Biomimetic PINNs for Cell-Induced Phase Transitions: UQ-R3 Sampling with Causal Gating
This addresses the problem of accurately simulating complex biological phase transitions for researchers in computational biophysics, though it appears incremental as an enhancement to existing physics-informed neural networks.
The paper tackles the challenge of modeling cell-induced phase transitions with nonconvex multi-well energies, which cause sharp interfaces and fine-scale microstructures that existing methods often over-smooth. The proposed Bio-PINNs framework consistently recovers sharp transition layers and tether morphologies, significantly outperforming state-of-the-art adaptive and ungated baselines across various benchmarks.
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.