BridgeNet: A Hybrid, Physics-Informed Machine Learning Framework for Solving High-Dimensional Fokker-Planck Equations

• URL: http://arxiv.org/abs/2506.04354v4
• Date: Tue, 15 Jul 2025 12:50:08 GMT
• Title: BridgeNet: A Hybrid, Physics-Informed Machine Learning Framework for Solving High-Dimensional Fokker-Planck Equations
• Authors: Elmira Mirzabeigi, Rezvan Salehi, Kourosh Parand,
• Abstract summary: BridgeNet is a novel framework that integrates convolutional neural networks with physics-informed neural networks to efficiently solve non-linear, high-dimensional Fokker-Planck equations (FPEs)<n>This work represents a substantial advancement in computational physics, offering a scalable and accurate solution methodology with promising applications in fields ranging from financial mathematics to complex system dynamics.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: BridgeNet is a novel hybrid framework that integrates convolutional neural networks with physics-informed neural networks to efficiently solve non-linear, high-dimensional Fokker-Planck equations (FPEs). Traditional PINNs, which typically rely on fully connected architectures, often struggle to capture complex spatial hierarchies and enforce intricate boundary conditions. In contrast, BridgeNet leverages adaptive CNN layers for effective local feature extraction and incorporates a dynamically weighted loss function that rigorously enforces physical constraints. Extensive numerical experiments across various test cases demonstrate that BridgeNet not only achieves significantly lower error metrics and faster convergence compared to conventional PINN approaches but also maintains robust stability in high-dimensional settings. This work represents a substantial advancement in computational physics, offering a scalable and accurate solution methodology with promising applications in fields ranging from financial mathematics to complex system dynamics.

