An inverse design system combines a large language model (LLM) with a task-specific optimizer, which includes a search function, a forward model, and a comparator. The LLM adjusts parameters of the optimizer's components in response to a design scenario. Then the optimizer processes the design scenario to produce design candidates. Optionally, the LLM learns from the design candidates in an iterative process. A stochastic predictive modeling system combines an LLM with input distributions and a forward model. The LLM adjusts one or more of the input distributions and/or the forward model in response to a forecast scenario. Then the forward model processes a sampling of the input distributions to produce a forward distribution. Optionally, the LLM informs the sampling process. Optionally, the LLM learns from the forward distribution.