PIBNet: a Physics-Inspired Boundary Network for Multiple Scattering Simulations

• URL: http://arxiv.org/abs/2512.02049v1
• Date: Wed, 26 Nov 2025 16:42:28 GMT
• Title: PIBNet: a Physics-Inspired Boundary Network for Multiple Scattering Simulations
• Authors: Rémi Marsal, Stéphanie Chaillat,
• Abstract summary: The boundary element method (BEM) provides an efficient numerical framework for solving multiple scattering problems in homogeneous domains.<n>We introduce PIBNet, a learning-based approach designed to approximate the solution trace.<n>We present a benchmark consisting of several datasets of different types of multiple scattering problems.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The boundary element method (BEM) provides an efficient numerical framework for solving multiple scattering problems in unbounded homogeneous domains, since it reduces the discretization to the domain boundaries, thereby condensing the computational complexity. The procedure first consists in determining the solution trace on the boundaries of the domain by solving a boundary integral equation, after which the volumetric solution can be recovered at low computational cost with a boundary integral representation. As the first step of the BEM represents the main computational bottleneck, we introduce PIBNet, a learning-based approach designed to approximate the solution trace. The method leverages a physics-inspired graph-based strategy to model obstacles and their long-range interactions efficiently. Then, we introduce a novel multiscale graph neural network architecture for simulating the multiple scattering. To train and evaluate our network, we present a benchmark consisting of several datasets of different types of multiple scattering problems. The results indicate that our approach not only surpasses existing state-of-the-art learning-based methods on the considered tasks but also exhibits superior generalization to settings with an increased number of obstacles. github.com/ENSTA-U2IS-AI/pibnet

Related papers

• 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)
• Self-Supervised Coarsening of Unstructured Grid with Automatic Differentiation [55.88862563823878]
  In this work, we present an original algorithm to coarsen an unstructured grid based on the concepts of differentiable physics.<n>We demonstrate performance of the algorithm on two PDEs: a linear equation which governs slightly compressible fluid flow in porous media and the wave equation.<n>Our results show that in the considered scenarios, we reduced the number of grid points up to 10 times while preserving the modeled variable dynamics in the points of interest.
  arXiv  Detail & Related papers  (2025-07-24T11:02:13Z)
• Multi-level Neural Networks for high-dimensional parametric obstacle problems [0.0]
  A new method to solve challenging (random) parametric obstacle problems is developed and analyzed.<n>The high-dimensional solution of the obstacle problem is approximated by a specifically constructed convolutional neural network (CNN)<n> Numerical experiments illustrate a state-of-the-art performance for this challenging problem.
  arXiv  Detail & Related papers  (2025-04-07T12:50:56Z)
• Optimizing Solution-Samplers for Combinatorial Problems: The Landscape of Policy-Gradient Methods [52.0617030129699]
  We introduce a novel theoretical framework for analyzing the effectiveness of DeepMatching Networks and Reinforcement Learning methods. Our main contribution holds for a broad class of problems including Max-and Min-Cut, Max-$k$-Bipartite-Bi, Maximum-Weight-Bipartite-Bi, and Traveling Salesman Problem. As a byproduct of our analysis we introduce a novel regularization process over vanilla descent and provide theoretical and experimental evidence that it helps address vanishing-gradient issues and escape bad stationary points.
  arXiv  Detail & Related papers  (2023-10-08T23:39:38Z)
• A Block-Coordinate Approach of Multi-level Optimization with an Application to Physics-Informed Neural Networks [0.0]
  We propose a multi-level algorithm for the solution of nonlinear optimization problems and analyze its evaluation complexity. We apply it to the solution of partial differential equations using physics-informed neural networks (PINNs) and show on a few test problems that the approach results in better solutions and significant computational savings.
  arXiv  Detail & Related papers  (2023-05-23T19:12:02Z)
• A DeepParticle method for learning and generating aggregation patterns in multi-dimensional Keller-Segel chemotaxis systems [3.6184545598911724]
  We study a regularized interacting particle method for computing aggregation patterns and near singular solutions of a Keller-Segal (KS) chemotaxis system in two and three space dimensions. We further develop DeepParticle (DP) method to learn and generate solutions under variations of physical parameters.
  arXiv  Detail & Related papers  (2022-08-31T20:52:01Z)
• 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)
• Physics and Equality Constrained Artificial Neural Networks: Application to Partial Differential Equations [1.370633147306388]
  Physics-informed neural networks (PINNs) have been proposed to learn the solution of partial differential equations (PDE) Here, we show that this specific way of formulating the objective function is the source of severe limitations in the PINN approach. We propose a versatile framework that can tackle both inverse and forward problems.
  arXiv  Detail & Related papers  (2021-09-30T05:55:35Z)
• Multipole Graph Neural Operator for Parametric Partial Differential Equations [57.90284928158383]
  One of the main challenges in using deep learning-based methods for simulating physical systems is formulating physics-based data. We propose a novel multi-level graph neural network framework that captures interaction at all ranges with only linear complexity. Experiments confirm our multi-graph network learns discretization-invariant solution operators to PDEs and can be evaluated in linear time.
  arXiv  Detail & Related papers  (2020-06-16T21:56:22Z)
• GACEM: Generalized Autoregressive Cross Entropy Method for Multi-Modal Black Box Constraint Satisfaction [69.94831587339539]
  We present a modified Cross-Entropy Method (CEM) that uses a masked auto-regressive neural network for modeling uniform distributions over the solution space. Our algorithm is able to express complicated solution spaces, thus allowing it to track a variety of different solution regions.
  arXiv  Detail & Related papers  (2020-02-17T20:21:20Z)

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.