1. Numerical Methods for Hamiltonian Systems: Theory, Numerics and Case Studies Open Access Author: Zhan, Hongyuan Title: Numerical Methods for Hamiltonian Systems: Theory, Numerics and Case Studies Area of Honors: Mathematics Keywords: numerical methodsHamiltonian system File: Download thesis_hzz5039.pdf Thesis Supervisors: Xiantao Li, Thesis SupervisorDr. Victoria V Sadovskaya, Thesis Honors Advisor
2. Comparisons between the Monte Carlo method and Finite Difference method for option price and interest rate models Open Access Author: Wu, Jiawei Title: Comparisons between the Monte Carlo method and Finite Difference method for option price and interest rate models Area of Honors: Mathematics Keywords: Numerical AnalysisFinancial MathematicsPartial Differential Equations File: Download Wu_Jiawei_Comparisons_between_the_Monte_Carlo_method_and_Finite_Difference_method_for_option_price_and_interest_rate_models.pdf Thesis Supervisors: Anna L Mazzucato, Thesis SupervisorXiantao Li, Thesis Honors Advisor
3. A new training method for neural network in solving PDEs Open Access Author: Liang, Fei Title: A new training method for neural network in solving PDEs Area of Honors: Mathematics Keywords: Neural NetworkPDEDeep-Ritztraining methodefficiency File: Download A_New_Training_Method_for_Deep_Neural_Network_in_Solving_PDEs.pdf Thesis Supervisors: Xiantao Li, Thesis SupervisorXiantao Li, Thesis Honors AdvisorWenrui Hao, Faculty Reader
4. Solution of Problems in Quadratic Programming Using Dykstra's Algorithm Open Access Author: Jin, Xin Title: Solution of Problems in Quadratic Programming Using Dykstra's Algorithm Area of Honors: Mathematics Keywords: quadratic programmingbest approximationdykstra algorithmellipsoid method File: Download latex_thesis_template-combined.pdf Thesis Supervisors: Ludmil Tomov Zikatanov, Thesis SupervisorLudmil Tomov Zikatanov, Thesis Honors AdvisorXiantao Li, Faculty Reader
5. Optimal Control of Alzheimer's Disease Restricted (Penn State Only) Author: Li, Zhiyuan Title: Optimal Control of Alzheimer's Disease Area of Honors: Mathematics Keywords: optimal controlAlzheimer's Diseasereaction-diffusion equation File: Login to Download Thesis Supervisors: Wenrui Hao, Thesis SupervisorXiantao Li, Thesis Honors Advisor
6. A mean-field theory for quantum neural networks Open Access Author: Cohen, Ryan Title: A mean-field theory for quantum neural networks Area of Honors: Mathematics Keywords: Quantum computingNeural networks File: Download Cohen_Ryan_Thesis.pdf Thesis Supervisors: Xiantao Li, Thesis SupervisorCarina Pamela Curto, Thesis Honors Advisor