Parameter Learning on Weighted Model Integration
Research Scholar, StarAI Lab, UCLA, 2019
- Advisor: Prof. Guy Van den Broeck
- Date: Nov 2019 - PRESENT
- Studied the Parameter Learning of Markov Logic Networks
- Analyzed the convexity of the log-likelihood function and log-partition function when the weight functions are different parametric formulas
Scaling Hybrid Probabilistic Inference with Logical Constraints by Relaxing and Compensating
Research Scholar, StarAI Lab, UCLA, 2019
- Advisor: Prof. Guy Van den Broeck
- Date: Sep 2019 - PRESENT
- Proposed a novel algorithm to approximate Model Integration (MI) inference within the RCR framework
- Devised various update rules for iterative optimization scheme in the compensation step, including probability matching and moment matching
- Analyzed the convergence property for update equations when the relaxed equivalence constraint both connect and disconnect the primal graph, using the fixed-point theorem
Hybrid Probabilistic Inference with Logical Constraints: Tractability and Message Passing
Research Scholar, StarAI Lab, UCLA, 2019
- Advisor: Prof. Guy Van den Broeck
- Date: Jul 2019 - Sep 2019
- Studied the basic theories and algorithms of Modeling and Reasoning with Bayesian Networks
- Proposed the moment calculation algorithm of the SMT($\mathcal{LRA}$) random variables for Weighted Model Integration (WMI), Derived the marginal probability density function for WMI
- Improved the numerical integration step for the algorithm of efficient search-based WMI using Gaussian quadrature rules
- Devised a novel formulation of MI via an exact message passing scheme on the tractable MI problems adopting symbolic integration, which is able to exactly compute all the variable marginal densities – as well as statistical moments – at once
- Proved the correctness and the amortization of message passing MI algorithm
- Analyzed the treewidth and diameter of the primal graph when the reduction from tree-shaped WMI with bivariate queries to MI played
- Constructed a representative example and Elaborated the procedure of the reduction from WMI to MI, passing by WMI$_{\mathbb{R}}$, including both boolean and continuous variables, both disjunction and conjunction
- Finished the paper-writing on this work and posted the paper to arXiv as joint first author
Some Studies on Adaptive Finite Element Method (AFEM) for Schrödinger Equation of Hydrogen Atom
Graduate Research, LSEC, UCAS, 2019
- Advisor: Prof. Aihui Zhou & Xiaoying Dai
- Date: Sep 2017 - May 2019
- Reviewed the basic theories and algorithms of AFEM for elliptic boundary value and eigenvalue problems, including a priori error estimation, a posteriori error estimation, adaptive mesh-refinement techniques, convergence rate and optimal complexity; oral presented at group meetings
- Reviewed the first principles electronic structure calculations, comprising the mathematical foundation and physical background
- Wrote shell scripts under Linux environment
- Parallel Calculated the finite element solutions to nonlinear partial differential equations, using C language based on Parallel Hierarchical Grid (PHG) package
- Visualized the 3D spherical harmonics solutions via ParaView and analyzed the accuracy of the finite element method with different iterations
- Designed algorithms to reduce the computation error and iterations caused by hydrogen atom’s small spectral gap in numerical solutions to generalized linear eigenvalue problems
- Proposed a more proper arrangement of initial mesh, Improved the effective polynomial order for the finite element in the discretization of Kohn-Sham equation
- Designed two integration strategies to calculate the singular integral, Suppressed the error caused by the singularity
- Analyzed the computation error from three aspects: model error, numerical error and approximation error
- Reduced the model error and numerical error, Obtained the variation curves of the approximation error which is the core of finite element approximation with the increase of the polynomial order for the finite element
Numerical Iterative Solutions to Two-Point Boundary Value Problems for Nonlinear Differential Equations
Undergraduate Research, ZJU, 2016
- Advisor: Prof. Xiaoliang Cheng
- Date: Jun 2015 - May 2016
- Designed MATLAB algorithm for the $Ka\breve{c}anov$ method, an iteration method for solving nonlinear problems via linearization
- Analyzed the convergence and the effectiveness of the method on different nonlinear PDEs
- Proposed a novel composite $Ka\breve{c}anov$ method with a wider application range, higher accuracy, and faster convergence speed
- Derived the analytical solutions to a special type of strain-limiting nonlinear elastic models, Inspired by the image patterns of numerical experiments
Traffic Signal Optimization at Plane Intersections
Student Research Training Program, ZJU, 2015
- Advisor: Prof. Shuping Chen
- Date: Jun 2014 - May 2015
- Abstracted the mathematical model for a real life problem: Designed various phase combinations for different intersections to improve traffic capacity and reduce vehicle delay
- Simplified the traffic flow into three phases using Graph Theory
- Proposed the linear programming for the best phase combination optimized for each intersection