Abstract: Nonlinear PDEs with uncertainties play a critical role in diverse fields such as fluid dynamics, climate modeling, biological systems, and engineering applications. Standard numerical methods often fail to preserve crucial structural properties, such as conservation laws, involution constraints, or long-term asymptotics, leading to unreliable results. Structure-preserving methods ensure that key qualitative features of the solution are retained at the discrete level, enhancing accuracy, stability, and reliability. When uncertainties are introduced—arising from incomplete data, model approximations, or inherent randomness—it becomes crucial to integrate structure-preserving numerical methods with uncertainty quantification techniques and develop approaches that can handle stochastic elements without compromising the structural properties of the underlying system.
The proposed workshop aims to bring together experts and early-career researchers to explore cutting-edge developments in structure-preserving numerical methods for solving nonlinear partial differential equations (PDEs) with uncertainties. The primary goals are to promote knowledge sharing, foster collaborations, and identify challenges and future directions in this rapidly evolving field. The focus will be on preserving the physical, geometric, and analytical properties of the underlying systems while addressing challenges posed by uncertainties in modeling, parameters, and data.