PDE-Constrained Optimization for Neural Image Segmentation with Physics Priors

• URL: http://arxiv.org/abs/2602.01069v1
• Date: Sun, 01 Feb 2026 07:28:14 GMT
• Title: PDE-Constrained Optimization for Neural Image Segmentation with Physics Priors
• Authors: Seema K. Poudel, Sunny K. Khadka,
• Abstract summary: Images of microscopy images constitutes an ill-posed inverse problem due to measurement noise, weak object boundaries, and limited labeled data.<n>In this work, image segmentation is formulated as a PDE-constrained optimization problem that integrates physically motivated priors into deep learning models.<n>Experiments are conducted on the LIVECell dataset, a high-quality, manually annotated collection of phase-contrast microscopy images.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Segmentation of microscopy images constitutes an ill-posed inverse problem due to measurement noise, weak object boundaries, and limited labeled data. Although deep neural networks provide flexible nonparametric estimators, unconstrained empirical risk minimization often leads to unstable solutions and poor generalization. In this work, image segmentation is formulated as a PDE-constrained optimization problem that integrates physically motivated priors into deep learning models through variational regularization. The proposed framework minimizes a composite objective function consisting of a data fidelity term and penalty terms derived from reaction-diffusion equations and phase-field interface energies, all implemented as differentiable residual losses. Experiments are conducted on the LIVECell dataset, a high-quality, manually annotated collection of phase-contrast microscopy images. Training is performed on two cell types, while evaluation is carried out on a distinct, unseen cell type to assess generalization. A UNet architecture is used as the unconstrained baseline model. Experimental results demonstrate consistent improvements in segmentation accuracy and boundary fidelity compared to unconstrained deep learning baselines. Moreover, the PDE-regularized models exhibit enhanced stability and improved generalization in low-sample regimes, highlighting the advantages of incorporating structured priors. The proposed approach illustrates how PDE-constrained optimization can strengthen data-driven learning frameworks, providing a principled bridge between variational methods, statistical learning, and scientific machine learning.

Related papers

• Robust Variational Model Based Tailored UNet: Leveraging Edge Detector and Mean Curvature for Improved Image Segmentation [7.638424494500011]
  This paper presents a robust version of Variational Model Based UNet (VM_TUNet)<n>VM_TUNet is a hybrid framework that integrates variational methods with deep learning.<n> experiments on three benchmark datasets indicate that the proposed method achieves a balanced trade-off between performance and computational efficiency.
  arXiv  Detail & Related papers  (2025-12-08T14:33:52Z)
• Graph Neural Regularizers for PDE Inverse Problems [62.49743146797144]
  We present a framework for solving a broad class of ill-posed inverse problems governed by partial differential equations (PDEs)<n>The forward problem is numerically solved using the finite element method (FEM)<n>We employ physics-inspired graph neural networks as learned regularizers, providing a robust, interpretable, and generalizable alternative to standard approaches.
  arXiv  Detail & Related papers  (2025-10-23T21:43:25Z)
• Physics-Constrained Fine-Tuning of Flow-Matching Models for Generation and Inverse Problems [3.3811247908085855]
  We present a framework for fine-tuning flow-matching generative models to enforce physical constraints and solve inverse problems in scientific systems.<n>Our approach bridges generative modelling and scientific inference, opening new avenues for simulation-augmented discovery and data-efficient modelling of physical systems.
  arXiv  Detail & Related papers  (2025-08-05T09:32:04Z)
• Low-Rank Tensor Recovery via Variational Schatten-p Quasi-Norm and Jacobian Regularization [49.85875869048434]
  We propose a CP-based low-rank tensor function parameterized by neural networks for implicit neural representation.<n>To achieve sparser CP decomposition, we introduce a variational Schatten-p quasi-norm to prune redundant rank-1 components.<n>For smoothness, we propose a regularization term based on the spectral norm of the Jacobian and Hutchinson's trace estimator.
  arXiv  Detail & Related papers  (2025-06-27T11:23:10Z)
• Paving the way for scientific foundation models: enhancing generalization and robustness in PDEs with constraint-aware pre-training [49.8035317670223]
  A scientific foundation model (SciFM) is emerging as a promising tool for learning transferable representations across diverse domains.<n>We propose incorporating PDE residuals into pre-training either as the sole learning signal or in combination with data loss to compensate for limited or infeasible training data.<n>Our results show that pre-training with PDE constraints significantly enhances generalization, outperforming models trained solely on solution data.
  arXiv  Detail & Related papers  (2025-03-24T19:12:39Z)
• Preconditioned Inexact Stochastic ADMM for Deep Model [35.37705488695026]
  This paper develops an algorithm, PISA, which enables scalable parallel computing and supports various preconditions.<n>It converges under the sole assumption of Lipschitz continuity of the gradient on a bounded region, removing the need for other conditions commonly imposed by methods.<n>It demonstrates its superior numerical performance compared to various state-of-the-art iterations.
  arXiv  Detail & Related papers  (2025-02-15T12:28:51Z)
• A theoretical framework for overfitting in energy-based modeling [5.1337384597700995]
  We investigate the impact of limited data on training pairwise energy-based models for inverse problems aimed at identifying interaction networks.<n>We show that optimal points for early stopping arise from the interplay between these timescales and the initial conditions of training.<n>We propose a generalization to arbitrary energy-based models by deriving the neural tangent kernel dynamics of the score function under the score-matching.
  arXiv  Detail & Related papers  (2025-01-31T14:21:02Z)
• Generalization Bounds of Surrogate Policies for Combinatorial Optimization Problems [53.03951222945921]
  We analyze smoothed (perturbed) policies, adding controlled random perturbations to the direction used by the linear oracle.<n>Our main contribution is a generalization bound that decomposes the excess risk into perturbation bias, statistical estimation error, and optimization error.<n>We illustrate the scope of the results on applications such as vehicle scheduling, highlighting how smoothing enables both tractable training and controlled generalization.
  arXiv  Detail & Related papers  (2024-07-24T12:00:30Z)
• Neural variational Data Assimilation with Uncertainty Quantification using SPDE priors [28.804041716140194]
  Recent advances in the deep learning community enables to address the problem through a neural architecture a variational data assimilation framework.<n>In this work we use the theory of Partial Differential Equations (SPDE) and Gaussian Processes (GP) to estimate both space-and time covariance of the state.
  arXiv  Detail & Related papers  (2024-02-02T19:18:12Z)
• A PAC-Bayesian Perspective on the Interpolating Information Criterion [54.548058449535155]
  We show how a PAC-Bayes bound is obtained for a general class of models, characterizing factors which influence performance in the interpolating regime. We quantify how the test error for overparameterized models achieving effectively zero training error depends on the quality of the implicit regularization imposed by e.g. the combination of model, parameter-initialization scheme.
  arXiv  Detail & Related papers  (2023-11-13T01:48:08Z)
• Reflected Diffusion Models [93.26107023470979]
  We present Reflected Diffusion Models, which reverse a reflected differential equation evolving on the support of the data. Our approach learns the score function through a generalized score matching loss and extends key components of standard diffusion models.
  arXiv  Detail & Related papers  (2023-04-10T17:54:38Z)
• Pseudo-Spherical Contrastive Divergence [119.28384561517292]
  We propose pseudo-spherical contrastive divergence (PS-CD) to generalize maximum learning likelihood of energy-based models. PS-CD avoids the intractable partition function and provides a generalized family of learning objectives.
  arXiv  Detail & Related papers  (2021-11-01T09:17:15Z)

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.