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Path Catalog
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This graduate-level path builds a rigorous theoretical foundation for computational fluid dynamics, starting from the governing equations of fluid motion and advancing through numerical discretization, stability analysis, grid generation, and turbulence modeling. It emphasizes the mathematical and physical principles underlying CFD methods, preparing learners for research or advanced application.
This advanced graduate learning path equips learners with the theoretical and practical knowledge to construct, analyze, and apply multiscale models that bridge length and time scales. It covers foundational numerical methods, scale-bridging techniques such as homogenization and coarse-graining, and applications across disciplines.
A graduate-level learning path covering the mathematical foundations and computational methods for solving inverse problems in science. Learners will explore ill-posedness, regularization techniques, Bayesian inversion, and parameter estimation, with a strong emphasis on practical algorithms and applications.
A comprehensive graduate-level learning path covering optimization methods essential for computational science. It builds from mathematical foundations through linear programming, nonlinear optimization, gradient-based methods, constrained optimization, and evolutionary algorithms, with a focus on practical application to computational problems.
This learning path equips graduate students and researchers with advanced parallel computing techniques for large-scale scientific applications. It covers shared and distributed memory programming, GPU acceleration, hybrid computing, performance profiling, and scalability, building from HPC fundamentals to advanced optimization strategies.
This path equips graduate students with advanced numerical techniques for solving complex scientific problems, covering spectral, multigrid, adaptive mesh refinement, mesh-free, and fast multipole methods. Learners will build a strong foundation in functional analysis, numerical linear algebra, and PDE discretizations before progressing to specialized methods. The path emphasizes the theoretical underpinnings, algorithmic implementation, and practical application of each method.
This advanced learning path equips computational science students with the knowledge to quantify and manage uncertainty in computational models. It covers foundational probability and statistics, numerical methods, and progresses through aleatory/epistemic uncertainty, Monte Carlo methods, polynomial chaos, Bayesian inference, and sensitivity analysis. The path emphasizes practical application and hands-on assessment.
This learning path equips advanced science students with the knowledge and skills to apply machine learning methods to scientific problems. It covers essential mathematical foundations, core ML paradigms (supervised, unsupervised, neural networks), and specialized techniques like physics-informed neural networks, culminating in practical applications across scientific domains.
A focused learning path for science students to acquire practical data science skills for scientific applications. It covers data cleaning, statistical analysis, machine learning basics, dimensionality reduction, and clustering, with a foundation in programming and statistics.
A systematic learning path for undergraduate science students to understand and apply computational modeling and simulation. It covers model construction, verification, validation, sensitivity analysis, and uncertainty quantification, building on basic programming and numerical methods.