Biomimetic PINNs for Cell-Induced Phase Transitions: UQ-R3 Sampling with Causal Gating

2026-03-30

AI Summary

This work addresses the challenge of modeling sharp interfacial transitions, fine-scale microstructures, and distance-dependent cell coupling arising from non-convex multi-well energy landscapes in cell-induced phase transitions—phenomena that conventional physics-informed neural networks (PINNs) often oversmooth, particularly in near-field regions. To overcome this limitation, the authors propose Bio-PINNs, a biologically inspired framework featuring a novel progressive distance-gating mechanism that encodes temporal causality into spatial causality. This approach is coupled with a deformation–uncertainty surrogate-driven adaptive collocation strategy—termed “retain–resample–release”—which implicitly enforces high-order regularity without explicit regularization terms. The method provides theoretical guarantees for persistent coverage under gating and bounded growth in both near- and far-field regimes. Extensive benchmarks demonstrate that Bio-PINNs robustly recover sharp phase-transition layers and anchored morphologies in single- and multicellular settings, significantly outperforming existing adaptive and non-gated baselines.

Abstract

Nonconvex multi-well energies in cell-induced phase transitions give rise to sharp interfaces, fine-scale microstructures, and distance-dependent inter-cell coupling, all of which pose significant challenges for physics-informed learning. Existing methods often suffer from over-smoothing in near-field patterns. To address this, we propose biomimetic physics-informed neural networks (Bio-PINNs), a variational framework that encodes temporal causality into explicit spatial causality via a progressive distance gate. Furthermore, Bio-PINNs leverage a deformation-uncertainty proxy for the interfacial length scale to target microstructure-prone regions, providing a computationally efficient alternative to explicit second-derivative regularization. We provide theoretical guarantees for the resulting uncertainty-driven ``retain-resample-release" adaptive collocation strategy, which ensures persistent coverage under gating and establishing a quantitative near-to-far growth bound. Across single- and multi-cell benchmarks, diverse separations, and various regularization regimes, Bio-PINNs consistently recover sharp transition layers and tether morphologies, significantly outperforming state-of-the-art adaptive and ungated baselines.

Problem

• cell-induced phase transitions
• nonconvex multi-well energies
• sharp interfaces
• fine-scale microstructures
• inter-cell coupling

Innovation

• Bio-PINNs
• causal gating
• UQ-R3 sampling
• uncertainty-driven adaptation
• cell-induced phase transitions