and fluid-mechanics simulations. The curriculum bridges the gap between theoretical probability and practical engineering, covering essential concepts from the Law of Large Numbers to complex Bayesian inverse problems and stochastic differential equations.A key highlight of the course is its hands-on approach: theory is immediately applied through Python-based implementations using NumPy, SciPy, and PyTorch. Students will learn to build Gaussian process surrogate models for expensive CFD simulations and utilize Karhunen–Loève expansions for field-valued inputs.
The program concludes by linking classical probabilistic sampling to modern scientific machine learning, including score-based diffusion models. By integrating rigorous lecture units with intensive exercise sessions, the course ensures that students can critically evaluate and implement stochastic methods to solve realistic engineering challenges.
Basic Python programming recommended, No prior knowledge of probability theory or statistics required.
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