About

Yunan Yang is an Associate Professor in the Department of Mathematics at Cornell University, affiliated with the College of Arts and Sciences. He earned his Ph.D. from the University of Texas at Austin in 2019. His research focuses on computational mathematics, particularly developing numerical methods for inverse problems, machine learning, PDE-constrained optimization, global optimization, and computational optimal transport with applications in data science. His work includes advancing numerical techniques for large-scale PDE-based optimization problems, inverse data matching using the quadratic Wasserstein metric, and applying optimal transport to seismic inversion and chaotic dynamics. Yunan Yang has contributed to the field through publications in prominent journals and conferences, emphasizing the development of efficient algorithms and methods for complex inverse problems and data-driven computational mathematics.

Research topics

• Computer Science
• Mathematical analysis
• Mathematical optimization
• Mathematics
• Applied mathematics
• Biology
• Medicine
• Geology
• Chemistry
• Internal medicine
• Pathology
• Cancer research
• Seismology
• Geometry
• Immunology
• Geophysics
• Physics

Selected publications

• Velocity Reconstruction from Flow-Induced Magnetic Fields

  Open MIND · 2026-02-25

  preprint

  We study the inverse problem of reconstructing an incompressible velocity field $\boldsymbol{v}$ from observations of the induced magnetic field $\boldsymbol{b}$. In the presence of a strong, constant background field $\mathbf{F}$, the evolution of the magnetic perturbation $\boldsymbol{b}$ is governed by the linearized induction equation. We analyze the system on both the entire space $Ω= \mathbb{R}^d$ and a periodic domain $Ω= \prod_{i=1}^d [0, L_i)$, which models a homogeneous medium with side lengths $L_i > 0$. We analyze this problem by decomposing it into the injectivity of a parabolic forward map and the solvability of a divergence-free transport sub-problem. On the whole space $\mathbb{R}^d$, we show that the transport sub-problem is well-posed when data is prescribed on a non-characteristic hypersurface transverse to $\mathbf{F}$. On the torus, we establish a sharp uniqueness criterion based on the rational dependence of the ratios $\{F_i/L_i\}_{i=1}^d$ between the background-field components and the corresponding domain periods. Furthermore, we show that for the reconstructed velocity to belong to $L^2$, a sufficient condition is that the background field must satisfy a Diophantine condition. The proof combines injectivity of the parabolic forward map with uniqueness for a steady transport equation along $\mathbf{F}$.

  DOI

• On the Unique Recovery of Transport Maps and Vector Fields from Finite Measure-Valued Data

  arXiv (Cornell University) · 2026-04-09

  articleOpen accessSenior author

  We establish guarantees for the unique recovery of vector fields and transport maps from finite measure-valued data, yielding new insights into generative models, data-driven dynamical systems, and PDE inverse problems. In particular, we provide general conditions under which a diffeomorphism can be uniquely identified from its pushforward action on finitely many densities, i.e., when the data $\{(ρ_j,f_\#ρ_j)\}_{j=1}^m$ uniquely determines $f$. As a corollary, we introduce a new metric which compares diffeomorphisms by measuring the discrepancy between finitely many pushforward densities in the space of probability measures. We also prove analogous results in an infinitesimal setting, where derivatives of the densities along a smooth vector field are observed, i.e., when $\{(ρ_j,\text{div} (ρ_j v))\}_{j=1}^m$ uniquely determines $v$. Our analysis makes use of the Whitney and Takens embedding theorems, which provide estimates on the required number of densities $m$, depending only on the intrinsic dimension of the problem. We additionally interpret our results through the lens of Perron--Frobenius and Koopman operators and demonstrate how our techniques lead to new guarantees for the well-posedness of certain PDE inverse problems related to continuity, advection, Fokker--Planck, and advection-diffusion-reaction equations. Finally, we present illustrative numerical experiments demonstrating the unique identification of transport maps from finitely many pushforward densities, and of vector fields from finitely many weighted divergence observations.

