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

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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.

Subjects:

Machine Learning (cs.LG); Numerical Analysis (math.NA)

Cite as: arXiv:2603.29184 [cs.LG]

(or arXiv:2603.29184v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2603.29184

arXiv-issued DOI via DataCite (pending registration)

Submission history

From: Wenju Zhao [view email] [v1] Tue, 31 Mar 2026 02:50:07 UTC (9,002 KB)