SPLIT-PINN: Separable Probability Learning Technique via Physics-Informed Neural Networks for High-Dimensional Probabilistic Modeling

• URL: http://arxiv.org/abs/2606.04000v1
• Date: Sat, 23 May 2026 18:34:53 GMT
• Title: SPLIT-PINN: Separable Probability Learning Technique via Physics-Informed Neural Networks for High-Dimensional Probabilistic Modeling
• Abstract summary: We present a framework for incorporating small-scale spatial heterogeneity into macroscopic descriptions of material behavior for polycrystalline metallic materials.<n>The framework is built on the inverse identification of a probabilistic transport model, formulated as a Liouville equation with an unknown drift term.<n>Using SPLIT-PINN, the drift field governing the temporal evolution of joint state PDFs is inferred directly from data.
• Score: 4.989924029015053
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: We present a probabilistic modeling framework for incorporating small-scale spatial heterogeneity into macroscopic descriptions of material behavior for polycrystalline metallic materials. Spatially heterogeneous material state fields are represented using probability density functions (PDFs), providing a principled statistical description of microstructural variability and state evolution across different computational polycrystalline realizations. The framework is built on the inverse identification of a probabilistic transport model, formulated as a Liouville equation with an unknown drift term. To enable accurate, stable, and interpretable inference of this drift field in high-dimensional, transport-dominated settings, we develop a Separable Probability Learning Technique via Physics-Informed Neural Networks (SPLIT-PINN). This method incorporates a marginal-correction drift decomposition, orthogonality constraints, and residual-based adaptive training to enhance well-posedness, numerical stability, and physical consistency without imposing restrictive parametric assumptions. Using SPLIT-PINN, the drift field governing the temporal evolution of joint state PDFs is inferred directly from data. After benchmark validation, the framework is applied to physical computational datasets describing the evolution of polycrystalline microstructural states, including von Mises stress, dislocation density, and equivalent plastic strain rate. The learned Liouville model, trained on a single dataset, is subsequently used in forward predictions of the temporal evolution of joint and marginal PDFs for multiple unseen polycrystal realizations. Quantitative comparisons with reference PDFs demonstrate that the proposed framework yields accurate and robust probabilistic predictions and generalizes effectively across datasets.

Related papers

• Equivariant Evidential Deep Learning for Interatomic Potentials [55.6997213490859]
  Uncertainty quantification is critical for assessing the reliability of machine learning interatomic potentials in molecular dynamics simulations.<n>Existing UQ approaches for MLIPs are often limited by high computational cost or suboptimal performance.<n>We propose textitEquivariant Evidential Deep Learning for Interatomic Potentials ($texte2$IP), a backbone-agnostic framework that models atomic forces and their uncertainty jointly.
  arXiv  Detail & Related papers  (2026-02-11T02:00:25Z)
• Machine learning assisted state prediction of misspecified linear dynamical system via modal reduction [0.0]
  Parametric models with fixed nominal parameters often omit critical physical effects due to simplifications in geometry, material behavior, damping, or boundary conditions.<n>This work introduces a comprehensive framework for MFE estimation and correction in high-dimensional finite element based structural dynamical systems.<n>To ensure computational tractability, the FE system is projected onto a reduced modal basis, and a mesh-invariant neural network maps modal states to discrepancy estimates.
  arXiv  Detail & Related papers  (2026-01-08T10:14:27Z)
• Linearized Optimal Transport for Analysis of High-Dimensional Point-Cloud and Single-Cell Data [45.87606039212519]
  Single-cell technologies generate high-dimensional point clouds of cells.<n>Each patient is represented by an irregular point cloud rather than a simple vector.<n>We adapt the Linear Optimal Transport framework to embed irregular point clouds into a fixed-dimensional Euclidean space.
  arXiv  Detail & Related papers  (2025-10-24T21:33:12Z)
• Physics-guided impact localisation and force estimation in composite plates with uncertainty quantification [2.526146573337397]
  This paper presents a hybrid framework for impact localisation and force estimation in composite plates.<n>It combines a data-driven implementation of First-Order Shear Deformation Theory (FSDT) with machine learning and uncertainty quantification.<n>The proposed method offers a scalable and transferable solution for impact monitoring and structural health management in composite aerostructures.
  arXiv  Detail & Related papers  (2025-07-13T16:17:25Z)
• Unified theoretical guarantees for stability, consistency, and convergence in neural PDE solvers from non-IID data to physics-informed networks [0.0]
  We establish a unified theoretical framework addressing the stability, consistency, and convergence of neural networks under realistic training conditions.<n>For standard supervised learning with dependent data, we derive uniform stability bounds for gradient-based methods.<n>In federated learning with heterogeneous data, we quantify model inconsistency via curvature-aware aggregation and information-theoretic divergence.
  arXiv  Detail & Related papers  (2024-09-08T08:48:42Z)
• Fast and Reliable Probabilistic Reflectometry Inversion with Prior-Amortized Neural Posterior Estimation [73.81105275628751]
  Finding all structures compatible with reflectometry data is computationally prohibitive for standard algorithms. We address this lack of reliability with a probabilistic deep learning method that identifies all realistic structures in seconds. Our method, Prior-Amortized Neural Posterior Estimation (PANPE), combines simulation-based inference with novel adaptive priors.
  arXiv  Detail & Related papers  (2024-07-26T10:29:16Z)
• Hybrid data-driven and physics-informed regularized learning of cyclic plasticity with Neural Networks [0.0]
  The proposed model architecture is simpler and more efficient compared to existing solutions from the literature. The validation of the approach is carried out by means of surrogate data obtained with the Armstrong-Frederick kinematic hardening model.
  arXiv  Detail & Related papers  (2024-03-04T07:09:54Z)
• Synthetic location trajectory generation using categorical diffusion models [50.809683239937584]
  Diffusion models (DPMs) have rapidly evolved to be one of the predominant generative models for the simulation of synthetic data. We propose using DPMs for the generation of synthetic individual location trajectories (ILTs) which are sequences of variables representing physical locations visited by individuals.
  arXiv  Detail & Related papers  (2024-02-19T15:57:39Z)
• Constrained Synthesis with Projected Diffusion Models [47.56192362295252]
  This paper introduces an approach to generative diffusion processes the ability to satisfy and certify compliance with constraints and physical principles. The proposed method recast the traditional process of generative diffusion as a constrained distribution problem to ensure adherence to constraints.
  arXiv  Detail & Related papers  (2024-02-05T22:18:16Z)
• A deep learning driven pseudospectral PCE based FFT homogenization algorithm for complex microstructures [68.8204255655161]
  It is shown that the proposed method is able to predict central moments of interest while being magnitudes faster to evaluate than traditional approaches. It is shown, that the proposed method is able to predict central moments of interest while being magnitudes faster to evaluate than traditional approaches.
  arXiv  Detail & Related papers  (2021-10-26T07:02:14Z)
• Towards a Kernel based Uncertainty Decomposition Framework for Data and Models [20.348825818435767]
  This paper introduces a new framework for quantifying predictive uncertainty for both data and models. We apply this framework as a surrogate tool for predictive uncertainty quantification of point-prediction neural network models.
  arXiv  Detail & Related papers  (2020-01-30T18:35:36Z)
• Learning Likelihoods with Conditional Normalizing Flows [54.60456010771409]
  Conditional normalizing flows (CNFs) are efficient in sampling and inference. We present a study of CNFs where the base density to output space mapping is conditioned on an input x, to model conditional densities p(y|x)
  arXiv  Detail & Related papers  (2019-11-29T19:17:58Z)

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.