The Applied and Computational Mathematics program at Caltech emphasizes numerical algorithms, data analysis, mathematical modeling, and scientific computing. These project ideas are designed to challenge graduate students to apply theory to real-world systems in engineering, physics, and biology.
Numerical Simulation of Incompressible Fluid Flow Using Finite Volume Methods
Mathematical Modeling of Epidemic Spread with Spatial Heterogeneity
Optimization Techniques in Large-Scale Scientific Computing
High-Performance Computing for Multiscale Simulation Problems
Machine Learning Applications in Solving Partial Differential Equations
Stability Analysis of Nonlinear Dynamical Systems in Biology
Inverse Problems in Medical Imaging Using Regularization Techniques
Computational Approaches to Electromagnetic Wave Propagation
Sparse Matrix Solvers for Large Linear Systems in Engineering
Data-Driven Modeling of Climate Systems Using Reduced Order Models
Mathematical Foundations of Deep Neural Networks
Asymptotic Methods for Singular Perturbation Problems
Numerical Study of Shock Waves and Hyperbolic Conservation Laws
Control and Optimization of Distributed Systems via PDE Constraints
Computational Finance: Option Pricing with Stochastic Differential Equations
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