Related papers

• Partially-Supervised Neural Network Model For Quadratic Multiparametric Programming [2.765106384328772]
  This study proposes a partially-supervised NN architecture that directly represents the mathematical structure of the global solution function.<n>In contrast to generic NN training approaches, the proposed PSNN method derives a large proportion of model weights directly from the mathematical properties of the optimization problem.
  arXiv  Detail & Related papers  (2025-06-05T20:26:18Z)
• Task-Oriented Real-time Visual Inference for IoVT Systems: A Co-design Framework of Neural Networks and Edge Deployment [61.20689382879937]
  Task-oriented edge computing addresses this by shifting data analysis to the edge. Existing methods struggle to balance high model performance with low resource consumption. We propose a novel co-design framework to optimize neural network architecture.
  arXiv  Detail & Related papers  (2024-10-29T19:02:54Z)
• Stable Weight Updating: A Key to Reliable PDE Solutions Using Deep Learning [0.0]
  This paper introduces novel residual-based architectures, designed to enhance stability and accuracy in physics-informed neural networks (PINNs) The architectures augment traditional neural networks by incorporating residual connections, which facilitate smoother weight updates and improve backpropagation efficiency. The Squared Residual Network, in particular, exhibits robust performance, achieving enhanced stability and accuracy compared to conventional neural networks.
  arXiv  Detail & Related papers  (2024-07-10T05:20:43Z)
• Auto-Train-Once: Controller Network Guided Automatic Network Pruning from Scratch [72.26822499434446]
  Auto-Train-Once (ATO) is an innovative network pruning algorithm designed to automatically reduce the computational and storage costs of DNNs. We provide a comprehensive convergence analysis as well as extensive experiments, and the results show that our approach achieves state-of-the-art performance across various model architectures.
  arXiv  Detail & Related papers  (2024-03-21T02:33:37Z)
• Enriched Physics-informed Neural Networks for Dynamic Poisson-Nernst-Planck Systems [0.8192907805418583]
  This paper proposes a meshless deep learning algorithm, enriched physics-informed neural networks (EPINNs) to solve dynamic Poisson-Nernst-Planck (PNP) equations. The EPINNs takes the traditional physics-informed neural networks as the foundation framework, and adds the adaptive loss weight to balance the loss functions. Numerical results indicate that the new method has better applicability than traditional numerical methods in solving such coupled nonlinear systems.
  arXiv  Detail & Related papers  (2024-02-01T02:57:07Z)
• Iterative Soft Shrinkage Learning for Efficient Image Super-Resolution [91.3781512926942]
  Image super-resolution (SR) has witnessed extensive neural network designs from CNN to transformer architectures. This work investigates the potential of network pruning for super-resolution iteration to take advantage of off-the-shelf network designs and reduce the underlying computational overhead. We propose a novel Iterative Soft Shrinkage-Percentage (ISS-P) method by optimizing the sparse structure of a randomly network at each and tweaking unimportant weights with a small amount proportional to the magnitude scale on-the-fly.
  arXiv  Detail & Related papers  (2023-03-16T21:06:13Z)
• NeuralStagger: Accelerating Physics-constrained Neural PDE Solver with Spatial-temporal Decomposition [67.46012350241969]
  This paper proposes a general acceleration methodology called NeuralStagger. It decomposing the original learning tasks into several coarser-resolution subtasks. We demonstrate the successful application of NeuralStagger on 2D and 3D fluid dynamics simulations.
  arXiv  Detail & Related papers  (2023-02-20T19:36:52Z)
• Pontryagin Optimal Control via Neural Networks [19.546571122359534]
  We integrate Neural Networks with the Pontryagin's Maximum Principle (PMP), and propose a sample efficient framework NN-PMP-Gradient. The resulting controller can be implemented for systems with unknown and complex dynamics. Compared with the widely applied model-free and model-based reinforcement learning (RL) algorithms, our NN-PMP-Gradient achieves higher sample-efficiency and performance in terms of control objectives.
  arXiv  Detail & Related papers  (2022-12-30T06:47:03Z)
• Auto-PINN: Understanding and Optimizing Physics-Informed Neural Architecture [77.59766598165551]
  Physics-informed neural networks (PINNs) are revolutionizing science and engineering practice by bringing together the power of deep learning to bear on scientific computation. Here, we propose Auto-PINN, which employs Neural Architecture Search (NAS) techniques to PINN design. A comprehensive set of pre-experiments using standard PDE benchmarks allows us to probe the structure-performance relationship in PINNs.
  arXiv  Detail & Related papers  (2022-05-27T03:24:31Z)
• An Adaptive Device-Edge Co-Inference Framework Based on Soft Actor-Critic [72.35307086274912]
  High-dimension parameter model and large-scale mathematical calculation restrict execution efficiency, especially for Internet of Things (IoT) devices. We propose a new Deep Reinforcement Learning (DRL)-Soft Actor Critic for discrete (SAC-d), which generates the emphexit point, emphexit point, and emphcompressing bits by soft policy iterations. Based on the latency and accuracy aware reward design, such an computation can well adapt to the complex environment like dynamic wireless channel and arbitrary processing, and is capable of supporting the 5G URL
  arXiv  Detail & Related papers  (2022-01-09T09:31:50Z)
• Adaptive Anomaly Detection for Internet of Things in Hierarchical Edge Computing: A Contextual-Bandit Approach [81.5261621619557]
  We propose an adaptive anomaly detection scheme with hierarchical edge computing (HEC) We first construct multiple anomaly detection DNN models with increasing complexity, and associate each of them to a corresponding HEC layer. Then, we design an adaptive model selection scheme that is formulated as a contextual-bandit problem and solved by using a reinforcement learning policy network.
  arXiv  Detail & Related papers  (2021-08-09T08:45:47Z)
• Optimal Transport Based Refinement of Physics-Informed Neural Networks [0.0]
  We propose a refinement strategy to the well-known Physics-Informed Neural Networks (PINNs) for solving partial differential equations (PDEs) based on the concept of Optimal Transport (OT) PINNs solvers have been found to suffer from a host of issues: spectral bias in fully-connected pathologies, unstable gradient, and difficulties with convergence and accuracy. We present a novel training strategy for solving the Fokker-Planck-Kolmogorov Equation (FPKE) using OT-based sampling to supplement the existing PINNs framework.
  arXiv  Detail & Related papers  (2021-05-26T02:51:20Z)
• Physics-informed attention-based neural network for solving non-linear partial differential equations [6.103365780339364]
  Physics-Informed Neural Networks (PINNs) have enabled significant improvements in modelling physical processes. PINNs are based on simple architectures, and learn the behavior of complex physical systems by optimizing the network parameters to minimize the residual of the underlying PDE. Here, we address the question of which network architectures are best suited to learn the complex behavior of non-linear PDEs.
  arXiv  Detail & Related papers  (2021-05-17T14:29:08Z)

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.