2026

1. Analysis of Bregman Proximal Point for the Obstacle Problem

   Brendan Keith, Haojun Qin, and Noe Reyes Rivas

   arXiv preprint arXiv:2609.23007, 2026

   arXiv Bib

   @article{keith2026analysis,
     title = {Analysis of Bregman Proximal Point for the Obstacle Problem},
     author = {Keith, Brendan and Qin, Haojun and Reyes Rivas, Noe},
     journal = {arXiv preprint arXiv:2609.23007},
     year = {2026},
   }

2. Exponential Adaptive Smoothing and Importance Sampling for Optimization of the Conditional Value-at-Risk

   Will Asness, Brendan Keith, Boyan Lazarov, Anton Malandii, and Stan Uryasev

   arXiv preprint arXiv:2606.11515, 2026

   arXiv Bib

   @article{asness2026exponential,
     title = {Exponential Adaptive Smoothing and Importance Sampling for Optimization of the Conditional Value-at-Risk},
     author = {Asness, Will and Keith, Brendan and Lazarov, Boyan and Malandii, Anton and Uryasev, Stan},
     journal = {arXiv preprint arXiv:2606.11515},
     year = {2026},
   }

3. The SiMPL Method for Multi-Material Topology Optimization

   Peter Gangl, Brendan Keith, Dohyun Kim, Boyan S. Lazarov, and Thomas M. Surowiec

   arXiv preprint arXiv:2605.11994, 2026

   arXiv Bib

   @article{gangl2026simpl,
     title = {The SiMPL Method for Multi-Material Topology Optimization},
     author = {Gangl, Peter and Keith, Brendan and Kim, Dohyun and Lazarov, Boyan S. and Surowiec, Thomas M.},
     journal = {arXiv preprint arXiv:2605.11994},
     year = {2026},
   }

4. Proximal Galerkin for the isometry constraint

   Brendan Keith and Frédéric Marazzato

   arXiv preprint arXiv:2605.07054, 2026

   arXiv Bib

   @article{keith2026proximal,
     title = {Proximal Galerkin for the isometry constraint},
     author = {Keith, Brendan and Marazzato, Frédéric},
     journal = {arXiv preprint arXiv:2605.07054},
     year = {2026},
   }

5. Proximal Galerkin for Phase Field Fracture

   Miguel Castillón, Biswajit Khara, Jørgen S. Dokken, Thomas M. Surowiec, Brendan Keith, and Yuri Bazilevs

   arXiv preprint arXiv:2604.26210, 2026

   arXiv Bib

   @article{castillon2026proximal,
     title = {Proximal Galerkin for Phase Field Fracture},
     author = {Castillón, Miguel and Khara, Biswajit and Dokken, Jørgen S. and Surowiec, Thomas M. and Keith, Brendan and Bazilevs, Yuri},
     journal = {arXiv preprint arXiv:2604.26210},
     year = {2026},
   }

6. Proximal Discontinuous Galerkin Methods for Variational Inequalities

   Alexandre Ern, Brendan Keith, Dohyun Kim, Rami Masri, and Beatrice Riviere

   arXiv preprint arXiv:2604.19708, 2026

   arXiv Bib

   @article{ern2026proximal,
     title = {Proximal Discontinuous Galerkin Methods for Variational Inequalities},
     author = {Ern, Alexandre and Keith, Brendan and Kim, Dohyun and Masri, Rami and Riviere, Beatrice},
     journal = {arXiv preprint arXiv:2604.19708},
     year = {2026},
   }

7. The proximal Galerkin method for non-symmetric variational inequalities

   Guosheng Fu, Brendan Keith, Dohyun Kim, Rami Masri, and Will Pazner

   arXiv preprint arXiv:2602.14967, 2026

   arXiv Bib

   @article{fu2026proximal,
     title = {The proximal Galerkin method for non-symmetric variational inequalities},
     author = {Fu, Guosheng and Keith, Brendan and Kim, Dohyun and Masri, Rami and Pazner, Will},
     journal = {arXiv preprint arXiv:2602.14967},
     year = {2026},
   }

