Mosaic: A Benchmark Suite for Differentiable Physics Solvers
For researchers using differentiable PDE solvers in ML training and inverse problems, Mosaic provides the first standardized benchmark to compare solver gradients, revealing practical barriers like memory limits and numerical stability.
The paper introduces Mosaic, a benchmarking framework for differentiable PDE solvers, and evaluates 14 solvers across fluid dynamics, structural mechanics, and heat transfer, revealing order-of-magnitude variation in computational cost and Jacobian conditioning, but all solvers converge to similar optima.
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 access to solver gradients. Each solver is packaged as a containerized component (Tesseract) exposing a uniform gradient API regardless of language or automatic differentiation (AD) strategy, enabling researchers to evaluate, compare, and build on non-trivial physical solvers. Our evaluation of 14 solvers across fluid dynamics, structural mechanics, and heat transfer demonstrates that the benchmark surfaces practically relevant differences: order-of-magnitude variation in computational cost and Jacobian conditioning, alongside structural incompatibilities that eliminate solvers from realistic tasks entirely. Despite this variation, all solvers that produce gradients converge to similar optima, indicating that the practical barriers are memory limits, numerical stability, and setup compatibility rather than gradient accuracy alone. Mosaic is open-source and available at https://github.com/pasteurlabs/mosaic.