Inverse simulation is used to identify the needed inputs in order generate a desired outcome. It has found widespread usage across sciences and engineering. These include designing temperature-regulating components in aircraft, fabricating fluid systems, and detecting tumors in brain. Due to widespread utility of inverse simulations, there exists a large set of mature computational methodologies for inverse simulation tasks, predominantly based on taking continuous space and dividing into discrete sections, which is called a discretization approach. Unfortunately, the dependence on using discrete spaces in inverse simulations and the amount of time and computation it requires means that the existing methodologies are severely constrained. In an era of increasing demand for large-scale inverse simulation for a range of important applications (e.g., fabrication, medicine, robotics), there is a critical demand for methods that can overcome the existing bottlenecks. The project will address this challenge by developing a suite of Monte Carlo methods for inverse simulation that are highly scalable, parallelizable, output-sensitive, and significantly expand the applicable types of physical phenomena and representations. The project will achieve this goal through three inter-connected research thrusts: First, the project will research methods for Monte Carlo differentiable simulation, developing mathematical formulations and computational algorithms that can compute derivatives o