PDE-based models are central to scientific simulation and provide an ideal testbed for this challenge. They require mathematical correctness, structure-preserving numerical methods, rigorous floating-point numerics, and robust software implementation and validation. AI is beginning to affect every part of this pipeline, from theorem proving and algorithm discovery to code generation, surrogate modeling, and automated test creation. These developments create an urgent need for new verification methods that connect formal proof, rigorous numerics, software verification, and scientific validation, and an urgent need for a scientific dialogue around these topics.

The two-day workshop has the following major goals:
•  initiate a cross-disciplinary dialog between mathematicians, computer scientists, and practitioners to identify verification challenges that arise when AI is used to generate or modify mathematical arguments, PDE algorithms, scientific software, and numerical experiments
•  build and reinforce scientific connections between researchers working on proof assistants, PDE analysis, numerical methods, scientific software, and DOE mission scientists
•  stimulate international collaboration between US and Japanese researchers