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

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

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

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

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

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

Fanqi Yan

Posts by Collection

portfolio

publications

talks

teaching