Mosaic: A Benchmark Suite for Differentiable Physics Solvers

• URL: http://arxiv.org/abs/2606.27895v1
• Date: Fri, 26 Jun 2026 09:38:33 GMT
• Title: Mosaic: A Benchmark Suite for Differentiable Physics Solvers
• Abstract summary: Differentiable partial differential equation (PDE) solvers underpin solver-in-the-loop ML training, gradient-based optimal control, and inverse problems.<n>We introduce Mosaic, a benchmarking framework for differentiable PDE solvers that standardizes access to solver gradients.
• Score: 2.574393697080417
• License: http://creativecommons.org/licenses/by/4.0/
• 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 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.

Related papers

• An End-to-End PyTorch Interface for Differentiable PDE Solvers: A RANS Model-Correction Study [0.0]
  This work presents an end-to-end strategy for solving inverse problems constrained by Partial Differential Equations.<n>We show how to optimize phi within a fully differentiable Python workflow by reformulating the PDE as an implicit layer.<n>A dataset is generated starting from the VKI LS-59 turbine blade geometry using the differentiable BROADCAST solver with the Spalart-Allmaras turbulence model.
  arXiv  Detail & Related papers  (2026-05-19T07:38:50Z)
• A Machine Learning accelerated geophysical fluid solver [6.1181801016029675]
  Data-driven discretization method presents a promising way of accelerating and improving existing PDE solver on structured grids.<n>It can improve the accuracy and stability of low-resolution simulation compared with using traditional finite difference or finite volume schemes.<n>In this thesis, we have implemented the shallow water equation and Euler equation classic solver under a different framework.
  arXiv  Detail & Related papers  (2026-02-09T13:55:26Z)
• Reclaiming First Principles: A Differentiable Framework for Conceptual Hydrologic Models [0.3058685580689604]
  We introduce a fully analytic and computationally efficient framework for differentiable hydrologic modeling based on exact parameter sensitivities.<n>The resulting gradients are deterministic, physically interpretable, and straightforward to embed in gradient-based vectors.
  arXiv  Detail & Related papers  (2026-02-06T06:55:49Z)
• DInf-Grid: A Neural Differential Equation Solver with Differentiable Feature Grids [73.28614344779076]
  We present a differentiable grid-based representation for efficiently solving differential equations (DEs)<n>Our results demonstrate a 5-20x speed-up over coordinate-based methods, solving differential equations in seconds or minutes while maintaining comparable accuracy and compactness.
  arXiv  Detail & Related papers  (2026-01-15T18:59:57Z)
• Parallel Diffusion Solver via Residual Dirichlet Policy Optimization [88.7827307535107]
  Diffusion models (DMs) have achieved state-of-the-art generative performance but suffer from high sampling latency due to their sequential denoising nature.<n>Existing solver-based acceleration methods often face significant image quality degradation under a low-dimensional budget.<n>We propose the Ensemble Parallel Direction solver (dubbed as EPD-EPr), a novel ODE solver that mitigates these errors by incorporating multiple gradient parallel evaluations in each step.
  arXiv  Detail & Related papers  (2025-12-28T05:48:55Z)
• PICT -- A Differentiable, GPU-Accelerated Multi-Block PISO Solver for Simulation-Coupled Learning Tasks in Fluid Dynamics [62.93137406343609]
  We present our fluid simulator PICT, a differentiable pressure-implicit solver coded in PyTorch with Graphics-processing-unit (GPU) support.<n>We first verify the accuracy of both the forward simulation and our derived gradients in various established benchmarks.<n>We show that the gradients provided by our solver can be used to learn complicated turbulence models in 2D and 3D.
  arXiv  Detail & Related papers  (2025-05-22T17:55:10Z)
• Decentralized Nonconvex Composite Federated Learning with Gradient Tracking and Momentum [78.27945336558987]
  Decentralized server (DFL) eliminates reliance on client-client architecture.<n>Non-smooth regularization is often incorporated into machine learning tasks.<n>We propose a novel novel DNCFL algorithm to solve these problems.
  arXiv  Detail & Related papers  (2025-04-17T08:32:25Z)
• Physics-constrained Unsupervised Learning of Partial Differential Equations using Meshes [1.066048003460524]
  Graph neural networks show promise in accurately representing irregularly meshed objects and learning their dynamics. In this work, we represent meshes naturally as graphs, process these using Graph Networks, and formulate our physics-based loss to provide an unsupervised learning framework for partial differential equations (PDE) Our framework will enable the application of PDE solvers in interactive settings, such as model-based control of soft-body deformations.
  arXiv  Detail & Related papers  (2022-03-30T19:22:56Z)
• Message Passing Neural PDE Solvers [60.77761603258397]
  We build a neural message passing solver, replacing allally designed components in the graph with backprop-optimized neural function approximators. We show that neural message passing solvers representationally contain some classical methods, such as finite differences, finite volumes, and WENO schemes. We validate our method on various fluid-like flow problems, demonstrating fast, stable, and accurate performance across different domain topologies, equation parameters, discretizations, etc., in 1D and 2D.
  arXiv  Detail & Related papers  (2022-02-07T17:47:46Z)
• Self Normalizing Flows [65.73510214694987]
  We propose a flexible framework for training normalizing flows by replacing expensive terms in the gradient by learned approximate inverses at each layer. This reduces the computational complexity of each layer's exact update from $mathcalO(D3)$ to $mathcalO(D2)$. We show experimentally that such models are remarkably stable and optimize to similar data likelihood values as their exact gradient counterparts.
  arXiv  Detail & Related papers  (2020-11-14T09:51:51Z)
• Solver-in-the-Loop: Learning from Differentiable Physics to Interact with Iterative PDE-Solvers [26.444103444634994]
  We show that machine learning can improve the solution accuracy by correcting for effects not captured by the discretized PDE. We find that previously used learning approaches are significantly outperformed by methods that integrate the solver into the training loop. This provides the model with realistic input distributions that take previous corrections into account.
  arXiv  Detail & Related papers  (2020-06-30T18:00:03Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.