software developers in simulation

Abstract: Machine-learning surrogates are increasingly proposed to replace phase-field fracture simulations in many-query tasks such as uncertainty quantification, inverse analysis and design. Little controlled evidence shows which architectures are reliable, for which fracture problems and how far beyond their training data. We introduce Fracture-Bench, an open benchmark of two phase-field datasets with fixed splits, common test metrics and a description of each dataset's physical regime. Dataset~1 contains 1,000 AT2 simulations of multiple cracks growing from a notched hole in a hyperelastic plate under random non-uniform biaxial boundary displacements (44 load steps, $128\times128$ grid). Dataset~2 contains 4,000 PF-CZM simulations of a pre-cracked plate with two inclusions, each ten times stiffer or more compliant than the matrix ($128\times256$ grid). We train a Fourier neural operator (FNO), DeepONet, Latent DeepONet, a UNet and a conditional diffusion model on identical splits and compare one test metric per dataset, training time, inference time and model size. On Dataset~1, FNO and Latent DeepONet attain mean test errors of order $10^{-6}$, about ten times lower than UNet and DeepONet. On Dataset~2, the diffusion model is most accurate, with about one sixth of the UNet error, but requires \SI{706}{s} per prediction versus \SI{6}{ms} for UNet. For all architectures, most of the error occurs in the final load steps, after crack localization. Dataset~2 contains initial cracks less than one grid cell apart that produce qualitatively different paths. Architecture rankings therefore depend on the task, and errors averaged over densely sampled inputs reveal little about near-bifurcation cases. Data, codes, splits, regime descriptors and generalization splits are public, with a protocol for adding under-represented regimes such as mixed-mode, three-dimensional and experimentally paired fracture.

Abstract: Controlling dynamical systems governed by partial differential equations (PDEs) remains a challenging task in scientific computing, owing to high-dimensional state spaces, distributed actuation, nonlinear dynamics, and stringent real-time constraints. Reinforcement learning (RL) has emerged as a promising paradigm for synthesizing feedback controllers that adapt to varying operating conditions and can be deployed efficiently in real-time. This review provides a unified perspective on RL and PDE-constrained optimization, and surveys model-free, model-based, and multi-agent RL approaches to PDE control, with particular emphasis on sample efficiency, generalization across parametric variations, and scalability to high-dimensional problems. Two demonstrative examples, the stabilization of a chaotic system and a flow control problem, illustrate the performance and pitfalls of RL agents in practice. Finally, we discuss evaluation and benchmarking practices, current limitations, and open research directions toward reliable, data-efficient, and scalable RL for scientific computing.