Selected Papers

Manifold Structured Data and its Impact on Learning

• Extrinsic Curvature Estimation by Closest Point Projection of Rays. Liangchen Liu and Richard Tsai. Preprint 2026. [paper]

• Linear Regression on Manifold Structured Data: the Impact of Extrinsic Geometry on Solutions. Liangchen Liu, Juncai He, and Richard Tsai. Proceedings of the 2nd Annual Workshop on Topology, Algebra, and Geometry in Machine Learning (TAG-ML, ICML 2023), PMLR 221 (2023): 557-576. [paper] [arXiv] [poster]

• Side-effects of Learning from Low Dimensional Data Embedded in a Euclidean Space. Juncai He, Richard Tsai and Rachel Ward. Research in the Mathematical Sciences 10.1 (2023): 13. [paper]

Least Squares Residual Minimization for Solving Differential Equations

• When does least-squares residual minimization solve a differential equation? Carlos Esteve-Yagüe, Richard Tsai, and Stanley Osher. Preprint 2026. [paper]

• Solving Hamilton-Jacobi Equations by Residual Minimization of Monotone Finite-difference Discretizations. Olivier Bokanowski, Carlos Esteve-Yagüe, and Richard Tsai. Preprint 2026. [paper]

• Finite-difference Least Square Methods for Solving Hamilton-Jacobi Equations using Neural Networks. Carlos Esteve-Yagüe, Richard Tsai, and Alex Massucco. Journal of Computational Physics 524 (2025): 113721. [paper] [arXiv]

Integral Equations

• A Multilevel Stochastic-gradient Neural Solver for Boundary Integral Equations. Bing-Ze Lu and Richard Tsai. Frontiers in Applied Mathematics (2026), accepted. [paper]

• Error Analysis for the Implicit Boundary Integral Method. Yimin Zhong, Kui Ren, Olof Runborg, and Richard Tsai. BIT Numerical Mathematics 65.1 (2025): 8. [paper] [arXiv]

• High-order Corrected Trapezoidal Rules for a Class of Singular Integrals. Federico Izzo, Olof Runborg, and Richard Tsai. Advances in Computational Mathematics 49.4 (2023): 60. [paper] [arXiv]

• Integration over Curves and Surfaces Defined by the Closest Point Mapping. Catherine Kublik and Richard Tsai. Research in the Mathematical Sciences 3.1 (2016): 3. [paper] [arXiv]

• An Implicit Interface Boundary Integral Method for Poisson's Equation on Arbitrary Domains. Catherine Kublik, Nicolay M. Tanushev, and Richard Tsai. Journal of Computational Physics 247 (2013): 279-311. [paper]

Multiscale Coupling Algorithms

• Learning Hamiltonian Flow Maps from Numerical-Scheme Residuals for Long-Time Multiscale Simulation. Rui Fang and Richard Tsai. Preprint 2025. [paper]
• Stabilization of parareal algorithms for long time computation of a class of highly oscillatory Hamiltonian flows using data. Rui Fang and Richard Tsai. Numerical Algorithms 96 (2024): 1163-1187. [paper] [arXiv]
• A Stable Parareal-like Method for the Second Order Wave Equation. Hieu Nguyen and Richard Tsai. Journal of Computational Physics 405 (2020): 109156. [paper]

Point Cloud Processing

• Nearest Neighbor Sampling of Point Sets using Rays. Liangchen Liu, Louis Ly, Colin Macdonald, and Yen-Hsi Richard Tsai. Communications on Applied Mathematics and Computation 6.2 (2024): 1131-1174. [paper][poster]

Exploration and Surveillance

• Efficient and robust Sensor Placement in Complex Environments. Lukas Taus and Yen-Hsi Richard Tsai. Preprint 2023 [paper][video]

• Autonomous Exploration, Reconstruction, and Surveillance of 3D Environments aided by Deep Learning. Louis Ly and Yen-Hsi Richard Tsai. 2019 International Conference on Robotics and Automation (ICRA). IEEE, 2019. [paper] [slides] [talk]

• Strategy Synthesis for Surveillance-evasion Games with Learning-enabled Visibility Optimization. Suda Bharadwaj, Louis Ly, Bo Wu, Yen-Hsi Richard Tsai, and Ufuk Topcu. 2019 Conference on Decision and Control (CDC). IEEE, 2019. [paper] [slides]

• An Efficient Algorithm for a Visibility-based Surveillance-evasion Game. Ryo Takei, Yen-Hsi Richard Tsai, Zhengyuan Zhou, and Yanina Landa. Communications in Mathematical Sciences 12.7 (2014): 1303-1327. [paper]

• A Practical Path-planning Algorithm for a Simple Car: a Hamilton-Jacobi Approach. Ryo Takei, Yen-Hsi Richard Tsai, Haochong Shen, and Yanina Landa. Proceedings of the 2010 American control conference. IEEE, 2010. [paper]

Source Localization

• Autonomous Source Discovery and Navigation in Complicated Environments. Yanina Landa, Haochong Shen, Ryo Takei, Yen-Hsi Richard Tsai. UCLA CAM Report 09-73 (2009). [paper]

• Discovery of Point Sources in the Helmholtz Equation posed in Unknown Domains with Obstacles. Yanina Landa, Nicolay Tanushev, Yen-Hsi Richard Tsai. Communications in Mathematical Sciences 9.3 (2011): 903-928. [paper] [slides]

• Point Source Identification in Nonlinear Advection–Diffusion–Reaction Systems. Alexander Mamonov and Yen-Hsi Richard Tsai. Inverse Problems 29.3 (2013): 035009. [paper] [slides]

• Heat Source Identification based on ℓ₁ Constrained Minimization. Yingying Li, Stanley Osher, and Yen-Hsi Richard Tsai. Inverse Problems and Imaging 8.1 (2014): 199-221. [paper]