arXiv:2606.27895v1 Announce Type: cross Abstract: Differentiable partial differential equation (PDE) solvers underpin solver-in-the-loop ML training, gradient-based optimal control, and inverse problems, yet the practical cost of obtaining correct, usable gradients from a given solver on a given problem is largely undocumented. Integration effort, computational cost, gradient accuracy, and numerical conditioning vary widely across solvers and are discoverable only by trial and error. We introduce Mosaic, an extensible benchmarking framework for differentiable PDE solvers that standardizes acce
The increasing reliance on differentiable physics solvers in advanced AI/ML applications necessitates standardized benchmarking to accelerate research and development in this critical domain.
A standardized benchmark reduces the trial-and-error costs associated with integrating differentiable PDE solvers, improving efficiency and reliability of AI models in scientific computing and engineering.
The introduction of Mosaic provides a common framework for evaluating and comparing differentiable physics solvers, enabling faster identification of optimal solutions and fostering collaboration across diverse research groups.
- · AI/ML researchers
- · Engineering R&D departments
- · Scientific computing sector
- · High-performance computing (HPC) providers
- · Proprietary, undocumented solver developers
- · Organizations relying solely on custom, non-standardized PDE solvers
Researchers gain clearer insights into the performance and gradient accuracy of differentiable PDE solvers.
Accelerated development of AI models for physical phenomena simulation, optimal control, and inverse problems across various industries.
Enhanced ability to integrate complex physical simulations into real-time AI agents for applications like advanced robotics or material design.
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Read at arXiv cs.LG