Recorded 15 July 2025. Alex Cloninger of the University of California, San Diego, presents "Using Linearized Optimal Transport to Predict the Evolution of Stochastic Particle Systems" at IPAM's Sampling, Inference, and Data-Driven Physical Modeling in Scientific Machine Learning Workshop. Abstract: We develop an algorithm to approximate the time evolution of a probability measure without explicitly learning an operator that governs the evolution. A particular application of interest is discrete measures that arise from particle systems. In many such situations, the individual particles move chaotically on short time scales, making it difficult to learn the dynamics of a governing operator, but the bulk distribution approximates an absolutely continuous measure that evolves “smoothly.” If the measure is known on some time interval, then linearized optimal transport theory provides an Euler-like scheme for approximating the evolution using its “tangent vector field”, which can be computed as a limit of optimal transport maps. We characterize conditions on the generated path that will enable this Euler scheme to be first-order accurate and to remain stable over a large number of Euler steps, as well as computable conditions that characterize a max step size. We also provide an analog of this Euler approximation to predict the evolution of the discrete measure. We demonstrate the efficacy of this approach with two illustrative examples where one only has access to a microscale simulation model, Gaussian diffusion and a cell chemotaxis model, and show that our method succeeds in predicting the bulk behavior over relatively large steps. This vastly reduces the number of microscale steps needed to reach the steady state distribution. This is joint work with Nick Karris, Vaki Nikitopoulos, Seungjoon Lee, and Yannis Kevrekidis. Learn more online at: https://www.ipam.ucla.edu/programs/workshops/sampling-inference-and-data-driven-physical-modeling-in-scientific-machine-learning-2/