze the generalization using techniques from microlocal analysis. Our result also provides sufficient conditions on training data to achieve generalization ability for reducing artifacts in limited angle tomography.

  • A convolutional deep Calderón method for Electrical Impedance Tomography (with T. Hu, B. Jin)
    Abstract: Electrical impedance tomography (EIT) is a noninvasive imaging technique utilizing electric properties of the imaging object. Due to its severe ill-posed nature, the problem is challenging to solve numerically. Recent studies using deep learning-based methods have shown promising empirical results but often face instability issues. In this work, we propose a new strategy, namely convolutional deep Calderón method (CDCM) to address the stability-accuracy trade-off in deep learning based approaches for EIT problems. The proposed method is based on a theoretical development that decouples the ill-posedness and nonlinearity of the EIT problem, which consists of a stable but nonlinear step and a linear but unstable deconvolution step. We illustrate the effectiveness of CDCM through numerical experiments, including perturbations with mixed-sign amplitudes, overlapping inclusions, noisy data and an inhomogeneous background. Numerically, we observe that CDCM consistently outperforms the standard deep Calderón method, and yields more stable reconstructions with fewer artifacts.

  • The Calderón problem for near Euclidean metrics (with G. Uhlmann)

  • The partial data Calderón problem in dimension three (with G. Uhlmann)

  • Recovering asymptotics of potentials from the scattering of relativistic Schrödinger operators (with G. Uhlmann)

  • A Lipschitz stability for the Calderón problem with small structure-free anisotropy (with J.-N. Wang)
    Abstract: In this paper, we study an anisotropic Calderón problem of recovering potentials by the boundary measurements. We consider the Laplace-Beltrami operator with any Riemannian metric which is a small perturbation of the Euclidean one. We prove that the Dirichlet-to-Neumann map associated with the Schrödinger operator determines the potential with a Lipschitz stability estimate in a negative Sobolev norm under a sign condition. In other words, assuming a priori sign condition, we are able to prove two new results in Calderón problem: small anisotropic media without structure assumption and a Lipchitz stability estimate of reconstructing potentials.

  • Rigidity of Lorentzian metrics with the same scattering relations
    Abstract: Consider small metric deformations of the Minkowski space. We prove that the scattering relation of null geodesics between two Cauchy surfaces uniquely determines the metric perturbation up to gauge obstructions.

  • Microlocal analysis of the light ray transform on globally hyperbolic Lorentzian manifolds

  • Determination of vacuum space-times from the Einstein-Maxwell equations (with M. Lassas, G. Uhlmann)

  • Resolvent and radiation fields on non-trapping asymptotically hyperbolic manifolds

Publications:

Last updated: 10-2026.