What do we mean by soft matter? Americans prefer to call it “complex fluids”. This is a rather ugly name, which tends to discourage the young students. But it does indeed bring in two of the major features: complexity and flexibility.
--P. de Gennes
My research lies at the intersection of variational modeling, scientific computing, and machine learning, with applications in physics, materials science, biology, and data science. I am particularly interested in developing multiscale, thermodynamically consistent variational models and structure-preserving numerical methods for complex dissipative systems, including liquid crystals, polymeric fluids, reaction–diffusion processes, and biological systems. More recently, I have been exploring how machine learning can enhance variational modeling and computation, by learning unknown dynamics, constructing coarse-grained closures, improving traditional numerical methods and solving high-dimensional PDEs. I also investigate variational perspectives on machine learning, interpreting learning dynamics as dissipative systems governed by energy–dissipation laws and designing algorithms inspired by structure-preserving numerical discretizations.
[1] Y. Wang, J. Chen, C. Liu, and L. Kang. Particle-based energetic variational inference. Stat Comput, 31(3):34, 2021.
[2] Y. Wang, T.-F. Zhang, and C. Liu. A two species micro-macro model of wormlike micellar solutions and its maximum entropy closure approximations: An energetic variational approach. J. Non-Newtonian Fluid Mech., 293:104559, 2021.
[3] Y. Wang, C. Liu, and B. Eisenberg. On variational principles for polarization responses in electrome-chanical systems. arXiv preprint arXiv:2108.11512, 2021.
[4] S. Patranabish, Y. Wang, A. Sinha, and A. Majumdar. Quantum-dots-dispersed bent-core nematic liquid crystal and cybotactic clusters: Experimental and theoretical insights. Phys. Rev. E, 103(5):052703, 2021.
[5] C. Liu, Y. Wang, and T.-F. Zhang. On a two-species micro-macro model for wormlike micellar solutions: dynamic stability analysis. arXiv preprint arXiv:2101.11455, 2021.
[6] C. Liu, C. Wang, Y. Wang, and S. M. Wise. Convergence analysis of the variational operator splitting scheme for a reaction-diffusion system with detailed balance. arXiv preprint arXiv:2105.09415, 2021.
[7] C. Liu, C. Wang, and Y. Wang. A structure-preserving, operator splitting scheme for reaction-diffusion equations with detailed balance. J. Comput. Phys., 436:110253, 2021.
[8] C. Liu, C. Wang, and Y. Wang. A second-order accurate, operator splitting scheme for reaction-diffusion systems in an energetic variational formulation. arXiv preprint arXiv:2109.02792, 2021.
[9] J. Liang, N. Jiang, C. Liu, Y. Wang, and T.-F. Zhang. On a reversible Gray-Scott type system from energetic variational approach and its irreversible limit. arXiv preprint arXiv:2107.08237, 2021.
[10] J. Yin, Y. Wang, J. Z. Chen, P. Zhang, and L. Zhang. Construction of a pathway map on a complicated energy landscape. Phys. Rev. Lett., 124(9):090601, 2020.
[11] Y. Wang, C. Liu, P. Liu, and B. Eisenberg. Field theory of reaction-diffusion: Law of mass action with an energetic variational approach. Phys. Rev. E, 102(6):062147, 2020.
[12] J. Noh, Y. Wang, H.-L. Liang, V. S. R. Jampani, A. Majumdar, and J. P. F. Lagerwall. Dynamic tuning of the director field in liquid crystal shells using block copolymers. Phys. Rev. Res., 2:033160, Jul 2020.
[13] C. Liu and Y. Wang. A variational Lagrangian scheme for a phase-field model: A discrete energetic variational approach. SIAM J. Sci. Comput., 42(6):B1541–B1569, 2020.
[14] C. Liu and Y. Wang. On Lagrangian schemes for porous medium type generalized diffusion equations: a discrete energetic variational approach. J. Comput. Phys., page 109566, 2020.
[15] G. Canevari, J. Harris, A. Majumdar, and Y. Wang. The well order reconstruction solution for three-dimensional wells, in the Landau–de Gennes theory. Int. J. Non Linear Mech., 119:103342, 2020.
[16] K. Bisht, Y. Wang, V. Banerjee, and A. Majumdar. Tailored morphologies in two-dimensional ferronematic wells. Phys. Rev. E, 101(2):022706, 2020.
[17] Y. Wang, G. Canevari, and A. Majumdar. Order reconstruction for nematics on squares with isotropic inclusions: A Landau–de Gennes study. SIAM J. Appl. Math., 79(4):1314–1340, 2019.
[18] S. Patranabish, Y. Wang, A. Sinha, and A. Majumdar. One-dimensional theoretical analysis of coupling and confinement effects on the cybotactic clusters of bent-core nematic liquid crystals. Phys. Rev. E, 99(1):012703, 2019.
[19] Y. Wang, P. Zhang, and J. Z. Y. Chen. Formation of three-dimensional colloidal crystals in a nematic liquid crystal. Soft Matter, 2018.
[20] A. Majumdar and Y. Wang. Remarks on uniaxial solutions in the Landau-de Gennes theory. J. Math. Anal. Appl., 464(1):328 – 353, 2018.
[21] Y. Wang, P. Zhang, and J. Z. Y. Chen. Topological defects in an unconfined nematic fluid induced by single and double spherical colloidal particles. Phys. Rev. E, 96(4):042702, 2017.
[22] Y. Tong, Y. Wang, and P. Zhang. Defects around a spherical particle in cholesteric liquid crystals. Numer. Math. Theor. Meth. Appl., 10(2):205–221, 2017.