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This tutorial provides an accessible and implementation-oriented introduction to Gaussian process learning-based model predictive control (GP-MPC), which combines probabilistic residual modeling with receding-horizon control. Its central tutorial contribution is a detailed, step-by-step derivation of multi-step mean and covariance propagation for GP-augmented prediction models. The derivation shows how commonly used propagation formulas follow from the laws of total expectation and total covariance, and clarifies the roles of the GP posterior mean, GP posterior covariance, uncertain inputs, and query-output cross-covariances. Building on this foundation, the article distinguishes mean-only unconstrained GP predictive control from uncertainty-aware constrained GP-MPC, clarifies regulation and output-tracking formulations, and provides concise implementation and computational-complexity guidance, including practical software-tool references and discussion of the scope of closed-loop guarantees. Mobile-robot path-following examples illustrate mean-only unconstrained implementations, whereas mixed-vehicle platooning illustrates uncertainty-aware constrained GP-MPC with uncertainty-dependent safety-distance tightening. The tutorial is intended to help researchers and practitioners understand, implement, and critically evaluate GP-MPC designs for robotic and autonomous systems operating under modeling uncertainty.

Inverse rendering for skin typically relies on offline path tracing to estimate physical properties, which fail to map directly to the approximate shaders utilized in interactive applications, such as game engines. We bridge this gap by directly estimating subsurface scattering parameters tailored for real-time rendering pipelines. We introduce a differentiable Screen-Space Subsurface Scattering (SSSS) framework that enables the joint optimization of spatially varying base textures and scattering distances. To account for local variations in skin thickness, we estimate these parameters across distinct facial regions, generating a blended profile map ready for production runtime engines. Our pipeline utilizes a low-cost, single-light, single-view capture setup designed for accessible and practical appearance acquisition. Optimization is driven by a masked loss function targeting regions where subsurface scattering effects are dominant. We validate our approach on a real-world dataset of $45$ individuals across the Monk Skin Tone Scale, ensuring demographic generalization. Furthermore, we complement this evaluation with synthetic data, a multi-light setup validating our single-light assumption, and a tilted-view configuration confirming angular consistency. Results demonstrate that our method effectively recovers scattering parameters from lightweight inputs, yielding realistic skin appearance directly compatible with standard real-time shaders.