8. Information geometric regularization for computing sensitivities of flows with shocks

   Florian Schäfer

   arXiv preprint arXiv:2608.09759, 2026

   arXiv Bib

   @article{schafer2026information,
     title = {Information geometric regularization for computing sensitivities of flows with shocks},
     author = {Schäfer, Florian},
     journal = {arXiv preprint arXiv:2608.09759},
     year = {2026},
   }

9. Discontinuous Galerkin Semidiscretization of the Information Geometric Regularized Compressible Euler Equations

   Brook Eyob, Jesus Arias, Spencer H. Bryngelson, and Florian Schäfer

   arXiv preprint arXiv:2608.02223, 2026

   arXiv Bib

   @article{eyob2026discontinuous,
     title = {Discontinuous Galerkin Semidiscretization of the Information Geometric Regularized Compressible Euler Equations},
     author = {Eyob, Brook and Arias, Jesus and Bryngelson, Spencer H. and Schäfer, Florian},
     journal = {arXiv preprint arXiv:2608.02223},
     year = {2026},
   }

10. Shock solutions for the one-dimensional information geometric regularization of compressible flow

    William Barham, Brian K. Tran, Ben S. Southworth, and Florian Schäfer

    arXiv preprint arXiv:2607.12693, 2026

    arXiv Bib

    @article{barham2026shock,
      title = {Shock solutions for the one-dimensional information geometric regularization of compressible flow},
      author = {Barham, William and Tran, Brian K. and Southworth, Ben S. and Schäfer, Florian},
      journal = {arXiv preprint arXiv:2607.12693},
      year = {2026},
    }

11. Shocks without shock capturing: Information geometric regularization of finite volume methods for Navier–Stokes-like problems

    Anand Radhakrishnan, Benjamin Wilfong, Spencer H. Bryngelson, and Florian Schäfer

    Computer Methods in Applied Mechanics and Engineering, 2026

    DOI arXiv Bib

    @article{radhakrishnan2026shocks,
      title = {Shocks without shock capturing: Information geometric regularization of finite volume methods for Navier--Stokes-like problems},
      author = {Radhakrishnan, Anand and Wilfong, Benjamin and Bryngelson, Spencer H. and Schäfer, Florian},
      journal = {Computer Methods in Applied Mechanics and Engineering},
      volume = {461},
      pages = {119216},
      year = {2026},
      doi = {10.1016/j.cma.2026.119216},
    }

12. A review of weakly enforced Dirichlet boundary conditions in computational flow analysis

    Ming-Chen Hsu, Monu Jaiswal, and Yuri Bazilevs

    arXiv preprint arXiv:2609.06314, 2026

    arXiv Bib

    @article{hsu2026review,
      title = {A review of weakly enforced Dirichlet boundary conditions in computational flow analysis},
      author = {Hsu, Ming-Chen and Jaiswal, Monu and Bazilevs, Yuri},
      journal = {arXiv preprint arXiv:2609.06314},
      year = {2026},
    }

13. Exact Total Variation Minimizers as Non-Oscillatory Limiters in High-Order Methods for Conservation Laws

    Gabriel P. Langlois, Jerome Darbon, Rongjie Lai, Chi-Wang Shu, and Xiangxiong Zhang

    arXiv preprint arXiv:2607.27416, 2026

    arXiv Bib

    @article{langlois2026exact,
      title = {Exact Total Variation Minimizers as Non-Oscillatory Limiters in High-Order Methods for Conservation Laws},
      author = {Langlois, Gabriel P. and Darbon, Jerome and Lai, Rongjie and Shu, Chi-Wang and Zhang, Xiangxiong},
      journal = {arXiv preprint arXiv:2607.27416},
      year = {2026},
    }

14. A naturally sharpened level-set formulation for incompressible free-surface flows

    Jongmin Rim, Jinhui Yan, and Yuri Bazilevs

    Computer Methods in Applied Mechanics and Engineering, 2026

    DOI Bib

    @article{rim2026naturally,
      title = {A naturally sharpened level-set formulation for incompressible free-surface flows},
      author = {Rim, Jongmin and Yan, Jinhui and Bazilevs, Yuri},
      journal = {Computer Methods in Applied Mechanics and Engineering},
      volume = {453},
      pages = {118798},
      year = {2026},
      doi = {10.1016/j.cma.2026.118798},
    }

