2026-08-12 –, Room 6
This talk presents recent advances in efficient boundary value problem solving within the SciML ecosystem, focusing on extending collocation-based and nonlinear programming formulations implemented in BoundaryValueDiffEq.jl. We demonstrate how BVPs can be reformulated as structured optimization problems, enabling seamless integration with SciML’s differentiable programming stack and modern optimization tools. Building on this perspective, we introduce strategies for improving performance and scalability, including structure-aware discretizations, GPU-parallel ensemble solving, and algorithmic techniques that bridge differential equation solvers with optimal control and dynamical optimization pipelines. We further show how these methods enable new application workflows, where differential equations, parameter estimation, and optimal control problems are solved within a unified composable framework.
This talk provides an in-depth overview of recent methodological and software advances in efficient boundary value problem solving within the SciML ecosystem. Boundary value problems arise naturally across scientific computing, optimal control, inverse problems, and dynamical system analysis, yet their efficient numerical treatment remains challenging due to strong global coupling, nonlinear constraints, and large-scale discretizations. We focus on recent developments in BoundaryValueDiffEq.jl, emphasizing how modern collocation-based formulations can be systematically extended using the composable abstractions provided by SciML.
A central theme of the talk is the reinterpretation of BVPs as structured nonlinear optimization problems. Instead of viewing collocation methods purely as discretizations of differential equations, we demonstrate how they naturally induce sparse and highly structured nonlinear programming formulations. This perspective enables direct interoperability with SciML’s differentiable programming infrastructure, allowing automatic differentiation, sensitivity analysis, and gradient-based optimization methods to be applied seamlessly. By leveraging tools such as ModelingToolkit.jl and Optimization.jl, BVP solvers become an important component in differentiable computational pipelines.
I am a master student in machine learning and industrial control systems at Zhejiang University. My research interest focuses on the intersection of machine learning and dynamical systems. I participated in GSoC 2023 with SciML under the NUMFOCUS umbrella.