Wenxin Liu

About Me

I am a Year-1 PhD student on the Mathematics CDT with interests in Numerical Optimization. My supervisor is Prof. Bertram During.

I also very interested in Computational PDEs, Numerical linear algebra, and Wasserstein gradient flows.

Publications:

Conference:

1. A PDE-constrained Optimization Approach to Optimal Trajectory Planning under Uncertainty via Reflected Schroedinger Bridges, W. Liu and D. Kalise,Proceedings ECC2026 [arxivLink opens in a new window].

2. Computational Methods for Generalized Schrödinger Bridge Problems,

   D. Inoue, D. Kalise, and W. Liu, 27th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2026), Waterloo, Canada, Aug. 21, 2026.

   (program)

Contact

Email: Wenxin.Liu.2@warwick.ac.uk

Experiences:

Master Project on Wasserstein Gradient Flows via Primal-Dual Splitting

Reproduced and implemented primal-dual dynamic JKO schemes for Wasserstein gradient flows, including porous-medium evolution and nonlinear Fokker–Planck dynamics. The implementation builds sparse continuity, no-flux, mass, and initial-condition operators, then solves the constrained kinetic-energy problem using pointwise proximal updates.

Optimal Transport Primal-Dual Method JKO Scheme Gradient Flows

Multiscale PDE: Super-Localized Orthogonal Decomposition

Implemented a standalone two-dimensional reproduction of the Super-Localized Orthogonal Decomposition (SLOD) method for convection-dominated diffusion problems. The code builds Q1 finite element discretizations, local element-response bases, standard FEM and SUPG baselines, and SLOD/SLOD-Galerkin variants.

AISLS: AI-Accelerated Sparse Linear Solvers

Developed learning-based tools for accelerating large sparse linear systems from scientific computing workloads, combining solver/preconditioner selection, AMG parameter autotuning, and GNN-based initial-guess prediction.

Subprojects and results:

• Solver/preconditioner selection: attention-fused CNN-MLP prediction over 26 solver combinations, reaching 80.3% accuracy and about 3.83× solve-time speed-up.

• AMG parameter autotuning: learned AMG strong-connection threshold θ/eps selection, giving about 1.27× time speed-up and 20.97% iteration reduction against a default setting.

• GNN initial guess: OpenFOAM pressure-Poisson tests achieved 1.67× average and 13.16× maximum iteration speed-up, plus 1.79× average and 19.51× maximum wall-time speed-up.

ECC 2026 : Generalized Schrödinger Bridge Computations

Developed finite element solvers for reflected Schrödinger bridge problems with obstacle geometry, nonlinear prior drift, and iterative forward-backward potential updates. This work supports ECC 2026 paper on PDE-constrained optimal trajectory planning under uncertainty.