  PublisherOA PDF

• Operator learning meets inverse problems

  Handbook of numerical analysis · 2026-01-01

  book-chapterSenior author
  PublisherDOI

• Velocity Reconstruction from Flow-Induced Magnetic Fields

  ArXiv.org · 2026-02-25

  articleOpen access

  We study the inverse problem of reconstructing an incompressible velocity field $\boldsymbol{v}$ from observations of the induced magnetic field $\boldsymbol{b}$. In the presence of a strong, constant background field $\mathbf{F}$, the evolution of the magnetic perturbation $\boldsymbol{b}$ is governed by the linearized induction equation. We analyze the system on both the entire space $Ω= \mathbb{R}^d$ and a periodic domain $Ω= \prod_{i=1}^d [0, L_i)$, which models a homogeneous medium with side lengths $L_i > 0$. We analyze this problem by decomposing it into the injectivity of a parabolic forward map and the solvability of a divergence-free transport sub-problem. On the whole space $\mathbb{R}^d$, we show that the transport sub-problem is well-posed when data is prescribed on a non-characteristic hypersurface transverse to $\mathbf{F}$. On the torus, we establish a sharp uniqueness criterion based on the rational dependence of the ratios $\{F_i/L_i\}_{i=1}^d$ between the background-field components and the corresponding domain periods. Furthermore, we show that for the reconstructed velocity to belong to $L^2$, a sufficient condition is that the background field must satisfy a Diophantine condition. The proof combines injectivity of the parabolic forward map with uniqueness for a steady transport equation along $\mathbf{F}$.

  PublisherOA PDF

• Well-posedness and efficient algorithms for inverse optimal transport with bregman regularization

  Inverse Problems · 2026-04-02

  articleOpen accessSenior author

  Abstract This work analyzes the inverse optimal transport problem under Bregman regularization. We establish well-posedness results, including existence, uniqueness (up to equivalence classes of solutions), and stability, under several structural assumptions on the cost matrix. On the computational side, we investigate the existence of solutions to the optimization problem with general constraints on the cost matrix and provide a sufficient condition guaranteeing existence. In addition, we propose an inexact block coordinate descent method for the problem with a strongly convex penalty term. In particular, when the penalty is quadratic, the subproblems admit a diagonal Hessian structure, which enables highly efficient element-wise Newton updates. We establish a linear convergence rate for the algorithm and demonstrate its practical performance through numerical experiments, including the validation of stability bounds, the investigation of regularization effects, and the application to a marriage matching dataset.

  PublisherDOI

• Adjoint DSMC Method for Spatially Inhomogeneous Boltzmann Equation with General Boundary Conditions

  ArXiv.org · 2026-03-21

  articleOpen accessSenior author

  This manuscript derives adjoint equations for the numerical solution of the spatially inhomogeneous Boltzmann equation using Direct Simulation Monte Carlo (DSMC). The formulation accounts for spatial transport and a range of boundary conditions, including periodic boundaries, specular reflection, thermal reflection, and prescribed inflow. Numerical experiments are presented to validate the resulting adjoint system. These adjoint formulations are intended for use in gradient-based optimization, sensitivity analysis, and design problems involving rarefied gas dynamics.

  PublisherOA PDF

• On the Unique Recovery of Transport Maps and Vector Fields from Finite Measure-Valued Data

