Phase-field models play a central role in the continuum description of phase separation, in which the bulk free-energy density and the interfacial thickness parameter determine pattern formation and microstructural evolution. In practice, these constitutive quantities are rarely known a priori and must be inferred from limited dynamical observations.
arXiv:2606. 24660v1 Announce Type: cross Abstract: Phase-field models play a central role in the continuum description of phase separation, in which the bulk free-energy density and the interfacial thickness parameter determine pattern formation and microstructural evolution.
arXiv:2606. 26128v1 Announce Type: new Abstract: The spatiotemporal evolution of many physical, chemical, and biological systems is described by nonlinear partial differential equations (PDEs).
The paper introduces a physics-constrained neural network surrogate that learns the microstructural evolution of binary mixtures governed by the Cahn‑Hilliard equation. By imposing conservation of the order parameter as a hard constraint on the network output, the model accurately predicts long‑time phase‑separation dynamics for both critical and off‑critical mixtures, maintaining mixture composition and matching the Lifshitz‑Slyozov domain‑growth law. A variant that enforces conservation only through a penalty term drifts from the initial composition and loses predictive accuracy over long rollouts, underscoring the necessity of the hard constraint for stability.
arXiv:2609.36504v1 Announce Type: new Abstract: Accurate prediction of three-dimensional (3D) microstructure evolution remains computationally demanding because high-fidelity phase-field simulations...
arXiv:2606. 19378v1 Announce Type: new Abstract: Scientific machine learning (SciML) has emerged as a promising approach for accelerating simulations of complex physical systems, yet achieving physically consistent and generalizable predictions for nonlinear, history-dependent problems remains a central challenge.
arXiv:2608. 06597v1 Announce Type: cross Abstract: A scientific theory of deep learning, comprising learning dynamics and statistical properties of learned models, is rapidly gaining attention.
arXiv:2603.27936v3 Announce Type: replace-cross Abstract: Nonlinear Partial Differential Equations (PDEs) are ubiquitous in mathematical physics and engineering. Although Physics-Informed Neural Netw...
arXiv:2606. 04000v1 Announce Type: cross Abstract: We present a probabilistic modeling framework for incorporating small-scale spatial heterogeneity into macroscopic descriptions of material behavior for polycrystalline metallic materials.
arXiv:2608. 09396v1 Announce Type: new Abstract: Invariant learning seeks representations that remain predictive across environments, yet the behavior of its objectives along the regularization path is often opaque.
Invariant learning seeks representations that remain predictive across environments, yet the behavior of its objectives along the regularization path is often opaque. We address this objective-behavior gap by viewing representation learning as multimode magnetization and deriving, from concrete invariant-learning objectives, a Landau-type effective free energy whose low-order coefficients form objective signatures and induce distinct regularization phenotypes.
The paper presents iPINN, an inverse physics‑informed neural network designed for broadband coherent anti‑Stokes Raman spectroscopy (BCARS) phase retrieval. iPINN predicts Lorentzian peak parameters from raw BCARS spectra and reconstructs the resonant susceptibility using a differentiable analytical forward model, employing a transformer encoder and a multi‑view consistency loss to handle varying non‑resonant background conditions. On a public benchmark it achieves the lowest mean absolute error (0.016) compared to other methods, and demonstrates depth‑invariant accuracy across multiple solvents and focal positions.
arXiv:2606. 28158v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) have recently emerged as a promising framework for addressing the Calder\'on inverse problem from limited boundary data.