2025

1. A priori error analysis of the proximal Galerkin method

   Brendan Keith, Rami Masri, and Marius Zeinhofer

   arXiv preprint arXiv:2507.13516, 2025

   arXiv Bib

   @article{keith2025priori,
     title = {A priori error analysis of the proximal Galerkin method},
     author = {Keith, Brendan and Masri, Rami and Zeinhofer, Marius},
     journal = {arXiv preprint arXiv:2507.13516},
     year = {2025},
   }

2. Hamiltonian Information Geometric Regularization of the Compressible Euler Equations

   William Barham, Brian K. Tran, Ben S. Southworth, and Florian Schäfer

   arXiv preprint arXiv:2512.13948, 2025

   arXiv Bib

   @article{barham2025hamiltonian,
     title = {Hamiltonian Information Geometric Regularization of the Compressible Euler Equations},
     author = {Barham, William and Tran, Brian K. and Southworth, Ben S. and Schäfer, Florian},
     journal = {arXiv preprint arXiv:2512.13948},
     year = {2025},
   }

3. TR2-D2: Tree Search Guided Trajectory-Aware Fine-Tuning for Discrete Diffusion

   Sophia Tang, Yuchen Zhu, Molei Tao, and Pranam Chatterjee

   arXiv preprint arXiv:2509.25171, 2025

   arXiv Bib

   @article{tang2025tr2,
     title = {TR2-D2: Tree Search Guided Trajectory-Aware Fine-Tuning for Discrete Diffusion},
     author = {Tang, Sophia and Zhu, Yuchen and Tao, Molei and Chatterjee, Pranam},
     journal = {arXiv preprint arXiv:2509.25171},
     year = {2025},
   }

4. Essential barrier height and a probabilistic approach in characterizing potential landscape

   Yao Li, Molei Tao, and Shirou Wang

   Stochastic Processes and their Applications, 2025

   DOI arXiv Bib

   @article{li2025essential,
     title = {Essential barrier height and a probabilistic approach in characterizing potential landscape},
     author = {Li, Yao and Tao, Molei and Wang, Shirou},
     journal = {Stochastic Processes and their Applications},
     volume = {190},
     pages = {104763},
     year = {2025},
     doi = {10.1016/j.spa.2025.104763},
   }

5. A Closer Look at Model Collapse: From a Generalization-to-Memorization Perspective

   Lianghe Shi, Meng Wu, Huijie Zhang, Zekai Zhang, Molei Tao, and Qing Qu

   arXiv preprint arXiv:2509.16499, 2025

   arXiv Bib

   @article{shi2025closer,
     title = {A Closer Look at Model Collapse: From a Generalization-to-Memorization Perspective},
     author = {Shi, Lianghe and Wu, Meng and Zhang, Huijie and Zhang, Zekai and Tao, Molei and Qu, Qing},
     journal = {arXiv preprint arXiv:2509.16499},
     year = {2025},
   }

6. MDNS: Masked Diffusion Neural Sampler via Stochastic Optimal Control

   Yuchen Zhu, Wei Guo, Jaemoo Choi, Guan-Horng Liu, Yongxin Chen, and Molei Tao

   arXiv preprint arXiv:2508.10684, 2025

   arXiv Bib

   @article{zhu2025mdns,
     title = {MDNS: Masked Diffusion Neural Sampler via Stochastic Optimal Control},
     author = {Zhu, Yuchen and Guo, Wei and Choi, Jaemoo and Liu, Guan-Horng and Chen, Yongxin and Tao, Molei},
     journal = {arXiv preprint arXiv:2508.10684},
     year = {2025},
   }

7. Improving Classifier-Free Guidance in Masked Diffusion: Low-Dim Theoretical Insights with High-Dim Impact

   Kevin Rojas, Ye He, Chieh-Hsin Lai, Yuhta Takida, Yuki Mitsufuji, and Molei Tao

   arXiv preprint arXiv:2507.08965, 2025

   arXiv Bib

   @article{rojas2025improving,
     title = {Improving Classifier-Free Guidance in Masked Diffusion: Low-Dim Theoretical Insights with High-Dim Impact},
     author = {Rojas, Kevin and He, Ye and Lai, Chieh-Hsin and Takida, Yuhta and Mitsufuji, Yuki and Tao, Molei},
     journal = {arXiv preprint arXiv:2507.08965},
     year = {2025},
   }