  arXiv (Cornell University) · 2026-04-09

  preprintOpen accessSenior author

  We establish guarantees for the unique recovery of vector fields and transport maps from finite measure-valued data, yielding new insights into generative models, data-driven dynamical systems, and PDE inverse problems. In particular, we provide general conditions under which a diffeomorphism can be uniquely identified from its pushforward action on finitely many densities, i.e., when the data $\{(ρ_j,f_\#ρ_j)\}_{j=1}^m$ uniquely determines $f$. As a corollary, we introduce a new metric which compares diffeomorphisms by measuring the discrepancy between finitely many pushforward densities in the space of probability measures. We also prove analogous results in an infinitesimal setting, where derivatives of the densities along a smooth vector field are observed, i.e., when $\{(ρ_j,\text{div} (ρ_j v))\}_{j=1}^m$ uniquely determines $v$. Our analysis makes use of the Whitney and Takens embedding theorems, which provide estimates on the required number of densities $m$, depending only on the intrinsic dimension of the problem. We additionally interpret our results through the lens of Perron--Frobenius and Koopman operators and demonstrate how our techniques lead to new guarantees for the well-posedness of certain PDE inverse problems related to continuity, advection, Fokker--Planck, and advection-diffusion-reaction equations. Finally, we present illustrative numerical experiments demonstrating the unique identification of transport maps from finitely many pushforward densities, and of vector fields from finitely many weighted divergence observations.

  PublisherDOI

• Adjoint DSMC Method for Spatially Inhomogeneous Boltzmann Equation with General Boundary Conditions

  SSRN Electronic Journal · 2026-01-01

  preprintOpen accessSenior author
  PublisherDOI

• Robust Frequency Domain Full-Waveform Inversion via HV-Geometry

  IEEE Transactions on Computational Imaging · 2025-01-01

  articleSenior author

  Conventional frequency-domain full-waveform inversion (FWI) is typically implemented with an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$L^{2}$</tex-math></inline-formula> misfit function, which suffers from challenges such as cycle skipping and sensitivity to noise. While the Wasserstein metric has proven effective in addressing these issues in time-domain FWI, its applicability in frequency-domain FWI is limited due to the complex-valued nature of the data and reduced transport-like dependency on wave speed. To mitigate these challenges, we introduce the HV metric (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$d_{\text{HV}}$</tex-math></inline-formula>), inspired by optimal transport theory, which compares signals based on horizontal and vertical changes without requiring the normalization of data. We implement <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$d_{\text{HV}}$</tex-math></inline-formula> as the misfit function in frequency-domain FWI and evaluate its performance on synthetic and real-world datasets from seismic imaging and ultrasound computed tomography (USCT). Numerical experiments demonstrate that <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$d_{\text{HV}}$</tex-math></inline-formula> outperforms the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$L^{2}$</tex-math></inline-formula> and Wasserstein metrics in scenarios with limited prior model information and high noise while robustly improving inversion results on clinical USCT data.

  PublisherDOI

• Invariant Measures in Time-Delay Coordinates for Unique Dynamical System Identification

  Physical Review Letters · 2025-09-26

  articleSenior author

  While invariant measures are widely employed to analyze physical systems when a direct study of pointwise trajectories is intractable, e.g., due to chaos or noise, they cannot uniquely identify the underlying dynamics. Our first result shows that, in contrast to invariant measures in state coordinates, e.g., [x(t),y(t),z(t)], the invariant measure expressed in time-delay coordinates, e.g., [x(t),x(t-τ),…,x(t-(m-1)τ)], can identify the dynamics up to a topological conjugacy. Our second result resolves the remaining ambiguity: by combining invariant measures constructed from multiple delay frames with distinct observables, the system is uniquely identifiable, provided that a suitable initial condition is satisfied. These guarantees require informative observables and appropriate delay parameters (m, τ), which can be limiting in certain settings. We support our theoretical contributions through a series of physical examples demonstrating how invariant measures expressed in delay coordinates can be used to perform robust system identification in practice.

  PublisherDOI

Recent grants

• An Optimal Transport Based Multiscale Method for Inverse Problems

  NSF · $176k · 2019–2022

Frequent coauthors

• Weibo Cai

  91 shared

• Hao Hong

  North China Electric Power University

  44 shared

• Alicia Y. Zhou

  National Institutes of Health

  36 shared

• Dong Xia

  36 shared

• Y Wang

  Intel (United States)

  36 shared

• Patrick

  University of Washington

  36 shared

• Todd E. Barnhart

  University of Wisconsin–Madison

  34 shared

• Björn Engquist

  30 shared

Education

• Ph.D., Mathematics

  The University of Texas at Austin

  2018

Awards & honors

• Twelve new Klarman Fellows