Machine learning has been successfully applied to grid-based PDE modeling in various scientific applications. However, learned PDE solvers based on Lagrangian particle discretizations, which are the preferred approach to problems with free surfaces or complex physics, remain largely unexplored. We present LagrangeBench, the first benchmarking suite for Lagrangian particle problems, focusing on temporal coarse-graining. In particular, our contribution is: (a) seven new fluid mechanics datasets (four in 2D and three in 3D) generated with the Smoothed Particle Hydrodynamics (SPH) method including the Taylor-Green vortex, lid-driven cavity, reverse Poiseuille flow, and dam break, each of which includes different physics like solid wall interactions or free surface, (b) efficient JAX-based API with various recent training strategies and three neighbor search routines, and (c) JAX implementation of established Graph Neural Networks (GNNs) like GNS and SEGNN with baseline results. Finally, to measure the performance of learned surrogates we go beyond established position errors and introduce physical metrics like kinetic energy MSE and Sinkhorn distance for the particle distribution. Our codebase is available under the URL: https://github.com/tumaer/lagrangebench.

Abstract In this paper we describe the successful application of the ProB tool for data validation in several industrial applications. The initial case study centred on the San Juan metro system installed by Siemens. The control software was developed and formally proven with B. However, the development contains certain assumptions about the actual rail network topology which have to be validated separately in order to ensure safe operation. For this task, Siemens has developed custom proof rules for Atelier B. Atelier B, however, was unable to deal with about 80 properties of the deployment (running out of memory). These properties thus had to be validated by hand at great expense, and they need to be revalidated whenever the rail network infrastructure changes. In this paper we show how we were able to use ProB to validate all of the about 300 properties of the San Juan deployment, detecting exactly the same faults automatically in a few minutes that were manually uncovered in about one man-month. We have repeated this task for three ongoing projects at Siemens, notably the ongoing automatisation of the line 1 of the Paris Métro. Here again, about a man month of effort has been replaced by a few minutes of computation. This achievement required the extension of the ProB kernel for large sets as well as an improved constraint propagation algorithm. We also outline some of the effort and features that were required in moving from a tool capable of dealing with medium-sized examples towards a tool able to deal with actual industrial specifications. We also describe the issue of validating ProB , so that it can be integrated into the SIL4 development chain at Siemens.

Abstract Initially, the Rodin platform for Event‐B did away with a textual representation for models. In this paper, we explain why a textual representation was required after all and we present the semantic‐aware text editor Camille for Rodin. We explain the design choices of Camille, such as splitting the syntax into two‐levels for machine and formula syntax. We also describe the challenges, such as synchronizing the textual representation with the Rodin database, and how they were overcome using an EMF abstraction layer. Copyright © 2011 John Wiley & Sons, Ltd.