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Subject offerings of new and developing areas of knowledge in computer science intended to augment the existing curriculum. See Class Schedule or departmental course information for topics and prerequisites. Course Information: May be repeated in the same or separate terms if topics vary.

This course provides a rigorous examination of differentiable Monte Carlo (MC) methods, an emerging framework for solving high-dimensional inverse problems in computer graphics and scientific computing. We will explore the mathematical foundations of computing gradients for stochastic estimators?focusing on adjoint methods and Reynolds transport theorem for handling geometric discontinuities?and apply these concepts to differentiable and inverse rendering to recover material and geometric properties from images. The curriculum further extends to physics-based simulation, detailing the grid-free Walk on Spheres (WoS) algorithm for solving Partial Differential Equations (PDEs) and its differentiable counterparts for inverse boundary value problems. By unifying light transport and physical simulation under a common stochastic gradient framework, students will equip themselves with the tools to perform efficient optimization in complex, continuous domains.