Fragment size density estimator for shrinkage-induced fracture based on a physics-informed neural network

• URL: http://arxiv.org/abs/2507.11799v2
• Date: Wed, 23 Jul 2025 00:44:03 GMT
• Title: Fragment size density estimator for shrinkage-induced fracture based on a physics-informed neural network
• Authors: Shin-ichi Ito,
• Abstract summary: This paper presents a neural network (NN)-based solver for an integro-differential equation that models shrinkage-induced fragmentation.<n>The proposed method directly maps input parameters to the corresponding probability density function without numerically solving the governing equation.<n>It enables efficient evaluation of the density function in Monte Carlo simulations while maintaining accuracy comparable to or even exceeding that of conventional finite difference schemes.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper presents a neural network (NN)-based solver for an integro-differential equation that models shrinkage-induced fragmentation. The proposed method directly maps input parameters to the corresponding probability density function without numerically solving the governing equation, thereby significantly reducing computational costs. Specifically, it enables efficient evaluation of the density function in Monte Carlo simulations while maintaining accuracy comparable to or even exceeding that of conventional finite difference schemes. Validatation on synthetic data demonstrates both the method's computational efficiency and predictive reliability. This study establishes a foundation for the data-driven inverse analysis of fragmentation and suggests the potential for extending the framework beyond pre-specified model structures.

Related papers

• LVM-GP: Uncertainty-Aware PDE Solver via coupling latent variable model and Gaussian process [9.576396359649921]
  We propose a novel framework, termed LVM-GP, for uncertainty quantification in solving PDEs with noisy data.<n>The architecture consists of a confidence-aware encoder and a probabilistic decoder.
  arXiv  Detail & Related papers  (2025-07-30T09:00:39Z)
• Generalizing Backpropagation for Gradient-Based Interpretability [103.2998254573497]
  We show that the gradient of a model is a special case of a more general formulation using semirings. This observation allows us to generalize the backpropagation algorithm to efficiently compute other interpretable statistics.
  arXiv  Detail & Related papers  (2023-07-06T15:19:53Z)
• Learning Unnormalized Statistical Models via Compositional Optimization [73.30514599338407]
  Noise-contrastive estimation(NCE) has been proposed by formulating the objective as the logistic loss of the real data and the artificial noise. In this paper, we study it a direct approach for optimizing the negative log-likelihood of unnormalized models.
  arXiv  Detail & Related papers  (2023-06-13T01:18:16Z)
• Non-Parametric Learning of Stochastic Differential Equations with Non-asymptotic Fast Rates of Convergence [65.63201894457404]
  We propose a novel non-parametric learning paradigm for the identification of drift and diffusion coefficients of non-linear differential equations.<n>The key idea essentially consists of fitting a RKHS-based approximation of the corresponding Fokker-Planck equation to such observations.
  arXiv  Detail & Related papers  (2023-05-24T20:43:47Z)
• D4FT: A Deep Learning Approach to Kohn-Sham Density Functional Theory [79.50644650795012]
  We propose a deep learning approach to solve Kohn-Sham Density Functional Theory (KS-DFT) We prove that such an approach has the same expressivity as the SCF method, yet reduces the computational complexity. In addition, we show that our approach enables us to explore more complex neural-based wave functions.
  arXiv  Detail & Related papers  (2023-03-01T10:38:10Z)
• Monte Carlo Neural PDE Solver for Learning PDEs via Probabilistic Representation [59.45669299295436]
  We propose a Monte Carlo PDE solver for training unsupervised neural solvers.<n>We use the PDEs' probabilistic representation, which regards macroscopic phenomena as ensembles of random particles.<n>Our experiments on convection-diffusion, Allen-Cahn, and Navier-Stokes equations demonstrate significant improvements in accuracy and efficiency.
  arXiv  Detail & Related papers  (2023-02-10T08:05:19Z)
• Low-rank statistical finite elements for scalable model-data synthesis [0.8602553195689513]
  statFEM acknowledges a priori model misspecification, by embedding forcing within the governing equations. The method reconstructs the observed data-generating processes with minimal loss of information. This article overcomes this hurdle by embedding a low-rank approximation of the underlying dense covariance matrix.
  arXiv  Detail & Related papers  (2021-09-10T09:51:43Z)
• Low-rank Characteristic Tensor Density Estimation Part II: Compression and Latent Density Estimation [31.631861197477185]
  Learning generative probabilistic models is a core problem in machine learning. This paper proposes a joint dimensionality reduction and non-parametric density estimation framework. We demonstrate that the proposed model achieves very promising results on regression tasks, sampling, and anomaly detection.
  arXiv  Detail & Related papers  (2021-06-20T00:38:56Z)
• Influence Estimation and Maximization via Neural Mean-Field Dynamics [60.91291234832546]
  We propose a novel learning framework using neural mean-field (NMF) dynamics for inference and estimation problems. Our framework can simultaneously learn the structure of the diffusion network and the evolution of node infection probabilities.
  arXiv  Detail & Related papers  (2021-06-03T00:02:05Z)
• SODEN: A Scalable Continuous-Time Survival Model through Ordinary Differential Equation Networks [14.564168076456822]
  We propose a flexible model for survival analysis using neural networks along with scalable optimization algorithms. We demonstrate the effectiveness of the proposed method in comparison to existing state-of-the-art deep learning survival analysis models.
  arXiv  Detail & Related papers  (2020-08-19T19:11:25Z)
• Relative gradient optimization of the Jacobian term in unsupervised deep learning [9.385902422987677]
  Learning expressive probabilistic models correctly describing the data is a ubiquitous problem in machine learning. Deep density models have been widely used for this task, but their maximum likelihood based training requires estimating the log-determinant of the Jacobian. We propose a new approach for exact training of such neural networks.
  arXiv  Detail & Related papers  (2020-06-26T16:41:08Z)
• Model Reduction and Neural Networks for Parametric PDEs [9.405458160620533]
  We develop a framework for data-driven approximation of input-output maps between infinite-dimensional spaces. The proposed approach is motivated by the recent successes of neural networks and deep learning. For a class of input-output maps, and suitably chosen probability measures on the inputs, we prove convergence of the proposed approximation methodology.
  arXiv  Detail & Related papers  (2020-05-07T00:09:27Z)

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.